Micro Economics (old course)

The Cobb-Douglas production function is $Q = AK^{\alpha}L^{\beta}$, where $A$ is the efficiency parameter and $\alpha$, $\beta$ are the output elasticities of capital and labour.

Properties

1. Output elasticities: $\alpha$ and $\beta$ are constants and measure the percentage change in output for a 1% change in capital and labour respectively.
2. Returns to scale: the function is homogeneous of degree $\alpha+\beta$. If $\alpha+\beta=1$, constant returns to scale; if greater than 1, increasing; if less than 1, decreasing returns to scale.
3. Marginal products: $MP_L = \beta Q/L$ and $MP_K = \alpha Q/K$ are positive and diminishing, so each input has diminishing returns.
4. Unit elasticity of substitution: the elasticity of substitution is equal to 1.
5. Isoquants: downward sloping, convex and asymptotic to the axes; the $MRTS = \dfrac{\beta K}{\alpha L}$.
6. Factor shares: with $\alpha+\beta=1$, labour gets $\beta$ and capital $\alpha$ of the output, so the product is exactly exhausted (Euler's theorem).
7. Linear in logs: $\ln Q = \ln A + \alpha \ln K + \beta \ln L$, so it can be easily estimated by regression.

Properties of the Cobb-Douglas production function $Q = AK^{\alpha}L^{\beta}$:

• It is homogeneous of degree $(\alpha+\beta)$, so returns to scale depend on the sum of the exponents ($>1$ increasing, $=1$ constant, $<1$ decreasing).
• The exponents $\alpha$ and $\beta$ are the output elasticities of capital and labour.
• Marginal products are positive but diminishing for each input.
• The elasticity of substitution between inputs is unity.
• Isoquants are downward sloping and convex to the origin; if $\alpha+\beta=1$ it is linearly homogeneous and the product is exhausted by factor payments (Euler's theorem).

The Cobb-Douglas production function is

$Q = A\,L^{\alpha}K^{\beta}$

where $Q$ is output, $L$ labour, $K$ capital, $A$ a constant (efficiency parameter) and $\alpha,\beta$ positive constants.

Properties

1. Output elasticities: $\alpha$ is the elasticity of output with respect to labour and $\beta$ that with respect to capital. They are constant.
2. Returns to scale: the sum $\alpha+\beta$ gives returns to scale: if $\alpha+\beta=1$, constant returns (linearly homogeneous); if $>1$, increasing; if $<1$, decreasing returns.
3. Marginal products: $MP_L=\alpha Q/L$ and $MP_K=\beta Q/K$; both are positive and diminishing as the input rises.
4. Share of factors: if $\alpha+\beta=1$, then under competitive pricing $\alpha$ and $\beta$ measure the relative shares of labour and capital in total output.
5. Elasticity of substitution: it equals unity ($\sigma=1$).
6. Isoquants: they are smooth, convex to the origin and never touch the axes, so both inputs are essential (if either input is zero, output is zero).
7. Log-linear form: $\ln Q=\ln A+\alpha\ln L+\beta\ln K$, so it is easy to estimate by regression.

In the long run a monopolist can adjust all factors, including plant size. It faces a downward-sloping AR curve with MR below it. It has no competitors, but barriers prevent entry, so supernormal profit can persist in the long run.

Equilibrium condition. The monopolist maximises profit where

$LMC = MR$

(with the LMC curve cutting MR from below), and also $SMC = LMC$ at that output, so the plant chosen is the best one for that output.

Determination

• Output $Q^*$ is set where LMC cuts MR.
• Price $P^*$ is read from the AR (demand) curve at $Q^*$.
• Cost per unit $C^*$ is read from the LAC curve at $Q^*$.

$\text{Supernormal profit} = (P^* - C^*)\times Q^*$

Price/Cost
 |\          LMC
 | \        /   LAC
 |P*\------*  /
 |C* |-----|-/
 |    \    |/  \ AR
 |     \   /\    \
 |      \ /  MR   \
 |_______Q*_________ Output

Because entry is blocked, new firms cannot compete the profit away. The monopolist, however, in the long run will not continue if $P^* < LAC$ (loss), and will leave the industry. Also the monopolist does not necessarily produce at the minimum LAC, so it may work with excess capacity. Price is higher and output lower than under perfect competition.

Monopoly is a market structure with a single seller of a product that has no close substitutes, with barriers to the entry of new firms. The firm is a price maker and faces the downward-sloping market demand curve.

Long-run equilibrium. In the long run the monopolist can vary all inputs, adjusting plant size so as to produce the profit-maximising output. Conditions:

1. $LMC = MR$
2. LMC cuts MR from below.

Diagram description: with a downward-sloping AR and MR (MR below AR), and the LAC and LMC curves, the output $Q^*$ is determined where $LMC = MR$. The price $P^*$ is read from the AR (demand) curve at $Q^*$. The long-run profit is $(P^* - LAC)\times Q^*$.

Since barriers to entry prevent new firms from entering, the monopolist can keep supernormal profit in the long run (it will not operate if $P<LAC$). The monopolist produces at a point where LAC is still falling (not at minimum LAC), so there is excess capacity, and $P > LMC$, which implies allocative inefficiency. It also chooses a plant such that SMC = LMC = MR at the equilibrium output, with SAC tangent to LAC at that output.

The relationship is

$MR = P\left(1 - \frac{1}{e_p}\right)$

If $e_p>1$, $MR>0$; if $e_p=1$, $MR=0$; if $e_p<1$, $MR<0$. A monopolist therefore operates only where demand is elastic.

Total revenue is $TR = P\times Q$ and marginal revenue is $MR = P\left(1-\dfrac{1}{e_d}\right)$. How TR responds to a price change depends on price elasticity of demand ($e_d$).

Explanation:

• Elastic demand: the percentage change in quantity is larger than the percentage change in price, so the gain from selling more outweighs the loss from the lower price. Price and TR move in opposite directions, and MR > 0.
• Unitary elasticity: the two effects offset each other, so TR is constant and at its maximum (MR = 0).
• Inelastic demand: quantity changes less than proportionately, so price and TR move in the same direction, and MR < 0.

Example: at P = Rs 10, Q = 100 (TR = 1000). If demand is elastic and price falls to Rs 8 with Q = 140, TR = 1120 and it rises. If demand is inelastic and Q = 110, TR = 880 and it falls.

On a straight line demand curve, the upper half is elastic, the midpoint is unitary elastic and the lower half is inelastic; TR rises, reaches its maximum at the midpoint, then falls as output increases. A firm facing inelastic demand should raise the price, and a firm facing elastic demand should cut it to increase revenue.

1. $MR = P\left(1-\dfrac{1}{e_d}\right)$: MR is positive when $e_d>1$, zero when $e_d=1$ and negative when $e_d<1$.
2. A monopolist maximising profit sets MR = MC > 0, so it always operates on the elastic part of the demand curve ($e_d>1$).

In the long run a monopolist can vary all factors, so it can adjust its plant size to the demand. It maximises profit where long-run marginal cost equals marginal revenue, subject to the slope condition:

$LMC = MR,\qquad LMC \text{ cutting } MR \text{ from below}$

Determination. The monopolist faces a downward-sloping demand curve ($AR$) with $MR$ below it. It can choose the plant size for which the short-run marginal cost (SMC) passes through the intersection of $LMC$ and $MR$.

1. Find the point $E$ where $LMC = MR$; the output is $Q_m$.
2. Draw a vertical line to $AR$ to get the price $P_m$.
3. At $Q_m$ the average cost is $LAC$; the profit per unit is $P_m - LAC$, so total (supernormal) profit $= (P_m - LAC) \times Q_m$.

The monopolist is protected by barriers to entry, so the supernormal profit persists in the long run. It will not stay in business if $P_m < LAC$; it must cover at least LAC in the long run.

Features of equilibrium: price is above $LMC$ ($P > MC$), output is restricted compared with perfect competition, and the monopolist may not produce at minimum LAC, which means it may have excess capacity or use a plant that is not optimal. The diagram has price (Rs) on the vertical axis and quantity on the horizontal axis, with $AR$, $MR$, $LAC$ and $LMC$ curves, the equilibrium at $E$, output $Q_m$, price $P_m$ and a profit rectangle.

Modern theory of rent (Joan Robinson and others) holds that rent is not specific to land but is a part of the earnings of any factor of production that is in less than perfectly elastic supply. Rent is therefore a surplus over the transfer earnings (opportunity cost) of the factor.

$\text{Economic rent}=\text{Actual earnings}-\text{Transfer earnings}$

Explanation

• Transfer earning is the minimum payment needed to keep a factor in its present use, equal to its earning in the next best alternative use.
• If a factor has no alternative use (supply perfectly inelastic, e.g. land as a whole), all of its earning is rent. If its supply is perfectly elastic, its earnings are all transfer earnings, so rent is zero.
• For a factor with an upward sloping supply curve, rent is the area between the factor price and the supply curve, i.e. the area above the supply curve and below the price line.

Diagram description: with the factor's supply curve $SS$ and demand $DD$ meeting at $E$, the price is $OP$ and the quantity $OQ$. Total earnings is area $OPEQ$; transfer earning is area under $SS$ ($OSEQ$ region); rent is area $PES$ (triangle).

• Vertical $SS$: whole earnings are rent.
• Horizontal $SS$: no rent.
• Upward sloping $SS$: partly rent and partly transfer earnings.

Features: rent is a surplus, not a cost to society as a whole but is a cost to an individual industry; it arises for all factors (e.g. a famous singer's extra income over what she would earn in her next best job); the greater the inelasticity of supply, the greater the rent.

Superiority over Ricardian theory: applies to all factors, not only land; does not need the no-rent margin; recognises scarcity and alternative uses.

The liquidity preference theory of interest was given by J. M. Keynes. According to it, the rate of interest is the price paid for parting with liquidity (cash), and it is determined by the demand for and supply of money.

Demand for money (liquidity preference). People prefer to hold money for three motives:

1. Transaction motive: to meet day-to-day expenditure, which depends on income.
2. Precautionary motive: to meet unforeseen contingencies, which also depends on income.
3. Speculative motive: to take advantage of changes in bond prices. This is inversely related to the interest rate: at a high interest rate bond prices are low and people expect them to rise, so they hold less cash; at a low rate they hold more cash.

Thus $L = L_1(Y) + L_2(r)$. The liquidity preference curve slopes downward, and becomes horizontal at a very low rate (the liquidity trap).

Supply of money. It is fixed by the central bank (and the banking system) at a given time, so the supply curve is vertical.

Determination of the rate of interest. The equilibrium interest rate $r^*$ is where the liquidity preference (demand for money) curve cuts the money supply curve, $M_d = M_s$. If $r > r^*$, people hold less money than supplied and buy bonds, pushing the interest rate down. If $r<r^*$, there is excess demand for money and the rate rises. An increase in money supply shifts the supply curve to the right and lowers the interest rate; an increase in liquidity preference raises it.

Criticism: it ignores real factors (productivity of capital, saving), is indeterminate (the demand for money depends on income, which depends on the interest rate), and does not explain the liquidity trap fully.

Under perfect competition the price is constant for the firm, so average revenue equals marginal revenue: $AR = MR = P$. Both are the same horizontal line, which is also the firm's demand curve.

A competitive firm is a price-taker: $P = AR = MR$. It maximises profit by producing where $MR = MC$, so $P = MC$, provided MC is rising.

Derivation

1. At price $P_1$, the firm produces $Q_1$ where $P_1 = MC$. When price rises to $P_2$ and $P_3$, output rises to $Q_2$ and $Q_3$. The points lie along the MC curve.
2. In the short run, fixed costs have to be paid anyway. The firm therefore produces as long as price covers AVC:
   • $P > AVC$: produce (profit, or loss smaller than total fixed cost).
   • $P < AVC$: shut down, as loss would be smaller if it did not produce.
3. At the shutdown point (price equal to minimum AVC, where MC cuts AVC), the firm is indifferent between producing and shutting down.

Result. The short-run supply curve of a competitive firm is the portion of its marginal cost curve above the minimum average variable cost. It is upward sloping because of the law of diminishing returns. For prices below minimum AVC, quantity supplied is zero.

Price/Cost
 |           MC = Supply curve (above min AVC)
 |          /
 |        /   ATC
 |  P2  -*------- 
 |  P1  *      AVC
 |     shutdown point
 |______Q1__Q2____ Output

Uses of microeconomics in business decision making:

1. Demand analysis and forecasting
2. Pricing of products under different market structures
3. Production and cost analysis (least-cost input combination)
4. Profit planning and output decisions ($MR = MC$)
5. Capital budgeting and investment decisions
6. Resource allocation and input pricing
7. Understanding competitors and market structure
8. Evaluating the effects of government policies such as taxes and subsidies

Price elasticity of demand measures the degree of responsiveness of quantity demanded to a change in the price of the good:

$e_p = \frac{\%\Delta Q_d}{\%\Delta P} = \frac{\Delta Q}{\Delta P}\cdot\frac{P}{Q}$

Uses in business decision making

• Pricing: if demand is elastic ($e_p>1$), cutting the price raises total revenue; if inelastic ($e_p<1$), raising the price raises revenue. At $e_p=1$ revenue is maximum.
• Monopoly and price discrimination: a monopolist charges a higher price in the market with less elastic demand and a lower price where demand is more elastic. Since $MR = P(1-1/e)$, it operates only in the elastic part of demand.
• Taxation and subsidy: the burden of a tax falls more on consumers when demand is inelastic, so governments tax goods with inelastic demand for revenue.
• Joint products and factor pricing: it guides the relative prices of joint products and the bargaining power of unions (inelastic demand for labour supports higher wage demands).
• Forecasting and planning: firms use it to forecast sales after a price change.
• International trade: elasticity decides the effect of devaluation or depreciation on the trade balance.

Microeconomics is the branch of economics that studies the economic behaviour of individual decision-making units such as consumers, firms and factor owners, and the determination of the prices of goods and factors in individual markets (hence also called price theory).

Uses in business decision making

• Demand analysis and forecasting: the theory of demand and elasticity helps decide the product, quantity and sales forecast.
• Pricing decisions: it explains pricing under different market structures (perfect competition, monopoly, monopolistic competition, oligopoly) and price discrimination.
• Production and cost analysis: the production function and cost curves help choose the least-cost input combination and the optimum scale and output.
• Profit planning: the $MR = MC$ rule helps maximise profit and decide whether to continue or shut down.
• Resource allocation and investment decisions: it guides the efficient use of scarce resources and capital budgeting.
• Factor pricing: the theories of wage, interest and rent help determine factor payments.
• Understanding government policy: the effects of taxes, subsidies and price controls on the firm can be assessed.

Thus microeconomics gives managers the analytical tools for rational decisions.

Arc elasticity measures price elasticity over a segment (arc) of the demand curve between two points, using the average of the initial and new price and quantity:

$e_p = \frac{Q_2-Q_1}{P_2-P_1}\cdot\frac{P_1+P_2}{Q_1+Q_2}$

Income elasticity by the arc method measures it between two points on the demand relation using the average of the initial and final values:

$e_Y = \frac{Q_2 - Q_1}{Y_2 - Y_1}\times\frac{Y_1 + Y_2}{Q_1 + Q_2}$

where $Q_1, Q_2$ are the quantities demanded and $Y_1, Y_2$ the incomes. It gives the same value whichever point is taken as the start.

1. Rationality: the consumer aims at maximum satisfaction given income and prices.
2. Ordinal utility: utility cannot be measured in numbers, only ranked.
3. Consistency and transitivity of choice: if A > B and B > C, then A > C.
4. Non-satiation: more of a good is always preferred to less (monotonic preferences).
5. Diminishing marginal rate of substitution.
6. Two goods only, with given tastes, income and prices, and the consumer has complete information.

In perfect competition the firm is a price taker, so $P = AR = MR$. It maximises profit at the output where $MC = MR = P$, with $MC$ rising (second-order condition).

Derivation. Take SAC, AVC and SMC curves. For different given market prices:

• At $P_1$ equal to the minimum of AVC (point $A$, the shut-down point) the firm covers only variable cost; output $q_1$.
• At $P_2 > P_1$, the firm equates $P_2 = MC$ at $q_2$ and earns a normal profit if this is the minimum SAC (the break-even point).
• At $P_3 > P_2$ output is $q_3$, with supernormal profit, and similarly at higher prices.
• At any $P <$ min AVC, the firm loses more by producing than by closing (loss would exceed fixed cost), so the firm produces zero.

Joining the points at which $P = MC$ for prices above minimum AVC traces out the quantity supplied at each price. Hence:

The short-run supply curve of a competitive firm is the rising portion of its SMC curve lying above the minimum point of AVC. Below min AVC supply is zero (the vertical axis section).

It slopes upward because of the law of diminishing returns (rising MC): a higher price is needed to induce more output. The industry short-run supply curve is the horizontal sum of the supply curves of all firms.

1. The consumer is rational and aims to maximise satisfaction.
2. Utility is ordinal: the consumer can rank bundles by preference but need not measure utility.
3. Preferences are consistent and transitive (if A is preferred to B and B to C, then A is preferred to C).
4. More of a good is preferred to less (non-satiation or monotonicity).
5. The marginal rate of substitution diminishes.

In perfect competition the firm is a price taker, so the price is the same at every level of output. Therefore $AR = MR = P$, and both are shown by the same horizontal line (the firm's demand curve).

Meaning. Price elasticity of demand ($e_p$) measures the responsiveness of quantity demanded to a change in the price of the good:

$e_p = \frac{\%\ \text{change in quantity demanded}}{\%\ \text{change in price}} = \left|\frac{\Delta Q}{\Delta P}\cdot\frac{P}{Q}\right|$

It is classified as elastic ($e_p>1$), unitary ($e_p=1$), inelastic ($e_p<1$), perfectly elastic ($e_p=\infty$) and perfectly inelastic ($e_p=0$).

Uses in business decision making

1. Pricing decisions: if demand is elastic, a price cut raises total revenue; if inelastic, a price rise raises total revenue. Managers use this to set the revenue-maximising price.
2. Price discrimination: a monopolist charges a higher price in the market with less elastic demand and a lower price in the more elastic one.
3. Effects of a tax or subsidy: the burden of an indirect tax falls more on consumers when demand is inelastic, so firms can pass the tax on.
4. Output and revenue planning: helps to forecast the effect of a price change on sales and revenue.
5. Wage bargaining and joint products: trade unions, and the pricing of joint products (such as railway passenger and freight rates), depend on elasticity.
6. Government policy: it guides decisions on taxation, minimum price and trade policy (for example, devaluation succeeds when export and import demand is elastic).

Microeconomics is the branch of economics that studies the economic behaviour of individual units such as consumers, firms and industries, and how prices of goods and factors are determined in particular markets. It is also called price theory.

Price elasticity of demand:

$E_d=\frac{\%\Delta Q}{\%\Delta P}=\frac{\Delta Q/Q}{\Delta P/P}$

Here $P=10$, $P_1=5$, so $\Delta P=-5$; $Q=500$, $Q_1=600$, so $\Delta Q=100$.

$E_d=\frac{100/500}{-5/10}=\frac{0.2}{-0.5}=-0.4$

Numerical value $|E_d|=0.4$, which is less than 1, so demand is inelastic.

• Cardinal utility approach: assumes utility can be measured numerically in units called utils (for example, Marshall's analysis based on marginal utility and the law of diminishing marginal utility).
• Ordinal utility approach: assumes utility cannot be measured in numbers but can only be ranked in order of preference (first, second, third). It uses indifference curves (Hicks and Allen).

1. Price of the commodity itself.
2. Prices of inputs (cost of production).
3. State of technology.
4. Prices of related goods.
5. Government policy (taxes and subsidies).
6. Number of sellers and expectations about future prices.

The iso-cost line is $C=wL+rK$, with $w=\text{Rs }5$ and $r=\text{Rs }10$:

$C=5L+10K$

For $C=\text{Rs }400$: $5L+10K=400$.

• If $K=0$, $L=400/5=80$.
• If $L=0$, $K=400/10=40$.

The line joins $(L=80,K=0)$ and $(L=0,K=40)$, i.e. $K=40-0.5L$.

For $C=\text{Rs }1000$: $5L+10K=1000$.

• If $K=0$, $L=1000/5=200$.
• If $L=0$, $K=1000/10=100$.

The line joins $(L=200,K=0)$ and $(L=0,K=100)$, i.e. $K=100-0.5L$.

Both lines have the same slope $-w/r=-0.5$, so they are parallel; the higher cost line lies farther from the origin.

With cost on the vertical axis and output on the horizontal axis, both AC and MC are U-shaped, with MC rising faster.

• When MC is below AC, AC falls (MC pulls the average down).
• When MC is above AC, AC rises.
• MC cuts AC at the minimum point of AC (MC = AC there).
• MC reaches its own minimum before AC does, so the MC curve lies to the left of AC's lowest point, then rises steeply and passes through AC's minimum from below.

Reason: the average rises only if the extra (marginal) unit costs more than the average, and falls if it costs less.

Variable cost is the cost that changes with the level of output; it is zero when output is zero and rises as more is produced.

Examples: (1) raw materials, (2) wages of casual or piece-rate labour, (3) electricity/fuel used in production (also packing materials).

1. Cement industry (a few producers such as Hetauda, Ghorahi, Shivam and Arghakhanchi dominate).
2. Telecommunication services (Nepal Telecom and Ncell).

Other examples are banking, airlines and cigarette manufacturing.

Under imperfect competition (monopoly, monopolistic competition, oligopoly) the firm faces a downward sloping demand curve, which is its AR curve. To sell more, the price of all units must fall, so

$MR<AR$

and the MR curve lies below the AR curve.

For a straight-line demand curve, MR has the same price intercept as AR but is twice as steep, so it cuts the horizontal axis halfway between the origin and the AR intercept.

Algebraically, $TR=P\cdot Q$, so $MR=\dfrac{dTR}{dQ}=P+Q\dfrac{dP}{dQ}=AR+Q\dfrac{dP}{dQ}$. Since $dP/dQ<0$, $MR<AR$. Also $MR=AR\left(1-\dfrac1{e}\right)$. MR is zero when elasticity equals 1 and negative when demand is inelastic.

J.B. Clark said profit arises from dynamic changes in the economy. The five changes are:

1. Changes in population.
2. Changes in the quantity of capital.
3. Changes in production methods (technology).
4. Changes in the form of industrial organisation (forms of business).
5. Changes in the wants (tastes and desires) of consumers.

An indifference curve (IC) is a curve showing all combinations of two goods that give the consumer the same level of satisfaction, so the consumer is indifferent among them. A set of such curves is an indifference map.

Properties

1. Slopes downward from left to right: to keep satisfaction constant, more of one good requires giving up some of the other. A rising or horizontal IC would imply more goods give the same utility, which is irrational.
2. Convex to the origin: because of the diminishing marginal rate of substitution (MRS). As the consumer has more of $X$, he gives up less and less of $Y$ for each extra unit of $X$.
3. Two indifference curves never intersect: if they did, the point of intersection would give two different utility levels, and by transitivity the two curves would be equal in satisfaction, which is a contradiction.
4. Higher indifference curves represent higher satisfaction: a curve farther from the origin contains more of at least one good (under non-satiation).
5. Do not touch the axes: the consumer is assumed to buy some of both goods (not corner solutions).
6. Slope equals MRS: the slope of the IC at any point is the marginal rate of substitution $MRS_{xy}=-\frac{\Delta Y}{\Delta X}=\frac{MU_x}{MU_y}$ which falls as we move down along the curve.

Statement: The law of variable proportions (law of diminishing returns) states that when more and more units of a variable factor are combined with a fixed quantity of other factors, the total product at first increases at an increasing rate, then at a decreasing rate, and eventually falls. Marginal product rises at first, then diminishes and may become negative.

Assumptions: only one factor varies, the rest are fixed; technology is constant; the units of the variable factor are homogeneous; the short run applies.

Illustration (land fixed, labour variable)

Three stages

• Stage I (increasing returns): TP rises at an increasing rate, MP rises to a maximum and AP rises until it equals MP. The fixed factor is under-utilised; specialisation and better use of the fixed factor help.
• Stage II (diminishing returns): TP rises at a decreasing rate up to its maximum, MP falls but stays positive, AP falls. The stage starts where MP = AP (AP maximum) and ends where MP = 0. This is the rational stage where a producer operates.
• Stage III (negative returns): TP falls, MP is negative. Overcrowding of the variable factor on the fixed one makes extra units harmful, so no rational producer operates here.

Relations: when MP > AP, AP rises; when MP < AP, AP falls; MP cuts AP at AP's maximum. TP is maximum when MP = 0.

Causes: the fixed factor becomes scarce relative to the variable factor, imperfect substitutability of factors, and limits to the division of labour.

Applicability: most evident in agriculture, but it holds in all short-run production.

Price discrimination is the practice of a monopolist charging different prices to different buyers (or in different markets) for the same product, where the price differences are not due to differences in cost.

Conditions: the seller has monopoly power; the markets can be separated and resale between them is impossible; the elasticities of demand differ across markets.

Types: personal, geographical/place, use-based and time-based discrimination; first, second and third degree discrimination.

Equilibrium under discriminating monopoly (two markets)

The monopolist must decide (i) the total output, and (ii) how to distribute it between the markets.

1. Total output: the monopolist adds the marginal revenue curves of the markets horizontally to get the combined marginal revenue $MR_c=MR_1+MR_2$. Profit is maximum where combined $MR_c=MC$. This fixes total output $Q=Q_1+Q_2$.
2. Distribution of output: the output is shared so that the marginal revenue is the same in each market and equal to MC: $MR_1=MR_2=MC$ If $MR_1>MR_2$, shifting output to market 1 raises total revenue until the two are equal.
3. Prices: from the equilibrium outputs $Q_1$ and $Q_2$, the prices $P_1$ and $P_2$ are read from the AR (demand) curve of each market.

Since $MR=P\left(1-\frac1{e}\right)$, $MR_1=MR_2$ implies $P_1\left(1-\frac1{e_1}\right)=P_2\left(1-\frac1{e_2}\right)$ so the market with less elastic demand gets the higher price, and the one with more elastic demand gets the lower price. If elasticities were equal, prices would be equal and discrimination would not be profitable.

Total profit = $(TR_1+TR_2)-TC$, which is greater than the profit under a single price.

Statement: The marginal productivity theory (J.B. Clark, Wicksteed) says that, under perfect competition, the wage of a worker equals the value of the marginal product of labour, which is the addition to total output (value) from employing the last worker. In equilibrium

$W=VMP_L=MP_L\times P=MRP_L$

Explanation

• An employer hires workers as long as the extra revenue from one more worker (MRP) exceeds the wage. He stops where $W=MRP$, because beyond that point the worker adds more to cost than to revenue.
• Because of diminishing returns, the MRP curve slopes downward, so more workers are hired only at a lower wage. The MRP curve is therefore the firm's demand curve for labour.
• The market wage is set by the intersection of labour demand (the sum of firms' MRP curves) and labour supply. Each firm takes this wage as given, and employs labour up to the point where wage = MRP.

Assumptions: perfect competition in product and factor markets; homogeneous labour; full mobility and full employment; law of diminishing returns; possible to measure marginal product; profit maximisation.

Example: if the last worker adds 10 units and the price per unit is Rs 50, VMP is Rs 500, so the wage is Rs 500.

Criticisms: it is mainly a demand-side theory and ignores supply; real labour markets are imperfect (unions, minimum wages, monopsony); difficult to measure marginal product when workers cooperate; labour is not homogeneous or perfectly mobile; ignores social and institutional factors.

The short-run average cost (SAC) curve is U-shaped: it falls at first, reaches a minimum, and then rises. SAC = AFC + AVC.

Reasons

1. Spreading of fixed costs: AFC falls continuously as output increases, since the same total fixed cost is spread over more units. This pulls SAC downward at the beginning.
2. Law of variable proportions: at first, increasing returns to the variable factor reduce AVC; after the optimum point, diminishing returns set in and AVC rises. The fixed plant gets over-used.
3. Better utilisation of fixed factors: initially the plant is under-used, so more output lowers cost; later, overcrowding and congestion increase costs.

Working: in the early stage the fall in AFC and AVC together makes SAC fall. In the later stage the rise in AVC exceeds the fall in AFC, so SAC rises. The minimum is reached where MC = SAC.

So SAC has a U shape, which is governed by the law of variable proportions.

An iso-quant (equal product curve) shows all combinations of two inputs (labour and capital) that produce the same level of output.

Properties

1. Slopes downward from left to right: if one input is reduced, the other must increase to keep output constant.
2. Convex to the origin: because of the diminishing marginal rate of technical substitution (MRTS). Inputs are not perfectly substitutable, so as more labour is used, less capital is given up for each additional unit of labour.
3. Two iso-quants never intersect: the point of intersection would imply that one input combination yields two different levels of output.
4. Higher iso-quants represent higher output: a curve farther from the origin has more of both inputs.
5. Do not touch the axes: both inputs are needed for production.
6. Slope is MRTS: $MRTS_{LK}=-\frac{\Delta K}{\Delta L}=\frac{MP_L}{MP_K}$
7. Need not be parallel or symmetrical: the shape depends on the substitutability of inputs.

Demand for a commodity depends on:

1. Price of the commodity: the lower the price, the greater the quantity demanded (law of demand).
2. Income of the consumer: for normal goods demand rises with income; for inferior goods it falls.
3. Prices of related goods: substitutes (tea and coffee) and complements (car and petrol) change demand in opposite ways.
4. Tastes and preferences: fashion, habit and advertising affect demand.
5. Expectations about future prices and income.
6. Population size and composition (age, sex): a larger population raises market demand.
7. Distribution of income: more equal distribution raises demand for necessities.
8. Other factors: climate, government policy (taxes, subsidies), credit availability.

Demand function: $Q_d=f(P,\;Y,\;P_r,\;T,\;E,\dots)$.

Cross elasticity of demand measures the responsiveness of the quantity demanded of one good (X) to a change in the price of another good (Y).

$E_c=\frac{\%\Delta Q_x}{\%\Delta P_y}=\frac{\Delta Q_x}{\Delta P_y}\times\frac{P_y}{Q_x}$

Types

1. Positive cross elasticity (substitutes): when the price of Y rises, demand for X rises. Examples: tea and coffee, Pepsi and Coke. The closer the substitutes, the higher $E_c$.
2. Negative cross elasticity (complements): when the price of Y rises, demand for X falls. Examples: car and petrol, pen and ink. $E_c<0$.
3. Zero cross elasticity (unrelated goods): a change in the price of Y does not change demand for X. Example: rice and shoes. $E_c=0$.

Cross elasticity is used by firms to understand how rivals' pricing affects their sales and to define markets and industries.

Price effect is the change in the quantity of a good purchased by a consumer when its price changes, keeping the consumer's money income, tastes and the prices of other goods constant.

Explanation with the indifference map

Let the consumer have income $M$ and buy goods $X$ and $Y$. The initial budget line $AB$ is tangent to indifference curve $IC_1$ at $E_1$, which is the equilibrium. Suppose the price of $X$ falls: the budget line pivots outward on the $X$ axis to $AB_1$, then $AB_2$ and so on, with the $Y$ intercept $A$ unchanged. Each new budget line is tangent to a higher indifference curve ($IC_2$, $IC_3$) at $E_2$, $E_3$.

Joining the equilibrium points $E_1,E_2,E_3$ gives the price consumption curve (PCC). The PCC shows how consumption changes as price changes.

• For a normal good, PCC slopes downward/rightward with quantity of $X$ rising as its price falls.
• If demand is elastic, PCC slopes downward; if unitary elastic, PCC is horizontal; if inelastic, it slopes upward (backward).

The price effect splits into the substitution effect and the income effect: $PE=SE+IE$. The demand curve of the consumer can be derived from the PCC by plotting price against quantity at each equilibrium.

Microeconomics is useful in several ways.

1. Explains price determination: it shows how prices of goods and factors are set by demand and supply.
2. Efficient allocation of resources: it explains how scarce resources are allocated among alternative uses to produce goods.
3. Guides consumers: it explains consumer behaviour and how to maximise satisfaction from limited income.
4. Guides producers: it helps firms decide what to produce, how much, and how, so as to minimise cost and maximise profit.
5. Basis for economic policy: it helps the government evaluate taxes, subsidies, price controls and minimum wages.
6. Explains distribution: it determines factor prices (rent, wage, interest and profit).
7. Welfare economics and international trade: it evaluates economic efficiency and gains from trade.
8. Basis for macroeconomics: it provides the foundation for understanding aggregates.

Microeconomics is the branch of economics that studies the economic behaviour of individual units such as consumers, firms and industries, and how prices of goods and factors are determined in particular markets. It is also called price theory.

The main determinants of demand are:

1. Price of the commodity.
2. Income of consumers.
3. Prices of related goods (substitutes and complements).
4. Tastes and preferences.
5. Consumer expectations about future prices and income.
6. Size and composition of population.
7. Distribution of income, and other factors such as climate and government policy.

The marginal rate of substitution (MRS) is the rate at which a consumer is willing to give up units of one good (Y) to obtain one more unit of another good (X) while staying on the same indifference curve.

$MRS_{xy}=-\frac{\Delta Y}{\Delta X}=\frac{MU_x}{MU_y}$

It diminishes as the consumer has more of $X$.

The ordinal utility analysis (Hicks and Allen) holds that utility cannot be measured in absolute numbers, but a consumer can rank combinations of goods in order of preference (more preferred, less preferred, indifferent). It uses indifference curves and budget lines to explain consumer equilibrium.

A budget line (price line) shows all combinations of two goods that a consumer can buy with a given money income at given prices.

$P_xX+P_yY=M$

Its slope is $-P_x/P_y$. Combinations on or below the line are affordable.

The price consumption curve (PCC) is the locus of consumer equilibrium points obtained by joining the tangency points of successive budget lines and indifference curves when the price of one good changes, while income, tastes and the price of the other good remain constant. It shows how the quantity bought changes with price and is used to derive the demand curve.

An iso-cost curve (iso-cost line) shows all combinations of two inputs (labour and capital) that a firm can buy for a given total cost at given input prices.

$C=wL+rK$

Its slope is $-w/r$. It is the producer's counterpart of the consumer's budget line.

Monopoly is a market structure in which there is a single seller of a product that has no close substitutes, with barriers to entry of other firms. The monopolist is a price maker and the firm is itself the industry.

With cost on the vertical axis and output on the horizontal axis, both AC and MC are U-shaped, with MC rising faster.

• When MC is below AC, AC falls (MC pulls the average down).
• When MC is above AC, AC rises.
• MC cuts AC at the minimum point of AC (MC = AC there).
• MC reaches its own minimum before AC does, so the MC curve lies to the left of AC's lowest point, then rises steeply and passes through AC's minimum from below.

Reason: the average rises only if the extra (marginal) unit costs more than the average, and falls if it costs less.

Selling costs are the expenses incurred by a firm to create, increase or maintain demand for its product, such as advertising, sales promotion, salesmen's salaries, samples and displays. They are important under monopolistic competition and oligopoly.

An indifference curve (IC) is a curve showing all combinations of two goods that give the consumer the same level of satisfaction, so the consumer is indifferent among them. A set of such curves is an indifference map.

Properties

1. Slopes downward from left to right: to keep satisfaction constant, more of one good requires giving up some of the other. A rising or horizontal IC would imply more goods give the same utility, which is irrational.
2. Convex to the origin: because of the diminishing marginal rate of substitution (MRS). As the consumer has more of $X$, he gives up less and less of $Y$ for each extra unit of $X$.
3. Two indifference curves never intersect: if they did, the point of intersection would give two different utility levels, and by transitivity the two curves would be equal in satisfaction, which is a contradiction.
4. Higher indifference curves represent higher satisfaction: a curve farther from the origin contains more of at least one good (under non-satiation).
5. Do not touch the axes: the consumer is assumed to buy some of both goods (not corner solutions).
6. Slope equals MRS: the slope of the IC at any point is the marginal rate of substitution $MRS_{xy}=-\frac{\Delta Y}{\Delta X}=\frac{MU_x}{MU_y}$ which falls as we move down along the curve.

Production function is the technical relationship between inputs and the maximum output obtained:

$Q=f(L,K)$

The short run is the period in which at least one factor (capital, say $\bar K$) is fixed and other factors (labour) are variable. The short-run production function is

$Q=f(L,\bar K)$

It is governed by the law of variable proportions.

Concepts

• Total product: $TP=Q$.
• Average product: $AP=\dfrac{TP}{L}$.
• Marginal product: $MP=\dfrac{\Delta TP}{\Delta L}=\dfrac{dTP}{dL}$.

Illustration

Stages

1. Stage I: from origin to the maximum AP; MP > AP, increasing returns.
2. Stage II: from maximum AP to MP = 0 (maximum TP); diminishing returns. The rational producer operates here.
3. Stage III: MP is negative, TP falls; no producer operates.

Relationships: MP cuts AP at AP's maximum; when MP = 0, TP is maximum; AP and MP are both derived from TP (the slope of the ray from origin gives AP, the slope of the tangent gives MP).

Features: capital is fixed, so output increases only by adding labour; diminishing returns eventually appear; cost curves in the short run (U-shaped AC) are derived from this production function.

Equilibrium: a market is in equilibrium at the price at which quantity demanded equals quantity supplied:

$Q_d=Q_s$

At a price above the equilibrium there is excess supply and sellers lower price; below it there is excess demand and the price rises. The price therefore settles at the equilibrium price $P_e$ with quantity $Q_e$, where the demand and supply curves intersect.

Example: $Q_d=100-2P$ and $Q_s=20+2P$. Setting equal: $100-2P=20+2P$, so $4P=80$ and $P_e=20$, $Q_e=60$.

Change in supply (demand unchanged)

• Increase in supply: the supply curve shifts right. At the old price there is excess supply, so the price falls and quantity demanded and traded rises. New equilibrium: lower price, larger quantity.
• Decrease in supply: the supply curve shifts left. There is excess demand at the old price, so price rises and quantity falls. New equilibrium: higher price, smaller quantity.

Example: if supply increases to $Q_s=40+2P$, then $100-2P=40+2P$, giving $P=15$ and $Q=70$ (price falls from 20 to 15 and quantity rises from 60 to 70).

The size of the changes depends on the elasticity of demand: the more inelastic the demand, the larger the price change and the smaller the quantity change.

Income consumption curve (ICC) is the locus of consumer equilibrium points obtained by joining the tangency points of the budget lines and indifference curves when the consumer's income changes, with prices of both goods and tastes constant.

Explanation: with prices of $X$ and $Y$ fixed, the budget line shifts parallel outward as income rises ($AB\to A_1B_1\to A_2B_2$). Each new budget line is tangent to a higher indifference curve ($IC_1,IC_2,IC_3$) at $E_1,E_2,E_3$. The curve through $E_1,E_2,E_3$ is the ICC.

Shapes of ICC

1. Both goods normal: ICC slopes upward to the right (positive slope); the consumer buys more of both as income rises. It may bend towards either axis, depending on the relative income elasticities.
2. One good inferior: if $X$ is inferior, the ICC bends backward (towards the $Y$ axis) at higher income, since quantity of $X$ falls as income rises. If $Y$ is inferior, the ICC bends towards the $X$ axis.
3. Straight line through origin: if proportions of the goods remain constant (homothetic preferences).

The ICC is used to derive the Engel curve, which relates the quantity of a good to income.

Price elasticity of demand is the degree of responsiveness of quantity demanded to a change in price:

$E_d=\frac{\%\Delta Q}{\%\Delta P}$

Methods of measurement

1. Percentage (proportionate) method: $E_d=\frac{\Delta Q/Q}{\Delta P/P}=\frac{\Delta Q}{\Delta P}\times\frac{P}{Q}$
2. Total outlay (expenditure) method (Marshall):

• If price falls and total expenditure rises, $E_d>1$ (elastic).
• If expenditure is unchanged, $E_d=1$.
• If price falls and expenditure falls, $E_d<1$ (inelastic).

3. Point method (geometric method): at a point on a straight-line demand curve, $E_d=\frac{\text{Lower segment}}{\text{Upper segment}}$ It is 1 at the midpoint, greater than 1 above it, and less than 1 below it; it is infinity at the price axis and zero at the quantity axis.
4. Arc method: for a large change in price, use the average of the initial and final values: $E_d=\frac{\Delta Q}{\Delta P}\times\frac{P_1+P_2}{Q_1+Q_2}$

Best method: The point method is the most accurate where the change in price is very small, since it measures elasticity at an exact point. For a finite change between two points, the arc method is better, as it gives the same answer whichever direction the change is made. The percentage method is the general basis, and the total outlay method is the simplest and useful for business decisions on pricing, but it only shows whether demand is elastic or inelastic, not the numeric value.

Imperfect competition is a market situation in which the conditions of perfect competition are not all fulfilled, so that individual firms have some power to influence the price. It includes monopoly, monopolistic competition, duopoly and oligopoly.

Oligopoly is a market structure with a few large sellers of a homogeneous or differentiated product.

Characteristics of oligopoly

1. Few sellers: a small number of firms dominate the market.
2. Interdependence: each firm's price and output decisions affect the rivals, who react. Firms must consider rivals' reactions.
3. Barriers to entry: large capital requirements, patents and economies of scale restrict new firms.
4. Product may be homogeneous or differentiated: pure oligopoly (steel, cement) or differentiated oligopoly (cars, mobile phones).
5. Advertising and selling costs: non-price competition is important.
6. Price rigidity: prices tend to be stable, as in the kinked demand curve model, because rivals match price cuts but not price rises.
7. Indeterminate demand curve: because reactions of rivals are uncertain, the firm's demand curve is not definite.
8. Possibility of collusion (cartels, price leadership) or conflict.

The least cost combination is the combination of inputs (labour $L$ and capital $K$) that produces a given output at the minimum total cost; it is the producer's equilibrium.

Tools: the iso-quant (equal output curve) and the iso-cost line, $C=wL+rK$ with slope $-w/r$.

Conditions of equilibrium

1. The iso-cost line is tangent to the iso-quant, so the slopes are equal: $MRTS_{LK}=\frac{MP_L}{MP_K}=\frac{w}{r}$
2. Equivalent form: $\frac{MP_L}{w}=\frac{MP_K}{r}$ i.e. the marginal product per rupee spent is the same for each input.
3. The iso-quant is convex to the origin at the point of tangency (MRTS is diminishing; second-order condition).

Explanation: the iso-quant $Q$ and several iso-cost lines are drawn. Points on a lower iso-cost line cannot produce $Q$. Points on a higher line are feasible but cost more. The lowest iso-cost line that touches the iso-quant, at point $E$, gives the least-cost combination $(L^*,K^*)$.

If $MP_L/w>MP_K/r$, the firm gains by using more labour and less capital until equality holds; the reverse also holds.

If the output is allowed to vary, the tangency points for different budgets trace the expansion path.

Schumpeter explained profit as the reward for innovation carried out by the entrepreneur. In a stationary "circular flow" economy, perfect competition drives price down to cost, so there is no profit. Profit arises only when the entrepreneur disturbs this equilibrium.

Innovation means carrying out new combinations, such as:

• introducing a new product or a new quality of a product
• adopting a new method of production
• opening a new market
• finding a new source of raw materials
• reorganising an industry, for example creating a monopoly

How profit arises. An innovation lowers cost or raises revenue, so the innovator earns a surplus over cost. This surplus is profit. Because it depends on the innovation, it is temporary. Imitators soon follow, competition rises, price falls to the new cost level and the profit vanishes. The entrepreneur must then innovate again to earn profit.

Key points

• The entrepreneur is an innovator, not necessarily a capitalist or risk-bearer. Risk is borne by the capitalist who lends the funds.
• Profit is a dynamic phenomenon and a return to innovation alone.
• Profit is not a permanent income. It is a temporary surplus that is competed away.

Criticism. The theory ignores the entrepreneur's other functions such as risk and uncertainty bearing, and not all profit comes from innovation (some arises from monopoly or luck).

Microeconomics is the branch of economics that studies the economic behaviour of individual decision-making units such as consumers, firms and industries. It deals with how they take decisions on prices, output and the allocation of resources in particular markets. It is also called price theory.

The main determinants of demand for a commodity are:

1. Price of the commodity
2. Price of related goods (substitutes and complements)
3. Income of the consumer
4. Tastes and preferences
5. Expectations about future prices and income
6. Number of consumers (population)

Giffen goods are special inferior goods for which the quantity demanded falls when the price falls, and rises when the price rises. The negative income effect is stronger than the substitution effect, so the demand curve slopes upward. Coarse staple foods consumed by very poor households are the usual example (named after Sir Robert Giffen).

The supply of a commodity is determined by:

1. Price of the commodity
2. Cost of production and prices of inputs
3. State of technology
4. Prices of related goods
5. Number of sellers in the market
6. Government policy (taxes and subsidies)
7. Expectations of future prices, and natural conditions

Income elasticity of demand is positive when the quantity demanded rises as consumer income rises, that is, for normal goods (necessities and luxuries). For these goods $E_Y = \frac{\%\Delta Q}{\%\Delta Y} > 0$. It is negative only for inferior goods.

Marginal product (MP) is the addition to total product caused by employing one more unit of a variable factor, other inputs held constant.

$MP = \frac{\Delta TP}{\Delta L}$

Implicit costs are the imputed costs of resources owned and used by the firm itself, for which no actual cash payment is made. Examples are the owner's own labour, the rent of the owner's own building and interest on the owner's own capital. They are estimated at what these resources could earn in their best alternative use.

Oligopoly is a market structure in which a few large sellers dominate the market for a product that may be homogeneous or differentiated. Firms are interdependent, so each firm's decision on price and output depends on its rivals' reactions. Examples are cement producers, mobile telecom companies (Ncell and Nepal Telecom) and airlines.

The Engel curve shows the quantity of a good purchased at different levels of consumer income, with the horizontal axis showing quantity (Q) and the vertical axis income (Y). For an inferior good, the curve slopes backward (negative slope): as income rises, the quantity bought falls because the consumer shifts to better goods.

Income (Y)
 |  \
 |   \
 |    \   Engel curve
 |     \  (inferior good)
 |______\________ Quantity (Q)

At low income the quantity consumed is high, and beyond a certain income it declines. Hence $E_Y < 0$.

According to J.B. Clark, profit arises only in a dynamic economy. The five changes that give rise to profit are:

1. Changes in population
2. Changes in the quantity of capital
3. Improvements in methods of production (technology)
4. Changes in the form of industrial organisation
5. Changes in the wants (tastes) of consumers

Indifference curve (IC). An indifference curve is the locus of all combinations of two goods that give the consumer the same level of satisfaction. The consumer is indifferent among all points on it. Its slope is the marginal rate of substitution:

$MRS_{xy} = -\frac{\Delta Y}{\Delta X} = \frac{MU_x}{MU_y}$

Properties: it slopes downward, is convex to the origin (diminishing MRS), higher curves show higher satisfaction, and two curves never intersect.

Consumer's equilibrium (ordinal approach).

Assumptions: the consumer is rational, has a fixed money income $M$, faces given prices $P_x$ and $P_y$, and has a consistent ordinal preference map.

Budget line. All affordable combinations satisfy

$P_x X + P_y Y = M$

Its slope is $-\frac{P_x}{P_y}$, with intercepts $M/P_x$ on the X-axis and $M/P_y$ on the Y-axis.

Equilibrium. The consumer chooses the combination on the highest attainable IC. This is the point where the budget line is tangent to an indifference curve.

Y
|\
| \  .
|  \   . IC3 (unattainable)
|   \E . IC2  <- equilibrium (tangent)
|    \ .   IC1
|     \
|______\________ X
   budget line

At the point of tangency, the slope of the IC equals the slope of the budget line:

$MRS_{xy} = \frac{MU_x}{MU_y} = \frac{P_x}{P_y}$

Why E is the equilibrium.

• On IC3 the combinations lie outside the budget line, so they are not affordable.
• At any point on IC1 that cuts the budget line, the consumer can move along the budget line to a higher IC, so such a point is not optimal.
• At the tangency point E on IC2, no move along the budget line raises satisfaction.

Second order condition. The IC must be convex to the origin at E, that is, MRS must be diminishing.

Hence the consumer is in equilibrium where the budget line is tangent to the highest possible IC, and the marginal rate of substitution equals the price ratio.

Price elasticity of demand. It is the degree of responsiveness of quantity demanded to a change in the price of the commodity.

$E_p = \frac{\%\ \text{change in quantity demanded}}{\%\ \text{change in price}} = \frac{\Delta Q}{\Delta P}\cdot\frac{P}{Q}$

Its absolute value is greater than 1 (elastic), equal to 1 (unitary), or less than 1 (inelastic).

Total outlay (expenditure) method. Proposed by Marshall, this method compares the consumer's total expenditure on the good, $TE = P \times Q$, before and after a price change.

Numerical illustration

Diagram. Plot price on the Y-axis and total outlay on the X-axis. The outlay curve slopes downward to the right where demand is elastic (price falls, outlay rises), becomes vertical at unitary elasticity, and slopes backward (upward as price rises) where demand is inelastic.

Rule. Price and total outlay move in opposite directions when demand is elastic, in the same direction when inelastic, and total outlay does not change when elasticity is unity.

Merit. It is simple and needs only price and expenditure data. Limitation. It only tells whether demand is elastic, unitary or inelastic, not the exact numerical value of elasticity.

Monopolistic competition is a market structure with many sellers selling close but differentiated products (Chamberlin, Robinson).

Main features

1. Large number of sellers, each with a small share of the market, so no one can control the market.
2. Product differentiation through brand, quality, packaging or location. Products are close substitutes but not identical.
3. Free entry and exit of firms in the long run.
4. Some control over price. Each firm faces a downward-sloping, fairly elastic demand curve.
5. Selling costs. Advertising and promotion are important.
6. Non-price competition (service, design, credit).
7. Each firm acts independently, as there are too many firms for mutual dependence.

Short-run price determination

The firm maximises profit where $MR = MC$, with MC cutting MR from below.

• The firm's AR (demand) curve slopes downward and MR lies below AR.
• The firm produces output $Q_0$ where $MR = MC$.
• Price $P_0$ is read from the AR curve at $Q_0$.

Supernormal profit. If $AR > AC$ at $Q_0$:

$\text{Profit} = (P_0 - AC_0)\times Q_0$

Normal profit. If $AR = AC$.

Loss. If $AR < AC$ but $AR \ge AVC$, the firm continues in the short run to minimise its loss. If $AR < AVC$, it shuts down.

Price/Cost
 |\     MC
 | \   /  AC
 |  \ /  /
 |P0 *--/--        shaded: supernormal profit
 |C0 *-/-           (P0 - C0) x Q0
 |    \/\ AR
 |     \  \
 |      \ MR\
 |_______Q0______ Output

In the long run, supernormal profits attract new firms, demand for each firm falls, and AR becomes tangent to AC, leaving only normal profit.

Statement. When one factor of production is increased while other factors are held fixed, the total product at first rises at an increasing rate, then at a diminishing rate, and eventually falls. Equivalently, the marginal product of the variable factor first rises, then falls and may become negative. It is also called the law of diminishing returns.

Assumptions

• One factor is variable, the others are fixed.
• Technology is constant.
• Units of the variable factor are homogeneous.
• The law applies in the short run.

Illustration (land fixed at 1 hectare, labour variable)

Three stages

Stage I (increasing returns). TP rises at an increasing rate, MP rises to a maximum and AP rises. It lasts until AP reaches its maximum, where $MP = AP$. The fixed factor is underutilised, and better division of labour and use of the fixed factor raise productivity.

Stage II (diminishing returns). TP rises at a diminishing rate up to its maximum. MP falls but stays positive, and AP falls. It ends where $MP = 0$ and TP is at its maximum. This is the rational stage for the producer.

Stage III (negative returns). TP falls and MP is negative. The fixed factor is overcrowded, so no rational producer operates here.

TP/MP/AP
 |        ___TP___
 |      /         \
 |    /             \
 |  /
 |    MP / AP shapes: MP rises, peaks, cuts AP at AP max,
 |    then falls, and becomes negative in stage III
 |__I__|___II___|___III___ Variable input

Causes. Initially the fixed factor is under-used. Beyond the optimum ratio, the fixed factor becomes scarce relative to the variable one, and imperfect substitutability of factors leads to diminishing returns.

Income consumption curve (ICC) is the locus of consumer equilibrium points obtained when income changes, with prices of goods and preferences held constant.

Derivation. Draw goods X and Y on the axes. With prices fixed, an increase in income shifts the budget line outward and parallel (intercepts $M/P_x$ and $M/P_y$ rise). Each budget line is tangent to a different indifference curve at $E_1, E_2, E_3, \dots$ (IC$_1$, IC$_2$, IC$_3$). Joining these equilibrium points gives the ICC.

Superior (normal) good X. As income rises, the consumer buys more of X. The ICC slopes upward to the right (positive slope). If the ICC bends towards the X-axis for X, then X is a necessity and Y a luxury. If it bends towards the Y-axis, X is a luxury.

Y
|        / ICC (X superior)
|      E3
|    E2 /
|  E1 /
|____/___________ X

Inferior good X. Beyond some income level, the consumer buys less of X as income rises. The ICC bends backward (towards the Y-axis) after a point, giving a negatively sloped section.

Y
|    E3
|   / ICC bends back
|  E2
| E1
|____________ X

The ICC is the basis for deriving the Engel curve (relationship of quantity and income).

The short-run average cost (SAC) curve is U-shaped: it falls at first, reaches a minimum and then rises. The reasons are as follows.

1. Law of variable proportions. In the short run some factors are fixed. When variable input is added, initially returns rise, so AVC falls. After the optimum factor ratio, diminishing returns set in and AVC rises. Since $AC = AFC + AVC$, AC follows this pattern.
2. Behaviour of AFC. AFC falls continuously as output rises because the fixed cost is spread over more units. This causes AC to fall initially.
3. Combined effect. At low output, the fall in AFC and AVC pulls AC down. At higher output, the rise in AVC outweighs the fall in AFC, so AC rises.
4. Fuller use of fixed plant. Up to the optimum capacity, better use of the fixed plant and specialisation lower AC. Beyond this, over-crowding, congestion and management strain raise AC.

The MC curve cuts the AC curve at its minimum point. While $MC < AC$ the AC falls, and when $MC > AC$ the AC rises.

The modern theory of rent treats rent as a payment for any factor of production whose supply is less than perfectly elastic. It holds that rent arises in all factors, not only land. It was developed by Mrs. Joan Robinson and Marshall's followers.

Concept: economic rent = transfer earnings surplus.

• Transfer earnings (opportunity cost) is the minimum payment needed to keep a factor in its present use, which equals what it could earn in its next best use.
• Economic rent is the excess of actual earnings over transfer earnings.

$\text{Economic rent} = \text{Actual earnings} - \text{Transfer earnings}$

Role of elasticity of supply

• Perfectly inelastic supply (like land for the economy as a whole): all earnings are rent, as transfer earnings are zero (vertical supply curve).
• Perfectly elastic supply: no rent, as all earnings are transfer earnings (horizontal supply curve).
• Elasticity between these: earnings are partly rent and partly transfer earnings.

Diagram. With price on the Y-axis and quantity on the X-axis, the rent is the area between the price line and the supply curve (above the supply curve, below the equilibrium price). The area under the supply curve is transfer earnings.

Example. A footballer earning Rs 100,000 who could earn Rs 20,000 in the next best job gets an economic rent of Rs 80,000.

Comparison with Ricardo. Ricardo's rent arises from differences in fertility and applies only to land. The modern theory applies to every factor with less than perfectly elastic supply.

Isoquant. An isoquant (equal product curve) is the locus of all combinations of two inputs (say labour L and capital K) that produce the same level of output. Its slope is the marginal rate of technical substitution:

$MRTS_{LK} = -\frac{\Delta K}{\Delta L} = \frac{MP_L}{MP_K}$

Properties

1. Negatively sloped (downward). To keep output constant, more of one input requires less of the other.
2. Convex to the origin. Because MRTS diminishes as one input replaces the other, as the factors are imperfect substitutes.
3. Two isoquants never intersect. Intersection would imply that the same combination gives two different outputs, which is contradictory.
4. Higher isoquants represent higher output. A curve further from the origin shows more output.
5. Isoquants need not be parallel, as the MRTS differs across curves.
6. They do not touch either axis, as both inputs are needed to produce output (except when a single input can produce it).
7. Within the economic region, isoquants are negatively sloped. Upward-sloping parts are uneconomic since they use more of both inputs for the same output.

Under perfect competition the firm is a price-taker, so its demand curve is horizontal: $P = AR = MR$. The firm maximises profit where $MR = MC$ (with MC rising).

Derivation

1. At price $P_1$, the firm equates $P_1 = MC$ and chooses output $Q_1$. At higher prices $P_2, P_3$ it chooses $Q_2, Q_3$. Each equilibrium output lies on the MC curve.
2. The firm covers its costs in the short run if price covers average variable cost. Fixed costs must be paid anyway.
   • If $P > AVC$: producing minimises loss or earns profit.
   • If $P < AVC$: the firm shuts down, producing nothing.
3. The shutdown point is the minimum of AVC, where MC cuts AVC.

Therefore, the short-run supply curve of the firm is that part of the MC curve lying above the minimum point of the AVC curve. At prices below minimum AVC, supply is zero.

Price/Cost
 |            MC (supply curve above S)
 |           /
 |          /    ATC
 |       P3/---
 |      P2/-- AVC
 |    S  *  <- shutdown point
 |____ Q1 Q2 Q3 ___ Output

The curve slopes upward, reflecting the law of diminishing returns (rising MC). The market short-run supply curve is the horizontal sum of the supply curves of all firms.

A monopolist is the single seller, so it faces the whole market demand curve, which slopes downward. To sell more, it must lower the price.

Average revenue (AR). $AR = \frac{TR}{Q} = P$, so the AR curve is the demand curve. It slopes downward to the right, and is relatively inelastic compared with that of a competitive firm.

Marginal revenue (MR). Since price must fall on all units to sell an extra unit,

$MR = \frac{\Delta TR}{\Delta Q} < AR$

The MR curve slopes downward and lies below the AR curve. For a straight-line AR, MR is also a straight line starting at the same point on the price axis but with twice the slope, so it cuts the horizontal axis at half the distance of AR. For example, if $P = 10 - Q$, then $TR = 10Q - Q^2$ and $MR = 10 - 2Q$.

Relationship with elasticity:

$MR = AR\left(1 - \frac{1}{e}\right)$

• $MR > 0$ when $e > 1$
• $MR = 0$ when $e = 1$ (TR maximum)
• $MR < 0$ when $e < 1$

Price
 |\
 | \
 |  \  AR
 |   \  \
 |    \  \ MR
 |_____\__\___ Quantity

Four determinants of demand for motorbikes in Nepal:

1. Price of motorbikes (and of fuel, which is a complementary good)
2. Income of consumers (remittances and salaries)
3. Road conditions, availability of credit/finance and import duty (taxes) policy
4. Tastes and preferences (brand, style, fuel efficiency) and prices of substitutes such as public transport or scooters/electric vehicles

An indifference curve is convex to the origin because of the diminishing marginal rate of substitution (MRS). As the consumer gets more of one good, he is willing to give up fewer and fewer units of the other good for each additional unit of it, since the marginal utility of the good in plenty falls and that of the scarce good rises.

Opportunity cost is the value of the next best alternative that is given up when a choice is made.

Using the relation between MR, price and elasticity:

$MR = P\left(1 - \frac{1}{e}\right)$

$5 = P\left(1 - \frac{1}{3}\right) = \frac{2P}{3}$

$P = \frac{5\times 3}{2} = \text{Rs } 7.50$

Cross elasticity of demand of tea for coffee:

$E_c = \frac{\Delta Q_t}{\Delta P_c}\cdot\frac{P_c}{Q_t} = \frac{70-60}{5-4}\times\frac{4}{60} = 10\times\frac{4}{60} = 0.67$

The cross elasticity is positive (about $0.67$), so tea and coffee are substitutes.

The law of increasing returns to scale states that when all inputs are increased in the same proportion, output increases in a larger proportion. For example, doubling all inputs more than doubles output. It is due to better division of labour and specialisation.

Two examples of price discrimination in Nepal:

1. Electricity (NEA) tariffs, with different rates per unit for households, industries and commercial users, and for different consumption slabs.
2. Different prices for different groups: airlines, cinemas or museum and entry tickets charging Nepali citizens, SAARC nationals and foreigners different rates. Telecom and Nepal Telecom/Ncell off-peak and peak package rates are another example.

A supply function shows the functional relationship between the quantity supplied of a commodity and its determinants:

$Q_s = f(P, P_r, C, T, N, G, \dots)$

where P is own price, $P_r$ prices of related goods, C cost of production, T technology, N number of sellers and G government policy. In the simple form, $Q_s = f(P)$, for example $Q_s = a + bP$.

According to Keynes, there are three motives for demanding (holding) money:

1. Transaction motive: to meet day-to-day expenditures on goods and services. It depends on income.
2. Precautionary motive: to meet unforeseen contingencies such as illness or accident. It also depends on income.
3. Speculative motive: to hold cash to take advantage of changes in bond prices or interest rates. It is inversely related to the rate of interest.

Microeconomics supplies the analytical tools a manager uses to take sound decisions on the use of scarce resources.

1. Demand analysis and forecasting. Knowledge of demand determinants and elasticity helps in forecasting sales and setting prices, and whether a price change will raise revenue.
2. Production and cost decisions. The theory of production and cost helps decide the least-cost input combination, the optimum scale and the output level at which cost is minimised ($MC = AC$ at minimum AC).
3. Pricing decisions. It explains price and output determination under perfect competition, monopoly, monopolistic competition and oligopoly, and strategies such as price discrimination.
4. Profit maximisation. The $MR = MC$ rule guides output decisions, and the break-even and shutdown analysis guide whether to continue or stop.
5. Resource allocation and input pricing. It guides decisions on hiring labour, capital investment and how much to produce of each product.
6. Market structure and competition. It helps in understanding rivals' behaviour and in choosing strategies such as product differentiation and advertising.
7. Evaluating government policy. Managers can assess the effect of taxes, subsidies and price controls on their business.

A worker has a fixed time (say 24 hours) to divide between work (income) and leisure. Income gives satisfaction through goods bought, leisure gives satisfaction directly, but more leisure means less income. The worker must choose the best combination.

Tools

• Indifference curves (IC) show combinations of income (Y) and leisure (H) giving equal satisfaction. They are downward sloping and convex, with slope $MRS_{HY}$ (income given up for one more hour of leisure).
• Budget (wage) line. If the wage rate is $w$ per hour and total time is $T$, the maximum income is $wT$ (no leisure) and the maximum leisure is $T$ (no income). Income earned is $Y = w(T - H)$. The slope of the line is the wage rate $w$.

Equilibrium. Put leisure on the X-axis and income on the Y-axis. The worker reaches maximum satisfaction at the point E where the wage line is tangent to the highest attainable indifference curve:

$MRS_{HY} = w$

Income (Y)
 |\
 | \   .  IC2
 |  \E .
 |   \  . IC1
 |____\______ Leisure (H)
 0  H*  T

At E the worker chooses leisure $H^*$, works $T - H^*$ hours and earns $w(T-H^*)$. At any other point on the wage line, the worker reaches a lower IC. The curves above E are unattainable.

If the wage rises, the substitution effect induces more work (leisure is dearer), while the income effect induces more leisure, which can give a backward-bending labour supply curve.

The innovation theory of profit was propounded by Joseph Schumpeter. According to it, profit is the reward for the entrepreneur's innovations.

Basis. In a static economy under perfect competition, price equals average cost and there is no profit. The entrepreneur, whose function is innovation, creates profit by disturbing this equilibrium.

Types of innovation

1. Introduction of a new product or a new quality
2. Introduction of a new method of production
3. Opening a new market
4. Use of a new source of raw materials
5. A new organisation of an industry (for example, a monopoly)

Working. A successful innovation lowers the cost of production or raises demand, so the innovator earns a surplus over cost. This surplus is profit. When others imitate the innovation, competition lowers price to the new cost level and profit disappears. Profit is therefore a temporary surplus, and the entrepreneur must keep innovating to earn it.

Features. The entrepreneur is an innovator and not the bearer of risk (the capitalist bears it). Profit arises only in a dynamic economy.

Criticism. The theory neglects the risk-bearing and uncertainty functions of the entrepreneur and ignores profit from other sources such as monopoly power. Also, innovation can result in losses if it fails.

Income elasticity of demand is the responsiveness of quantity demanded to a change in consumer income:

$E_Y = \frac{\%\Delta Q}{\%\Delta Y} = \frac{\Delta Q}{\Delta Y}\cdot\frac{Y}{Q}$

Positive income elasticity ($E_Y > 0$) occurs when demand rises as income rises. It is typical of normal goods.

Types of positive income elasticity

1. Income elasticity greater than unity ($E_Y > 1$). Demand rises more than proportionately to income. These are luxury goods, such as cars and jewellery.
2. Income elasticity equal to unity ($E_Y = 1$). Demand rises in the same proportion as income. The share of income spent on the good remains constant.
3. Income elasticity less than unity ($0 < E_Y < 1$). Demand rises less than proportionately to income. These are necessities such as food grains and clothing.

(Zero income elasticity applies to neutral goods like salt, and negative elasticity applies to inferior goods.)