Economics

Price elasticity of demand (PED): It measures the degree of responsiveness of the quantity demanded of a good to a change in its price.

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

It is taken in absolute value because price and quantity move in opposite directions.

Types of price elasticity (five):

1. Perfectly elastic demand ($e_p = \infty$): A negligible change in price causes an infinite change in quantity demanded. The demand curve is a horizontal straight line parallel to the X-axis. (Example: a firm in perfect competition faces this.)

2. Perfectly inelastic demand ($e_p = 0$): Quantity demanded does not change at all when price changes. The demand curve is a vertical line parallel to the Y-axis. (Example: life-saving drugs, salt.)

3. Unitary elastic demand ($e_p = 1$): The percentage change in quantity equals the percentage change in price. The demand curve is a rectangular hyperbola, and total expenditure remains constant.

4. Relatively elastic demand ($e_p > 1$): The proportionate change in quantity is greater than that in price. The demand curve is relatively flat. (Example: luxury goods.) A fall in price raises total revenue.

5. Relatively inelastic demand ($e_p < 1$): The proportionate change in quantity is less than that in price. The demand curve is relatively steep. (Example: necessities such as rice, salt.) A fall in price reduces total revenue.

Diagrams (price on the Y-axis, quantity on the X-axis):

• Perfectly elastic: horizontal line $DD$ at the given price.
• Perfectly inelastic: vertical line $DD$ at the given quantity.
• Unitary: curve $DD$ bowing toward the origin where $P\times Q$ is constant.
• Elastic: flat downward-sloping $DD$, where a small fall $P_1 P_2$ leads to a large rise $Q_1 Q_2$.
• Inelastic: steep downward-sloping $DD$, where a large fall $P_1 P_2$ leads to a small rise $Q_1 Q_2$.

Summary: $e_p = \infty$ (perfectly elastic), $e_p > 1$ (elastic), $e_p = 1$ (unitary), $e_p < 1$ (inelastic), $e_p = 0$ (perfectly inelastic).

Perfect competition

A perfectly competitive market is a market structure in which a very large number of buyers and sellers deal in a homogeneous product, so that no single firm can influence the market price. Its main features are:

• Large number of buyers and sellers, each too small to affect price.
• Homogeneous (identical) product.
• Free entry and exit of firms.
• Perfect knowledge of prices and technology among buyers and sellers.
• Perfect mobility of factors of production.
• No government or collusive interference.

Because of these features the firm is a price taker: its demand curve is a horizontal line at the market price, so $AR = MR = P$.

Price determination (industry level)

The market price is fixed by the interaction of market demand and market supply. At the equilibrium price $P_0$, quantity demanded equals quantity supplied ($Q_d = Q_s$). The firm accepts $P_0$ and adjusts only its output.

Output determination of the firm in the short run

A firm maximises profit where

$MR = MC \quad \text{and } MC \text{ cuts } MR \text{ from below.}$

Since $MR = P$, the condition becomes $P = MC$. In the short run, the number of firms and the plant size are fixed, so three outcomes are possible:

(a) Super-normal profit: if $P > AC$ at equilibrium output $Q_e$, profit $= (P - AC)\times Q_e$.

(b) Normal profit: if $P = AC$ at $Q_e$ (the firm is at the minimum point of AC), $TR = TC$ and the firm just covers all costs.

(c) Loss: if $P < AC$ but $P \ge AVC$, the firm continues production in the short run, because it recovers all variable cost and part of fixed cost. Loss is $(AC - P)\times Q_e$, which is less than the loss from shutting down (total fixed cost).

If $P < AVC$, the firm shuts down. The portion of the MC curve above the minimum AVC is therefore the firm's short-run supply curve.

Thus, in the short run, the price is set by market demand and supply, and each firm produces the output at which $P = MR = MC$.

Given: A: $P=7, Q=500$; C: $P=5, Q=1250$.

Proportional (percentage) method

Formula: $E_d = \dfrac{\Delta Q / Q}{\Delta P / P}$, using the starting point as the base.

A to C: $\Delta Q = 1250-500 = 750$, $\Delta P = 5-7 = -2$

$E_d = \frac{750/500}{-2/7} = \frac{1.5}{-0.2857} = -5.25$

C to A: $\Delta Q = 500-1250 = -750$, $\Delta P = 7-5 = 2$

$E_d = \frac{-750/1250}{2/5} = \frac{-0.6}{0.4} = -1.5$

So $|E_d| = 5.25$ for A to C and $1.5$ for C to A. The value differs with the direction of movement because the base differs.

Arc (midpoint) method

$E_d = \frac{\Delta Q}{\Delta P}\times\frac{(P_1+P_2)/2}{(Q_1+Q_2)/2}$

Average price $= (7+5)/2 = 6$; average quantity $= (500+1250)/2 = 875$.

$E_d = \frac{750}{-2}\times\frac{6}{875} = -375\times 0.006857 = -2.57$

The arc elasticity is $|E_d| = 2.57$ for both A to C and C to A, so demand is elastic ($>1$) and the result is the same in either direction.

Perfect competition

A perfectly competitive market has a very large number of buyers and sellers dealing in a homogeneous product, with free entry and exit, perfect knowledge and perfect mobility of factors. No single firm can affect the price, so the firm is a price taker and faces a horizontal demand curve: $P = AR = MR$.

Price determination

Price is determined at the industry level by the intersection of market demand and market supply at $(P_0, Q_0)$. Every firm accepts this price.

Output determination

A firm maximises profit at the output where $MR = MC$ and MC is rising. Because $MR = P$, the condition is $P = MC$.

Short run: the firm's plant is fixed and the number of firms is fixed. Depending on the relation of price to average cost:

• $P > AC$: super-normal profit of $(P-AC)\times Q$.
• $P = AC$: normal profit only.
• $AVC \le P < AC$: loss, but the firm continues production since it covers variable cost.
• $P < AVC$: the firm shuts down.

Long run: super-normal profits attract new firms, which shifts industry supply right and lowers price. Losses cause exit, which raises price. Entry and exit continue until each firm earns only normal profit:

$P = MR = MC = AR = AC \text{ (minimum point)}$

Each firm then produces at the minimum point of its long-run average cost curve, so there is both productive and allocative efficiency.

Definition

Income elasticity of demand ($E_Y$) measures the responsiveness of quantity demanded to a change in consumer income, other factors remaining constant.

$E_Y = \frac{\%\ \text{change in quantity demanded}}{\%\ \text{change in income}} = \frac{\Delta Q}{\Delta Y}\times\frac{Y}{Q}$

Types

1. Positive income elasticity ($E_Y > 0$, normal goods). Demand rises as income rises. It has three sub-types:

• Greater than unity ($E_Y > 1$): demand rises by a larger proportion than income (luxuries such as cars). The Engel curve is flatter than the 45-degree line from the origin when income is on the Y-axis.
• Equal to unity ($E_Y = 1$): demand rises in the same proportion as income. The demand-income curve is a straight line from the origin.
• Less than unity ($0 < E_Y < 1$): demand rises by a smaller proportion than income (necessities such as food).

2. Zero income elasticity ($E_Y = 0$). Demand does not change as income changes (for example salt or matches). The curve is vertical.

3. Negative income elasticity ($E_Y < 0$, inferior goods). Demand falls as income rises (for example coarse grain). The curve bends backward (slopes downward).

Diagram (description)

Draw quantity demanded on the X-axis and income on the Y-axis. Curves: (a) $E_Y>1$ - rising curve with a flatter slope relative to the quantity axis; (b) $E_Y=1$ - straight line through the origin; (c) $E_Y<1$ - steeper line; (d) $E_Y=0$ - vertical line; (e) $E_Y<0$ - backward-sloping line.

Data: A (6, 0), B (5, 1000), C (4, 2000), D (3, 3000).

(a) Proportional method, $E_d = \dfrac{\Delta Q/Q}{\Delta P/P}$

B to D: $\Delta Q = 3000-1000 = 2000$, $\Delta P = 3-5 = -2$

$E_d = \frac{2000/1000}{-2/5} = \frac{2}{-0.4} = -5$

D to B: $\Delta Q = 1000-3000 = -2000$, $\Delta P = 5-3 = 2$

$E_d = \frac{-2000/3000}{2/3} = \frac{-0.667}{0.667} = -1$

So $|E_d| = 5$ for B to D and $1$ for D to B.

(b) Arc method between A and C

$P_1 = 6, Q_1 = 0$; $P_2 = 4, Q_2 = 2000$.

Average price $= 5$; average quantity $= 1000$.

$E_d = \frac{\Delta Q}{\Delta P}\times\frac{\bar P}{\bar Q} = \frac{2000}{-2}\times\frac{5}{1000} = -5$

The arc elasticity is $|E_d| = 5$ for both A to C and C to A, so demand is elastic.

Indifference curve (IC): An indifference curve is a curve showing all combinations of two goods that give the consumer the same level of satisfaction. Since every point yields equal utility, the consumer is indifferent among them. An indifference map is a set of ICs; a higher IC represents a higher level of satisfaction.

Example schedule: (1 X, 12 Y), (2 X, 8 Y), (3 X, 5 Y), (4 X, 3 Y) all give the same satisfaction.

Consumer's equilibrium (ordinal approach): The ordinal approach assumes utility cannot be measured in numbers but can be ranked. Assumptions: the consumer is rational and wants to maximise satisfaction; prefers more to less; the two goods X and Y have diminishing marginal rate of substitution (MRS); income and prices are given and constant; ICs are convex to the origin.

The consumer's budget line is $P_x X + P_y Y = M$ with slope $-P_x/P_y$. The budget line shows all combinations that can be bought with income $M$.

The consumer reaches equilibrium at the point where the budget line is tangent to the highest attainable IC (point E). At this point:

1. The slope of the IC equals the slope of the budget line: $MRS_{xy} = \frac{MU_x}{MU_y} = \frac{P_x}{P_y}$
2. The IC is convex to the origin at E (second-order condition: MRS diminishing).

Explanation: Suppose the budget line cuts IC$_1$ at points A and B. At these points $MRS \neq P_x/P_y$, so the consumer can move along the budget line to reach a higher IC (e.g. IC$_2$). Moving to the IC above IC$_2$ (IC$_3$) is impossible because it lies beyond the budget line. Only at the tangency point E, on IC$_2$, is satisfaction maximised given income. At E, the consumer's subjective willingness to trade (MRS) equals the market rate of exchange ($P_x/P_y$), so no further gain is possible.

Thus the consumer buys $OX_1$ of X and $OY_1$ of Y, the equilibrium bundle.

National income: National income is the total money value of all final goods and services produced by the residents of a country in one year, plus net factor income from abroad. Strictly, national income is the total of factor incomes earned (wages, rent, interest, profit) by a country's factors of production in a year, i.e. $NNP$ at factor cost.

Difficulties of measuring national income in developing countries like Nepal:

1. Large non-monetary (subsistence) sector: A large share of agricultural output is consumed by farmers themselves or bartered and is not sold in markets, so valuation and inclusion are difficult.
2. Lack of reliable data and statistics: Poor record keeping, scattered production and the absence of accounts among small producers and farmers make data collection inaccurate.
3. Illiteracy: Many producers cannot give correct information about output, income and expenditure.
4. Unorganised sector and informal activities: Small shops, street vendors, home-based production and cottage industries lack records.
5. Underground and illegal activities: Black-market trade, smuggling and unreported income are not captured.
6. Remittance and foreign income: In Nepal, large flows of remittance and informal (hundi) transfers are difficult to measure.
7. Occupational specialisation is poor: Many people do multiple jobs (farming, trading, labour), making classification and double counting a problem.
8. Unpaid household and family services: Work by family members, such as household chores and unpaid labour on family farms, is excluded.
9. Double counting: Lack of clear separation between intermediate and final goods leads to double counting.
10. Price instability and inflation: Changing prices make comparison and valuation difficult, and administrative capacity for surveys is limited.

Because of these problems, the national income estimates of developing countries are only approximate.

Features of monopoly:

1. Single seller: One firm is the sole producer, so the firm is the industry.
2. No close substitutes: The product has no close substitute.
3. Barriers to entry: Legal (patents, licences), economic or natural barriers prevent new firms from entering.
4. Price maker: The firm controls price (or quantity) and faces a downward-sloping demand curve, so $AR > MR$.
5. Possibility of price discrimination: The monopolist can charge different prices to different buyers.
6. Abnormal profit possible even in the long run.

(The question says "monopolistic market", but the features and equilibrium asked are those of monopoly.)

Equilibrium of a monopoly firm: The firm maximises profit where

1. $MR = MC$, and
2. the MC curve cuts the MR curve from below.

Since the demand (AR) curve slopes downward, MR lies below AR. The price is read from the AR curve at the equilibrium output.

Short-run equilibrium: The firm has fixed capacity and faces SAC and SMC curves. At output $Q_0$ where $SMC = MR$, price is $P_0$ on the demand curve.

• Profit per unit $= P_0 - SAC$; total profit $= (P_0 - SAC) \times Q_0$. If $AR > SAC$, the firm earns abnormal profit.
• If $AR = SAC$, the firm earns only normal profit.
• If $AR < SAC$ (but $AR \geq AVC$), the firm incurs a loss but continues in the short run as long as it covers AVC.

Long-run equilibrium: All factors are variable, the firm can adjust plant size, and entry is blocked. The firm produces where $LMC = MR = SMC$ and the SAC curve is tangent to the LAC curve at that output. The monopolist adjusts the plant to the optimal size for that output, so $P > LAC$ and it continues to earn abnormal profit in the long run $= (P - LAC) \times Q$. A monopolist may produce at less than the minimum LAC (excess capacity), unlike perfect competition. If the firm cannot cover LAC, it will shut down in the long run.

An expansionary (easy) monetary policy aims to increase money supply and credit, lower interest rates and stimulate investment and employment, usually during recession or unemployment. The central bank (Nepal Rastra Bank) uses these quantitative (general) instruments:

1. Bank rate / policy rate cut: Lowering the rate at which the central bank lends to commercial banks reduces their borrowing cost, so they cut lending rates and credit expands.
2. Open market operations: The central bank buys government securities from banks and the public, injecting cash into banks and raising their lending capacity.
3. Reducing the cash reserve ratio (CRR): Banks must keep less cash with the central bank, so they have more funds to lend and credit expands through the money multiplier.
4. Reducing the statutory liquidity ratio (SLR): Banks can hold fewer liquid assets and lend more.
5. Repo and reverse-repo operations: Lowering the repo rate and injecting liquidity encourages banks to lend more.

Together these increase money supply, reduce interest rates, increase investment and consumption, and raise output and employment.

Demand: $P = 12 - 0.4Q$ and cost: $C = 5 + 4Q + 0.6Q^2$. This is the monopoly (single-firm) profit-maximising problem, so equilibrium requires $MR = MC$.

$TR = P \cdot Q = 12Q - 0.4Q^2 \Rightarrow MR = 12 - 0.8Q$ $MC = \frac{dC}{dQ} = 4 + 1.2Q$

Setting $MR = MC$: $12 - 0.8Q = 4 + 1.2Q \Rightarrow 8 = 2Q \Rightarrow Q = 4$

Price: $P = 12 - 0.4(4) = 12 - 1.6 = 10.4$

Total revenue: $TR = 10.4 \times 4 = 41.6$

Total cost: $TC = 5 + 4(4) + 0.6(16) = 5 + 16 + 9.6 = 30.6$

Total profit: $\pi = TR - TC = 41.6 - 30.6 = 11$

Second-order check: slope of MC ($1.2$) exceeds slope of MR ($-0.8$), so profit is maximised.

Equilibrium price = 10.4, quantity = 4, TR = 41.6, TC = 30.6, profit = 11.

Using the expenditure approach (Rs in crores):

$GDP_{MP} = C + G + I + NX$

where $I$ = gross fixed capital formation + net change in stock $= 200 + 26 = 226$.

$GDP_{MP} = 500 + 150 + 226 + (-14) = 862$

$GNP_{MP} = GDP_{MP} + \text{Net factor income from abroad} = 862 + 50 = 912$

$NNP_{MP} = GNP_{MP} - \text{Capital consumption allowance} = 912 - 80 = 832$

(For reference, $NNP_{FC} = NNP_{MP} - \text{Net indirect taxes} = 832 - 94 = 738$.)

GDP at market price = Rs 862 crores, GNP at market price = Rs 912 crores, NNP (at market price) = Rs 832 crores (Rs 738 crores at factor cost).

Economics is defined as the study of how individuals and society choose to use scarce resources to satisfy unlimited wants. Scarcity and choice are indeed its central issues.

Scarcity: Human wants are unlimited and keep growing, but resources (land, labour, capital, time) are limited and have alternative uses. This gap between unlimited wants and limited means is the problem of scarcity. If resources were unlimited, there would be no economic problem and no need to economise, and goods would be free.

Choice: Because of scarcity, every individual, firm and government must choose what to produce, how to produce and for whom to produce, and which wants to satisfy first. Choosing one alternative means giving up another, so every choice involves an opportunity cost. The production possibility curve shows this: producing more of one good requires giving up some of the other.

Linkage: Scarcity forces choice, choice involves opportunity cost, and the study of rational choice under scarcity is the subject matter of economics. Consumers choose goods to maximise utility, producers choose inputs to minimise cost and maximise profit, and governments allocate budgets among competing needs. Hence, the statement is justified.

The quantity of a good demanded depends on many factors, called the determinants of demand: $Q_d = f(P_x, P_r, Y, T, N, E, \dots)$.

1. Price of the good itself: By the law of demand, a fall in price raises quantity demanded and vice versa (movement along the curve).
2. Prices of related goods: For substitutes (tea and coffee), a rise in the price of one raises demand for the other. For complements (car and petrol), a rise in the price of one lowers demand for the other.
3. Income of the consumer: For normal goods, demand rises with income; for inferior goods, demand falls as income rises.
4. Tastes, preferences and fashion: A favourable change in taste increases demand.
5. Population size and composition: More population raises market demand; age and sex structure also matter.
6. Distribution of income: Equal distribution generally raises demand for necessities and mass goods.
7. Expectations about future prices and income: If prices are expected to rise, current demand increases.
8. Advertisement and sales promotion, credit availability, weather and season, and government policy (taxes, subsidies) also influence demand.

Changes in these factors shift the demand curve (increase or decrease in demand).

Percentage method: $e_d = \frac{\%\Delta Q}{\%\Delta P} = \frac{\Delta Q / Q}{\Delta P / P}$ using the initial price and quantity as the base.

Price falls from 40 to 20 (Q: 10 to 20): $\%\Delta Q = \frac{20-10}{10}\times 100 = 100\%, \qquad \%\Delta P = \frac{20-40}{40}\times 100 = -50\%$ $|e_d| = \frac{100}{50} = 2$

Price rises from 20 to 40 (Q: 20 to 10): $\%\Delta Q = \frac{10-20}{20}\times 100 = -50\%, \qquad \%\Delta P = \frac{40-20}{20}\times 100 = 100\%$ $|e_d| = \frac{50}{100} = 0.5$

Comparison: For the same price range, the elasticity is 2 (elastic) when price falls from 40 to 20, but 0.5 (inelastic) when price rises from 20 to 40. The percentage method gives different values depending on the direction of change, because the base (starting point) differs. This is a limitation of the method; the arc (mid-point) method removes it and gives the same value in both directions.

Returns to scale describes how output changes when all inputs are increased in the same proportion in the long run (no input is fixed). Three stages are observed:

1. Increasing returns to scale: Output increases by a larger proportion than inputs. If inputs double, output more than doubles. Causes: division of labour and specialisation, use of better machinery, managerial efficiency, and bulk-buying economies.
2. Constant returns to scale: Output increases in the same proportion as inputs (doubling inputs doubles output). It occurs when the economies of scale are just balanced by diseconomies.
3. Decreasing returns to scale: Output increases by a smaller proportion than inputs. Causes: managerial difficulties of coordination and control, labour problems and technical limits to expansion.

Example:

Graphically, using isoquants, the isoquants for equal output increments are spaced closer together under increasing returns, equidistant under constant returns, and farther apart under decreasing returns along the expansion path. The law explains the shape of the long-run average cost curve (U-shaped).

Marginal rate of substitution (MRS): MRS of X for Y is the amount of good Y that a consumer is willing to give up to obtain one more unit of good X while remaining on the same indifference curve (same satisfaction).

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

It is the slope of the indifference curve at a point.

Diminishing MRS: As the consumer gets more of X and less of Y, the amount of Y he is willing to sacrifice for each additional unit of X decreases. This is why ICs are convex to the origin.

Reasons:

1. Diminishing marginal utility: As more X is consumed, the marginal utility of X falls, while as Y decreases its marginal utility rises. So the consumer will give up less and less Y for one more X.
2. Imperfect substitutability: Goods are not perfect substitutes; as the stock of Y falls, it becomes scarcer and more valuable relative to X.
3. Rational behaviour: The relative preference for the good in scarce supply grows.

If MRS were constant, the IC would be a straight line (perfect substitutes); with increasing MRS it would be concave.

With TFC $= 100$:

$TC = TFC + TVC$, $AFC = TFC/Q$, $AVC = TVC/Q$, $AC = TC/Q$, $MC = \Delta TC/\Delta Q = \Delta TVC/\Delta Q$.

Indifference curve (IC): An indifference curve is the locus of all combinations of two goods that give the consumer equal satisfaction. The consumer is indifferent among all points on the curve. A set of ICs is called an indifference map; a higher IC shows a higher level of satisfaction.

Example: combinations A (1X, 12Y), B (2X, 8Y), C (3X, 5Y), D (4X, 3Y) lie on one IC.

Properties of indifference curves:

1. Downward sloping (negative slope): To keep satisfaction constant, if the quantity of one good rises, the other must fall. An upward-sloping IC would mean more of both goods give the same satisfaction, which is irrational.
2. Convex to the origin: Due to the diminishing marginal rate of substitution ($MRS_{xy} = MU_x/MU_y$), the consumer sacrifices less and less of Y for each extra unit of X, so the IC bends toward the origin.
3. Two ICs never intersect: At the point of intersection, two different levels of satisfaction would be equal, which violates the assumptions of transitivity and non-satiation.
4. Higher IC shows higher satisfaction: A curve farther from the origin contains more of at least one good (assuming monotonic preferences).
5. ICs do not touch the axes: A consumer is assumed to buy some of both goods; touching an axis would imply consuming only one good.
6. ICs are not necessarily parallel: Their slopes at corresponding points may differ.

These properties rest on the assumptions of rational consumers, non-satiation, transitivity of preference and diminishing MRS.

Scarcity means that human wants are unlimited, while the resources (land, labour, capital, enterprise) available to satisfy them are limited. Because resources have alternative uses, not all wants can be satisfied. Scarcity is the basic economic problem and exists in rich and poor countries alike.

Choice is the necessary result of scarcity. Since all wants cannot be met, individuals, firms and governments must decide which wants to satisfy first and which to give up. Every choice involves an opportunity cost, the value of the next best alternative forgone.

Scarcity therefore forces choice, and choice creates opportunity cost. Society must answer the questions of what to produce, how to produce and for whom to produce. This is the central subject matter of economics.

(a) TFC is the total cost at zero output, so $TFC = 300$ at all levels. $TVC = TC - TFC$, $AFC = TFC/Q$, $AVC = TVC/Q$, $AC = TC/Q$, $MC = \Delta TC$.

(b) Graph and relationship

Plot output on the X-axis and cost on the Y-axis. Both AC and MC are U-shaped. MC falls to its minimum at 3 units (18), then rises steeply and cuts the AC curve from below at its minimum point.

Relationship between AC and MC:

• When $MC < AC$ (output 1 to 4), AC falls.
• When $MC > AC$ (output 7 to 9), AC rises.
• When $MC = AC$ (about 5 to 6 units, where $AC = 90$), AC is at its minimum.

This is because the average is pulled down by a lower marginal value and pushed up by a higher marginal value. MC always cuts AC at the minimum point of AC.

Given: $M = 2000$, $P_x = 400$, $P_y = 200$.

(a) Budget line

$P_x X + P_y Y = M \;\Rightarrow\; 400X + 200Y = 2000 \;\Rightarrow\; 2X + Y = 10$

$Y = 10 - 2X$

Intercepts: if all income is spent on X, $X = 2000/400 = 5$ units; if all on Y, $Y = 2000/200 = 10$ units. The budget line joins $(5, 0)$ and $(0, 10)$, and its slope is $-P_x/P_y = -2$.

(b) Equilibrium with equal expenditure

Half the budget goes to each good: Rs 1000 on X and Rs 1000 on Y.

$X = \frac{1000}{400} = 2.5 \text{ units}, \qquad Y = \frac{1000}{200} = 5 \text{ units}$

Check: $400(2.5) + 200(5) = 1000 + 1000 = 2000$, so the point $(2.5, 5)$ lies on the budget line and exhausts income.

The consumer is in equilibrium at $(2.5, 5)$ where the highest attainable indifference curve is tangent to the budget line, so that

$MRS_{xy} = \frac{MU_x}{MU_y} = \frac{P_x}{P_y} = 2$

(This holds if his preferences are such that this bundle is optimal; the point is the midpoint of the budget line.)

Governments intervene in markets to protect consumers or producers, to raise revenue, or to correct market outcomes.

1. Price ceiling

A maximum legal price set below the equilibrium price, to protect consumers (for example rent control or price caps on essential goods). At the ceiling, quantity demanded exceeds quantity supplied, which creates shortages, queues, black markets and rationing.

2. Price floor

A minimum legal price set above the equilibrium price, to protect producers (for example minimum support price for farm products, or the minimum wage). At the floor, quantity supplied exceeds quantity demanded, which creates surplus or unemployment. The government may need to buy the surplus.

3. Tax effect

A per-unit tax on a good shifts the supply curve upward (to the left) by the amount of the tax. The result is a higher price paid by buyers, a lower price received by sellers, and a lower equilibrium quantity. The burden of the tax is shared between buyers and sellers, depending on the elasticities of demand and supply: the less elastic side bears more of the tax. The government earns revenue equal to tax per unit times the new quantity, but there is a deadweight loss.

Monetary policy is the control of money supply and credit by the central bank (Nepal Rastra Bank) to achieve economic goals. Its instruments are:

Quantitative (general) instruments

1. Bank rate: the rate at which the central bank lends to commercial banks. A higher rate makes borrowing dearer and reduces credit.
2. Open market operations: buying or selling government securities. Selling securities absorbs money; buying injects money.
3. Cash reserve ratio (CRR): the share of deposits banks must keep with the central bank. Raising it reduces lending capacity.
4. Statutory liquidity ratio (SLR): the share of deposits banks must hold in liquid assets.
5. Repo and reverse repo, standing liquidity facility: short-term lending and deposit windows that steer interest rates.

Qualitative (selective) instruments

6. Credit rationing and margin requirements: limits on credit for particular sectors or purposes.
7. Moral suasion and direct action: persuading or directing banks to follow the policy.
8. Directives on sectoral lending, for example priority-sector lending.

When a firm uses two variable inputs (say labour $L$ and capital $K$) to produce a given output, it must choose the combination that gives least cost, or maximum output for a given cost.

Condition (least-cost combination)

$\frac{MP_L}{P_L} = \frac{MP_K}{P_K}$

or equivalently $MRTS_{LK} = \dfrac{MP_L}{MP_K} = \dfrac{P_L}{P_K}$, where $P_L$ and $P_K$ are the wage rate and the price of capital.

Explanation: the slope of the isoquant (MRTS) must equal the slope of the isocost line ($P_L/P_K$). At the tangency point the last rupee spent on each input adds the same amount to output.

• If $MP_L/P_L > MP_K/P_K$, the firm should use more labour and less capital.
• If $MP_L/P_L < MP_K/P_K$, it should use more capital and less labour.

Second-order condition: the isoquant must be convex to the origin at the point of tangency (MRTS diminishing). In the diagram, the isocost line is tangent to the highest feasible isoquant at point $E$, which gives the optimum input combination $(L^*, K^*)$.

A free market (capitalist) economy is one in which economic decisions are made by individuals and firms through the price mechanism with little or no government interference. Its features are:

1. Private ownership: individuals own land, capital and other resources and can use them freely.
2. Freedom of enterprise and choice: producers choose what and how to produce, and consumers choose what to consume.
3. Price mechanism: prices determined by demand and supply allocate resources and coordinate decisions.
4. Profit motive: the main incentive for production is private profit.
5. Competition: firms compete for customers, which promotes efficiency.
6. Consumer sovereignty: consumer demand determines what is produced.
7. Limited role of government: the state protects property rights, law and order, and enforces contracts.
8. Inequality: income and wealth tend to be unevenly distributed.

Expenditure approach (Rs in millions).

Gross investment $I$ = gross private domestic fixed investment + change in inventories $= 950 + 100 = 1050$

Net exports $= X - M = 900 - 1200 = -300$

$GDP_{MP} = C + I + G + (X-M) = 6500 + 1050 + 2500 - 300 = 9750$

GDP = Rs 9750 million

Now move to national income:

$GNP = GDP + \text{net factor income from abroad} = 9750 + (-100) = 9650$

$NNP_{MP} = GNP - \text{depreciation} = 9650 - 200 = 9450$

$NI = NNP_{FC} = NNP_{MP} - \text{indirect taxes less subsidies} = 9450 - 150 = 9300$

National income = Rs 9300 million

(Foreign investment of 250 is a capital-account item and is not part of the calculation.)

Definition

Elasticity of supply ($E_s$) measures the responsiveness of quantity supplied to a change in the price of the good.

$E_s = \frac{\%\ \text{change in quantity supplied}}{\%\ \text{change in price}} = \frac{\Delta Q_s}{\Delta P}\times\frac{P}{Q_s}$

Because supply is upward sloping, $E_s$ is normally positive.

Types

1. Perfectly elastic supply ($E_s = \infty$): the supply curve is horizontal. Producers will supply any quantity at one price, but nothing at a lower price.

2. Elastic supply ($E_s > 1$): quantity supplied changes by a larger proportion than price. The supply curve is flatter and, if extended, meets the Y-axis (price axis) at a positive intercept.

3. Unitary elastic supply ($E_s = 1$): quantity changes in the same proportion as price. The supply curve is a straight line through the origin.

4. Inelastic supply ($E_s < 1$): quantity changes by a smaller proportion than price. The supply curve is steep and, if extended, meets the X-axis (quantity axis).

5. Perfectly inelastic supply ($E_s = 0$): the supply curve is vertical. Quantity is fixed whatever the price (for example land, or a perishable good on the market day).

Diagram (description)

Draw five panels with price (P) on the Y-axis and quantity (Q) on the X-axis: a horizontal line (infinite), a flat upward line cutting the P-axis (elastic), a line from the origin (unitary), a steep line cutting the Q-axis (inelastic) and a vertical line (zero).

Determinants

Time period, availability of inputs, nature of the product (perishable or durable), production technology, spare capacity and ease of storage.

Production function

A production function is the technical relationship between the physical quantity of inputs used and the maximum quantity of output obtainable, given the state of technology.

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

where $Q$ is output, $L$ is labour and $K$ is capital.

Cobb-Douglas production function

Proposed by C. W. Cobb and P. H. Douglas, it takes the form

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

where $A$ is a constant (efficiency or technology parameter), and $\alpha$ and $\beta$ are the output elasticities of labour and capital.

Features

1. Output elasticities are constant: $\alpha$ is the percentage change in output for a 1% change in labour, and $\beta$ the same for capital.
2. Returns to scale are measured by $\alpha + \beta$:
   • $\alpha+\beta = 1$: constant returns to scale (the original Cobb-Douglas form);
   • $\alpha+\beta > 1$: increasing returns;
   • $\alpha+\beta < 1$: decreasing returns.
3. Marginal products: $MP_L = \alpha Q/L$ and $MP_K = \beta Q/K$; both are positive and diminish as the input rises, assuming $\alpha, \beta < 1$.
4. Factor shares: under constant returns and competitive pricing, $\alpha$ is the share of labour and $\beta$ the share of capital in total output.
5. Elasticity of substitution is unity: the isoquants are smooth and convex to the origin and never touch the axes.
6. Homogeneous of degree $\alpha+\beta$: multiplying both inputs by $\lambda$ multiplies output by $\lambda^{\alpha+\beta}$.
7. Linear in logarithms: $\ln Q = \ln A + \alpha\ln L + \beta\ln K$, which makes estimation by regression easy.
8. Both inputs are essential: if either $L$ or $K$ is zero, output is zero.

Limitations: it assumes a constant elasticity of substitution equal to one and a constant share of each factor, which may not hold in practice.

A mixed economy combines features of capitalism and socialism: the private sector and the public sector operate side by side. Nepal is an example. Its features are:

1. Co-existence of public and private sectors: the government owns key industries and utilities, while private individuals own other enterprises.
2. Cooperative sector: along with the public and private sectors, cooperatives play a role (as recognised in the Constitution of Nepal).
3. Economic planning: the state sets national plans and priorities, while private enterprise works within them.
4. Price mechanism with regulation: most prices are market determined, but the government regulates or fixes prices of essential goods.
5. Private property with limits: private property is protected, but regulated for public interest.
6. Social welfare: the state provides education, health and social security and works to reduce inequality.
7. Role of government: it corrects market failure through taxes, subsidies and regulation.
8. Freedom of choice for consumers and producers, with state supervision.

Scarcity is the situation in which human wants are unlimited but resources to satisfy them are limited and have alternative uses. It is the root of all economic problems.

Choice arises because resources are scarce: since everything cannot be produced or consumed, a decision must be made among competing alternatives.

Role in decision making

• Opportunity cost: every choice means giving up the next best option. For example, using Rs 1000 for books means forgoing other goods worth Rs 1000.
• Consumers must allocate limited income among goods to maximise satisfaction.
• Producers must allocate scarce inputs to maximise profit.
• Government must allocate a limited budget among competing needs such as health, education and defence.
• Society must decide what to produce, how to produce and for whom to produce.

So, scarcity forces choice and choice involves opportunity cost; rational decision making weighs the benefits of an option against its opportunity cost.

Given: B: income 2, demand 160; C: income 4, demand 120.

(i) Proportional method

$E_Y = \frac{\Delta Q/Q}{\Delta Y/Y}$

B to C: $\Delta Q = 120-160 = -40$, $\Delta Y = 4-2 = 2$

$E_Y = \frac{-40/160}{2/2} = \frac{-0.25}{1} = -0.25$

C to B: $\Delta Q = +40$, $\Delta Y = -2$

$E_Y = \frac{40/120}{-2/4} = \frac{0.333}{-0.5} = -0.67$

(ii) Midpoint (arc) method

Average income $=(2+4)/2 = 3$; average quantity $=(160+120)/2 = 140$.

$E_Y = \frac{\Delta Q}{\Delta Y}\times\frac{\bar Y}{\bar Q} = \frac{-40}{2}\times\frac{3}{140} = -0.43$

This is the same for B to C and C to B.

Interpretation: $E_Y$ is negative in every case, so the good is an inferior good (demand falls as income rises).

Price consumption curve

The price consumption curve (PCC) is the locus of equilibrium points of a consumer when the price of one good (say X) changes, while the consumer's income, the price of the other good and tastes remain constant. It shows how the optimum bundle changes as the price changes.

PCC for a Giffen good

A Giffen good is a strongly inferior good whose negative income effect is larger than its substitution effect, so a fall in its price reduces the quantity demanded.

Derivation: Place good X (Giffen good) on the X-axis and all other goods on the Y-axis.

1. Initially the budget line is $MN_1$ and the consumer is in equilibrium at $E_1$ on indifference curve $IC_1$, buying $X_1$.
2. When the price of X falls, the budget line pivots outward to $MN_2$, and the consumer reaches equilibrium $E_2$ on a higher curve $IC_2$.
3. For the Giffen good the substitution effect increases X, but the negative income effect (the consumer now feels richer and cuts consumption of this inferior good) is larger. Net result: $X_2 < X_1$.
4. A further price fall to $MN_3$ gives $E_3$ with still less X.

Joining $E_1, E_2, E_3$ gives the PCC, which is backward bending (sloping upward-left) instead of the normal outward slope. The resulting demand curve, with price on the Y-axis, is upward sloping, which violates the law of demand.

(a) $TFC = 120$. $TC = TFC + TVC$; $AFC = TFC/Q$; $AVC = TVC/Q$; $ATC = TC/Q$.

(b) Graph

Plot output on the X-axis and cost per unit on the Y-axis.

• AFC is a rectangular hyperbola that falls continuously (120 down to 17.14) and never touches either axis.
• AVC is U-shaped: it falls to a minimum of 35 at 4 to 5 units and then rises.
• ATC is also U-shaped, with its minimum (about 58.33) at 6 units. It lies above AVC, and the vertical gap between them is AFC, which shrinks as output rises, so ATC approaches AVC but never meets it.

An indifference curve shows all combinations of two goods that give the consumer equal satisfaction. Its properties are:

1. Slopes downward from left to right: to keep satisfaction constant, more of one good requires less of the other.
2. Convex to the origin: because the marginal rate of substitution (MRS) diminishes, the consumer gives up less and less of Y for each extra unit of X.
3. Two indifference curves never intersect: an intersection would imply that two different levels of satisfaction are equal, which is a contradiction.
4. Higher curves represent higher satisfaction: a curve further from the origin has more of at least one good (assuming non-satiation).
5. Does not touch either axis: the consumer is assumed to consume both goods.
6. Not necessarily parallel: the curves in a map need not be parallel to each other.
7. Ordinal: the curves show only the rank order of satisfaction, not its amount.

Under monopoly the firm is the only seller, so it faces the downward-sloping market demand curve. To sell more, it must lower the price on all units. Hence $AR = P$ is falling, and MR falls faster than AR and lies below it.

Numerical example

where $TR = P\times Q$ and $MR = \Delta TR/\Delta Q$.

Figure: with output on the X-axis and revenue on the Y-axis, both AR and MR slope downward. For a straight-line demand curve, MR has the same intercept on the price axis but is twice as steep, so it cuts the X-axis at half the distance of AR:

$AR = a - bQ,\qquad MR = a - 2bQ$

Relationships

• $MR < AR$ at every output.
• When MR is positive, TR rises and demand is elastic ($e>1$); when $MR=0$, TR is maximum ($e=1$); when MR is negative, TR falls ($e<1$).
• MR can become negative, while AR is always positive.
• The relationship $MR = AR\left(1 - \dfrac{1}{e}\right)$ holds.

Fiscal policy is the use of government spending and taxation to influence the economy.

Through the multiplier, a change in spending or taxes changes national income by more than the initial change.

All values in Rs million.

Step 1: GDP at market price (expenditure approach)

Gross investment $=$ gross fixed capital formation + change in stock $= 300 + 50 = 350$

$GDP_{MP} = C + I + G + NX = 900 + 350 + 150 + (-50) = 1350$

Step 2: GNP at market price

$GNP_{MP} = 1350 + 50 = 1400$

Step 3: NNP at market price

$NNP_{MP} = 1400 - 50 = 1350$

Step 4: National income (NNP at factor cost)

Net indirect taxes $= 250 - 50 = 200$

$NI = 1350 - 200 = 1150$

National income = Rs 1150 million

Indifference curve

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 the points on it. A set of ICs is an indifference map.

The slope at any point is the marginal rate of substitution:

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

Properties

1. Downward sloping (negative slope): more of one good must be offset by less of the other to keep utility constant.
2. Convex to the origin: MRS diminishes as the consumer substitutes X for Y, because the more of X he has, the less Y he is willing to give up for another unit.
3. Higher IC means higher satisfaction: bundles on a curve farther from the origin contain more goods (monotonicity).
4. ICs never intersect: if two curves crossed at point A, with B on one and C on the other, then $B \sim A \sim C$ would imply $B \sim C$, though one of them has more goods; this contradicts the assumption.
5. ICs do not touch the axes: the consumer is assumed to buy some of both goods.
6. ICs are ordinal: they rank bundles but do not measure the amount of satisfaction.
7. Two ICs need not be parallel, as MRS can differ at the same quantities on different curves.

Exceptions: for perfect substitutes the IC is a straight line; for perfect complements it is L-shaped.

Monopoly

A monopoly is a market structure with a single seller of a product that has no close substitutes, and with barriers to entry (legal rights, ownership of a key resource, patent, economies of scale). The monopolist is a price maker, and the firm is the industry.

Because the firm faces the downward-sloping market demand curve, $AR = P$ falls with output and $MR < AR$.

Price and output determination

The monopolist maximises profit where

1. $MR = MC$ (first-order condition), and
2. MC cuts MR from below (second-order condition).

Steps in the diagram (price and cost on Y, output on X):

• The MC curve cuts the MR curve at point $E$, which determines the equilibrium output $Q_m$.
• Going up to the AR (demand) curve at $Q_m$ gives the price $P_m$ the monopolist charges. Note $P_m > MC$.
• Average cost at $Q_m$ is read from the AC curve.

Profit

$\text{Profit} = (P_m - AC)\times Q_m$

Short run: the monopolist may earn super-normal profit ($P>AC$), normal profit ($P=AC$) or a loss ($P<AC$); it continues only if $P \ge AVC$.

Long run: barriers to entry mean super-normal profit can persist, since no new firms can enter.

Result

The monopoly output is lower and the price higher than under perfect competition, resulting in a deadweight loss and allocative inefficiency.

The production possibility curve (PPC), also called the production possibility frontier or transformation curve, shows the different maximum combinations of two goods that an economy can produce with its given resources and technology, when all resources are fully and efficiently employed.

Illustration: an economy produces wheat and cloth. By shifting resources, it can have combinations such as A (0 cloth, 100 wheat), B (10, 90), C (20, 70), D (30, 40), E (40, 0).

Points on the diagram

• Points on the curve: efficient, full employment of resources.
• Points inside the curve: unemployment or inefficiency.
• Points outside the curve: unattainable with current resources.

Shape: it is usually concave to the origin because of increasing opportunity cost: as more of one good is produced, resources less suited to it must be transferred, so more of the other good is given up for each extra unit. The slope is the marginal rate of transformation (MRT).

Shifts: growth of resources or better technology shifts the curve outward (economic growth); a fall in resources shifts it inward.

Uses: it illustrates scarcity, choice, opportunity cost and efficiency.

A mixed economy combines elements of capitalism and socialism, with both the private and public sectors playing a role. Its features:

1. Dual ownership: public ownership of key industries and utilities, and private ownership of other enterprises; the cooperative sector also operates.
2. Economic planning: the government prepares plans to guide development, within which private firms operate.
3. Role of the price mechanism: market forces determine most prices and resource allocation, with state regulation.
4. Economic freedom with control: people have freedom of occupation, consumption and enterprise, but within legal limits.
5. Social welfare orientation: the state provides public goods, education, health and social security, and aims to reduce inequality.
6. Government intervention: taxes, subsidies, price controls and regulations correct market failures and stabilise the economy.
7. Both profit motive and social objective drive production.
8. Protection of private property along with state power to acquire it for public purpose.

Nepal and India are examples of mixed economies.

(a) $TFC = 200$ at all outputs. $TC = TFC + TVC$; $AFC = TFC/Q$; $AVC = TVC/Q$; $AC = TC/Q$; $MC = \Delta TC/\Delta Q$.

(b) Curves and relationship

With output on the X-axis and cost on the Y-axis:

• TFC is a horizontal line at 200.
• TVC starts at the origin, rises, first at a decreasing rate and then at an increasing rate (an inverted-S shape), reflecting the law of variable proportions.
• TC has the same shape as TVC, but starts at 200 on the Y-axis (it is TVC shifted up by TFC).

Relationship: $TC = TFC + TVC$, so the vertical distance between TC and TVC is constant and equals TFC at every output. The slope of TC equals the slope of TVC (both equal MC), because fixed cost does not change with output.

(a) Equilibrium without tax

Set $Q_d = Q_s$:

$500 - 5P = 100 + 5P \;\Rightarrow\; 400 = 10P \;\Rightarrow\; P = 40$

$Q = 500 - 5(40) = 300$

Equilibrium price = Rs 40, output = 300 units.

(b) With a sales tax of Rs 10 per unit

The tax is levied on sellers, so sellers keep $P - 10$ per unit. The new supply function is

$Q_s = 100 + 5(P-10) = 50 + 5P$

Equate to demand:

$500 - 5P = 50 + 5P \;\Rightarrow\; 450 = 10P \;\Rightarrow\; P = 45$

$Q = 500 - 5(45) = 275$

New equilibrium price (paid by buyers) = Rs 45, output = 275 units.

Sellers receive $45 - 10 =$ Rs 35. Buyers pay Rs 5 more and sellers receive Rs 5 less, so the burden is shared equally. Tax revenue $=10\times 275 =$ Rs 2750.

Monetary policy is the action of the central bank (Nepal Rastra Bank) to regulate money supply, credit and interest rates. Its main objectives are:

1. Price stability: keeping inflation low and stable so that the purchasing power of money is maintained. This is usually the primary objective.
2. Economic growth: providing adequate credit to productive sectors to raise output.
3. Full employment: supporting job creation through low interest rates and credit availability.
4. Exchange rate stability: keeping the external value of the currency stable (in Nepal, the peg with the Indian rupee) and managing foreign exchange reserves.
5. Balance of payments equilibrium: maintaining adequate foreign reserves and a sustainable external position.
6. Financial stability: safe and sound banking and financial system, with sufficient liquidity.
7. Promotion of savings, investment and financial inclusion, including priority-sector lending.

Definition

An isoquant (equal-product curve) shows all the combinations of two inputs (labour and capital) 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. Downward sloping: if one input is reduced, the other must increase to keep output constant.
2. Convex to the origin: MRTS diminishes because inputs are imperfect substitutes.
3. Do not intersect: an intersection would show two different output levels as equal at the same input combination.
4. Higher isoquant means higher output: a curve farther from the origin represents a larger output.
5. Do not touch either axis: both inputs are needed to produce the good.
6. Not necessarily parallel to one another.

Special cases: perfect substitutes give linear isoquants; perfect complements give L-shaped isoquants.

Cartel: a cartel is a formal agreement among independent firms in an oligopolistic industry to coordinate their prices, output or market shares, so as to act like a single monopolist and maximise joint profit. A central body usually fixes industry output and price and allocates quotas among the members.

Why it is illegal: in most countries cartels are prohibited by competition (antitrust) law because they:

• raise prices and restrict output, harming consumers;
• reduce competition, efficiency and innovation;
• create barriers for new entrants;
• cause a deadweight loss and transfer income from consumers to producers.

Examples

• OPEC (Organization of the Petroleum Exporting Countries), an international cartel of oil-producing countries. It is not usually prosecuted since it is formed by sovereign states.
• Price-fixing cartels in cement, vitamins, cooking oil or transport in various countries (such as the vitamin cartel in the 1990s).
• Syndicates in local markets, such as transport or traders' associations that fix fares and prices.

Cartels are unstable because each member has an incentive to cheat on its quota.

GDP and GNP

Problems of measuring national income in Nepal

1. Large non-monetary sector: subsistence agriculture and self-consumption are difficult to value.
2. Illiteracy and lack of records: many producers do not maintain accounts.
3. Unorganised sector and informal economy: most activity is unregistered.
4. Unreliable and insufficient data: statistical systems are weak.
5. Black market and underground activities are not recorded.
6. Remittance and informal flows: a large share of income is received informally, which is hard to measure.
7. Non-marketed services: household work and voluntary services are excluded.
8. Price changes and double counting: difficult to avoid in the absence of proper classification.
9. Occupational specialisation is limited, so output is hard to separate by sector.