Price Elasticity of Demand

Price elasticity of demand is the degree of responsiveness of quantity demanded of a commodity to a change in its price. It is measured as the ratio of the percentage change in quantity demanded to the percentage change in price.

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

where $P$ and $Q$ are the original price and quantity, and $\Delta P$ and $\Delta Q$ are the changes in price and quantity.

Degrees of Price Elasticity of Demand

On the basis of the numerical value of the coefficient $E_p$, price elasticity of demand is classified into five degrees:

1. Perfectly Elastic Demand ($E_p = \infty$) Quantity demanded changes infinitely for a very small change in price. Even a negligible rise in price reduces demand to zero, and a negligible fall makes it infinite. The demand curve is a horizontal straight line parallel to the X-axis. It is a theoretical concept and is not found in practice.

2. Perfectly Inelastic Demand ($E_p = 0$) Quantity demanded does not change at all whatever the change in price. The demand curve is a vertical straight line parallel to the Y-axis. This also applies to extreme necessities such as salt and life-saving medicines.

3. Relatively Elastic Demand ($E_p > 1$) The percentage change in quantity demanded is greater than the percentage change in price. A small fall in price causes a more than proportionate rise in demand. The demand curve is a flat curve. This is found in the case of luxuries such as gold, jewellery and cars.

4. Relatively Inelastic Demand ($E_p < 1$) The percentage change in quantity demanded is less than the percentage change in price. A large fall in price causes only a small rise in demand. The demand curve is a steep curve. This is found in the case of necessities such as food grains, salt and kerosene.

5. Unitary Elastic Demand ($E_p = 1$) The percentage change in quantity demanded is exactly equal to the percentage change in price. The demand curve is a rectangular hyperbola. Total expenditure of the consumer on the commodity remains constant whether price rises or falls. This is found in the case of normal goods.

Numerical Illustration

Suppose the price of a commodity falls from Rs 10 to Rs 8 and quantity demanded rises from 100 units to 140 units.

$E_p = \frac{\Delta Q}{\Delta P} \times \frac{P}{Q} = \frac{40}{2} \times \frac{10}{100} = 2$

Since $E_p = 2 > 1$, demand is relatively elastic.

Marginal Rate of Technical Substitution (MRTS)

MRTS measures the rate at which one input can be reduced when one more unit of another input is added, keeping output constant. It is the slope of the isoquant.

If labour (L) is increased by ΔL and capital (K) is reduced by ΔK so that output stays the same:

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

The negative sign is dropped because the slope of an isoquant is already negative. In the limit:

$MRTS_{L,K} = \frac{MP_L}{MP_K}$

Numerical illustration

All combinations give the same output (say 100 units). As we move down the isoquant, MRTS falls from 4 to 1.

Why MRTS Diminishes

MRTS diminishes because of the law of diminishing marginal returns applied to both inputs:

1. As labour increases, each extra worker adds less to output, so MP_L falls.
2. As capital decreases, capital becomes scarce, so each remaining unit of capital is more productive — MP_K rises.

Since MRTS = MP_L / MP_K, a falling numerator and a rising denominator make MRTS fall continuously. This is why isoquants are convex to the origin: to keep output constant, successively smaller amounts of capital are given up for each additional unit of labour.

Conclusion: MRTS is the slope of the isoquant, equal to the ratio of marginal products. It diminishes because of diminishing marginal productivity of the input being increased and increasing relative scarcity of the input being reduced.

a. Calculation of MR, MC and Profit

Formulae used:

$MR_n = TR_n - TR_{n-1}$ $MC_n = TC_n - TC_{n-1}$ $\text{Profit} = TR - TC$

Equilibrium from TR–TC approach

Profit is maximum where the vertical difference between TR and TC is greatest.

From the table, maximum profit is Rs 100 at output 3 and output 4.
But at output 3, $MR > MC$, so the firm can still gain by producing more. At output 4, $MR = MC$ and MC is rising. Therefore, the equilibrium output is:

$\boxed{Q = 4 \text{ units}}$

Equilibrium from MR–MC approach

At output 4, marginal revenue equals marginal cost:

$MR = MC = Rs\ 100$

Before output 4, $MR > MC$, so profit rises. After output 4, $MR < MC$, so profit falls. Hence, equilibrium output is:

$\boxed{Q = 4 \text{ units}}$

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b. Graphical Presentation

Plot the following points on a graph.

TR curve:

$(0,0),\ (1,220),\ (2,400),\ (3,540),\ (4,640),\ (5,700),\ (6,720),\ (7,700)$

TC curve:

$(0,120),\ (1,270),\ (2,370),\ (3,440),\ (4,540),\ (5,670),\ (6,830),\ (7,1020)$

Profit curve:

$(0,-120),\ (1,-50),\ (2,30),\ (3,100),\ (4,100),\ (5,30),\ (6,-110),\ (7,-320)$

On the figure:

• The TR curve rises up to output 6 and then falls at output 7.
• The TC curve rises continuously.
• The vertical distance between TR and TC shows profit.
• The TR and TC curves cross between output 1 and 2, and again between output 5 and 6. These are break-even points.
• The maximum vertical gap between TR and TC occurs at output 3 and output 4.
• At output 4, the slopes of TR and TC are equal, i.e. $MR = MC$.

Therefore, from the figure also, the equilibrium level of output is:

$\boxed{Q = 4 \text{ units}}$

Derivation of the Short Run Supply Curve of a Firm and Industry

1. Meaning

The short run supply curve shows the quantity of output a firm (or the whole industry) is willing to offer at each possible price, other things remaining the same. In the short run, the number of firms and the plant size are fixed; only the variable factor (labour) can be changed.

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2. Derivation of the Firm's Short Run Supply Curve

(a) Under Perfect Competition — the firm is a price taker

The firm maximises profit where:

$MC = MR = AR = P$

Since price is given, the firm's marginal revenue equals price. So the profit-maximising condition becomes:

$P = MC \quad \text{(with MC rising)}$

(b) The Shut-down Point

The firm will produce only if price covers at least average variable cost. The shut-down point is the minimum point of AVC, where:

$P = \min AVC$

Below this price, the firm stops production (output = 0) because it cannot even cover its variable costs.

(c) The Supply Curve

Therefore, the firm's short run supply curve is the portion of the rising MC curve that lies above the minimum point of AVC.

• If $P < \min AVC$ → output $= 0$
• If $P \ge \min AVC$ → output is read off the rising MC curve

Diagram (description)

Plotting price on the vertical axis and quantity on the horizontal axis, the supply curve SS starts at the shut-down point and slopes upward — it is the MC curve above AVC.

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3. Derivation of the Industry's Short Run Supply Curve

The industry consists of all the firms producing the same product. The industry supply curve is obtained by horizontal summation of the individual firms' supply curves.

Steps

1. Take the supply curve of each firm (MC above AVC).
2. At each price, add the quantities supplied by all firms.
3. Plot the total quantity against each price.

$Q_s = q_1 + q_2 + q_3 + \dots + q_n$

Diagram (description)

If there are $n$ identical firms, the industry supply curve is $n$ times the firm's supply at every price. It lies to the right of the firm's supply curve and is flatter (more elastic), because a small rise in price brings forth a larger total increase in output from many firms.

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4. Conclusion

• The firm's short run supply curve is the rising part of its MC curve above the minimum AVC.
• The industry's short run supply curve is the horizontal sum of all firms' short run supply curves.
• Both slope upward, confirming the law of supply: price and quantity supplied are directly related in the short run.

Given: Price of product (P = \text{Rs. }600).

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a) Marginal product of labor

[ MP_L = \frac{\Delta TP}{\Delta L} ]

So,

[ MP_L = 100,\ 80,\ 60,\ 40,\ 20 ]

for the 1st, 2nd, 3rd, 4th and 5th units of labor respectively.

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b) Value of marginal product of labor and VMP curve

[ VMP_L = MP_L \times P ]

[ VMP_L = MP_L \times \text{Rs. }600 ]

Thus,

[ VMP_L = \text{Rs. }60{,}000,\ \text{Rs. }48{,}000,\ \text{Rs. }36{,}000,\ \text{Rs. }24{,}000,\ \text{Rs. }12{,}000 ]

The (VMP_L) curve is downward sloping because (MP_L) falls as more labor is employed. It is also the firm’s demand curve for labor.

Schematic figure:

VMP/w
(Rs '000)
60 | ●
   |  \
48 |---●---------------- w = 48,000  → E2 at L = 2
   |    \
36 |-----●-------------- w = 36,000  → E1 at L = 3
   |      \
24 |       ●
   |        \
12 |         ●
   |__________\________ L
   0 1 2 3 4 5

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c) Profit-maximizing employment when wage rate is Rs. 36,000

Profit-maximizing condition:

[ VMP_L = w ]

If (VMP_L > w), the firm hires more labor.
If (VMP_L < w), the firm reduces labor.

Therefore,

[ \boxed{L^* = 3} ]

The firm employs 3 workers.

At (L = 3), (VMP_L = w = \text{Rs. }36{,}000).
In the figure, this is point (E_1), where the downward-sloping (VMP_L) curve intersects the horizontal wage line (w = \text{Rs. }36{,}000).

Note: Profit at (L = 2) and (L = 3) is equal at Rs. 36,000, but the marginal condition gives equilibrium employment at (L = 3).

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d) Change in equilibrium when wage rate rises to Rs. 48,000

Now,

[ w = \text{Rs. }48{,}000 ]

Therefore,

[ \boxed{L^* = 2} ]

The firm now employs 2 workers.

In the figure, the wage line shifts upward from Rs. 36,000 to Rs. 48,000. The new equilibrium is point (E_2), where the (VMP_L) curve intersects the higher wage line at (L = 2).

So, when the wage rate rises from Rs. 36,000 to Rs. 48,000, employment falls from 3 workers to 2 workers. This shows the downward-sloping demand for labor curve.

Given: Income $M =$ Rs 3,750, $P_x =$ Rs 150, $P_y =$ Rs 50.

(a) Indifference curves, budget line and equilibrium (7 marks)

Budget line. If all income is spent on X: $3750/150 = 25$ units. If all is spent on Y: $3750/50 = 75$ units. The budget line joins $(X=25, Y=0)$ and $(X=0, Y=75)$; its slope is $P_x/P_y = 150/50 = 3$.

Cost of each combination at the original prices ($150X + 50Y$):

Plot X on the horizontal axis and Y on the vertical axis, draw the two convex indifference curves IC₁ (A to E) and IC₂ (F to J) and the budget line from $(25,0)$ to $(0,75)$.

Only combination C costs exactly Rs 3,750, so IC₁ touches the budget line at C. Every point of IC₂ costs more than Rs 3,750, so IC₂ is out of reach. IC₁ is the highest curve attainable, hence the initial equilibrium is at C: 15 units of X and 30 units of Y, where the budget line is tangent to IC₁ and $MRS_{xy} = P_x/P_y = 3$.

(b) New equilibrium when $P_x$ falls to Rs 75 (3 marks)

The new budget line has intercepts $3750/75 = 50$ units of X and still 75 units of Y; its slope is $75/50 = 1.5$.

Cost at the new prices ($75X + 50Y$): C = 2,625, D = 2,600, E = 2,625 on IC₁ (all affordable, but below the budget); on IC₂, G = 5,250, H = 4,025, J = 4,025, and I (20, 45) = 1,500 + 2,250 = 3,750.

Combination I lies exactly on the new budget line, so IC₂ is tangent to it at I. The new equilibrium is at I: 20 units of X and 45 units of Y, with $MRS_{xy} = 1.5$.

(c) Consumer's equilibrium and price effect (5 marks)

Consumer's equilibrium. A consumer maximises satisfaction by reaching the highest indifference curve the budget allows. This is where the budget line is tangent to an indifference curve:

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

with the indifference curve convex to the origin (second-order condition). In the figure this is point C on IC₁ at the original prices. Points such as B or D on IC₁ cost more than the income, and IC₂ cannot be reached.

Price effect. The price effect is the change in the quantity consumed of a good when its own price changes, other things (income, tastes, price of Y) constant. When $P_x$ falls from Rs 150 to Rs 75, the budget line pivots outward on the Y-intercept, from the line with X-intercept 25 to the line with X-intercept 50. The consumer moves from C on IC₁ to I on the higher curve IC₂.

Joining the equilibrium points C and I gives the price consumption curve (PCC). Demand for X rises from 15 to 20 units as its price falls, which gives the downward-sloping demand curve (the points $(P_x, X) = (150, 15)$ and $(75, 20)$). The total price effect combines the substitution effect (X is now relatively cheaper than Y) and the income effect (real income rises as the price of X falls).

TU BBS — First Year Subject: Microeconomics Full Marks: 15

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1. Meaning of Market Equilibrium (5 marks)

Market equilibrium is the situation in a market where the quantity demanded of a commodity by buyers is exactly equal to the quantity supplied by sellers, at a particular price. At this price, there is neither excess demand (shortage) nor excess supply (surplus), so there is no tendency for the price to change. This price is called the equilibrium price, and the corresponding quantity is called the equilibrium quantity.

Conditions of equilibrium:

• Quantity Demanded (Qd) = Quantity Supplied (Qs)
• The demand curve and supply curve intersect at a single point, called the equilibrium point (E).

Diagrammatic representation:

 Price (Rs)
   |
 P*|------- E  (Equilibrium Point)
   |      / \
   |     /   \  S
   |    /     \
   |   /       \
   |  D         \
   |________________ Quantity
        Q*

At price P*, the market clears. If price rises above P*, Qs > Qd → surplus → price falls back to P*. If price falls below P*, Qd > Qs → shortage → price rises back to P*. Hence P* is a stable equilibrium.

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2. Effect of Government Policy of Tax on Equilibrium Price and Quantity (5 marks)

When the government imposes a tax on the production or sale of a good (say, an excise duty or per-unit tax), the cost of production rises. As a result, producers are willing to supply less at each price, and the supply curve shifts leftward (upward) from S to S₁. The demand curve remains unchanged.

Effects:

1. Price rises from P to P₁ (the tax is partly shifted to consumers).
2. Quantity falls from Q to Q₁.
3. The burden of tax is shared between consumers (higher price) and producers (lower net price received).

Diagram:

 Price (Rs)
   |
 P₁|---- E₁
   |    /  \
 P |---E    \  S₁
   |  / \    \
   | /   \    \ S
   |/     \    \
   |_______D____\____ Quantity
      Q₁  Q

Conclusion: A tax raises the equilibrium price and reduces the equilibrium quantity. The extent of the rise depends on the elasticity of demand and supply — the more inelastic the demand, the greater the share borne by consumers.

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3. Effect of Government Policy of Subsidy on Equilibrium Price and Quantity (5 marks)

A subsidy is a grant given by the government to producers to encourage production. It reduces the cost of production, so producers supply more at each price. The supply curve shifts rightward (downward) from S to S₁. Demand remains unchanged.

Effects:

1. Price falls from P to P₁ (benefit partly passed to consumers).
2. Quantity rises from Q to Q₁.
3. The benefit of subsidy is shared between consumers (lower price) and producers (higher net revenue).

Diagram:

 Price (Rs)
   |
 P |---E
   |  / \  S
   | /   \
 P₁|/---- E₁
   |      \  S₁
   |       \
   |___D____\________ Quantity
      Q   Q₁

Conclusion: A subsidy lowers the equilibrium price and increases the equilibrium quantity. The more elastic the demand, the greater the benefit passed on to consumers.

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Summary Table

Thus, government tax and subsidy policies directly influence market equilibrium by shifting the supply curve, thereby changing both equilibrium price and quantity.

Price discrimination means a monopolist selling the same product, at the same time, at different prices to different buyers or in different markets, where the price difference is not explained by cost differences.

Conditions for price discrimination (5 marks)

1. Monopoly power. The seller must control supply and have a downward-sloping demand curve, so that it can set the price and is not a price taker.
2. Separable markets. The market must be divisible into sub-markets by place, age, income, use, time or type of buyer (for example, Nepalese and foreign tourists, peak and off-peak electricity, student and general fares).
3. No resale (no seepage). A buyer in the cheap market must not be able to resell to the dear market; otherwise the price difference disappears. This is easier for services (a doctor's fee, transport) and where the law or distance prevents resale.
4. Different elasticities of demand. The markets must have different price elasticities; otherwise there is no gain from charging different prices.
5. Profitability. The extra revenue must exceed the cost of separating and policing the markets.
6. Consumer ignorance or preference (for example, brand or ignorance of prices elsewhere) and legal permission also help the practice survive.

Third-degree price discrimination (10 marks)

Here the monopolist divides total demand into two or more independent markets and sets a separate price in each, according to its elasticity of demand. There are two decisions: how much to produce in total, and how to share it between the markets.

Equilibrium rule. For two markets (1 and 2) with marginal revenues $MR_1$ and $MR_2$ and common marginal cost $MC$:

1. Allocation: $MR_1 = MR_2$. If $MR_1 > MR_2$, shifting a unit from market 2 to market 1 raises revenue, so the monopolist keeps adjusting until the two marginal revenues are equal.
2. Total output: $MR_1 = MR_2 = MC$, where $MR$ (the horizontal sum of $MR_1$ and $MR_2$) cuts $MC$.

Since $MR = P\left(1 - \frac{1}{e}\right)$, equality of marginal revenues gives

$P_1\left(1 - \frac{1}{e_1}\right) = P_2\left(1 - \frac{1}{e_2}\right)$

so the price is higher in the market with less elastic demand and lower in the market with more elastic demand. If $e_1 = e_2$, the prices are equal and discrimination does not pay.

Diagram (three panels side by side). Panel A shows market 1 with $D_1$ and $MR_1$ (less elastic). Panel B shows market 2 with $D_2$ and $MR_2$ (more elastic). Panel C shows the combined $MR = MR_1 + MR_2$ (horizontal summation) and $MC$. The $MR$ curve meets $MC$ at E, which fixes total output $Q$ and the common marginal revenue level. Drawing a horizontal line from E across Panels A and B, it meets $MR_1$ and $MR_2$ at the outputs $Q_1$ and $Q_2$ with $Q_1 + Q_2 = Q$. Going up from $Q_1$ and $Q_2$ to $D_1$ and $D_2$ gives $P_1$ and $P_2$, with $P_1 > P_2$.

Numerical illustration. Let $MC = 10$, $P_1 = 50 - Q_1$ (so $MR_1 = 50 - 2Q_1$) and $P_2 = 30 - Q_2$ (so $MR_2 = 30 - 2Q_2$).

• Market 1: $50 - 2Q_1 = 10 \Rightarrow Q_1 = 20$, $P_1 = 30$
• Market 2: $30 - 2Q_2 = 10 \Rightarrow Q_2 = 10$, $P_2 = 20$

Total output is 30 units; revenue is $30 \times 20 + 20 \times 10 = 800$. Without discrimination, the single price is found from the combined demand $Q = 80 - 2P$ (for $P \le 30$): $MR = 40 - Q$, so $40 - Q = 10$ gives $Q = 30$ and $P = 25$, with revenue 750. Discrimination raises revenue (and profit) by 50.

Effects. The monopolist earns more profit than under a single price. The buyers in the elastic market gain from the lower price while those in the inelastic market lose, so the welfare judgement is mixed. Examples in Nepal are different tariffs for domestic and industrial electricity, and separate air fares and entry fees for Nepalese, SAARC and other foreign visitors.