Market Equilibrium — NCERT Solutions

Case 1: Fixed number of firms

• The market supply curve is upward sloping (fixed number of firms, each supplying more at higher prices).
• When demand shifts rightward:
• Equilibrium price increases.
• Equilibrium quantity increases.
• The increase in quantity is limited because existing firms can only expand output along their upward-sloping supply curves.
• The increase in price is significant.

Case 2: Free entry and exit

• The long-run market supply curve is perfectly elastic (horizontal) at $p =$ min AC.
• When demand shifts rightward:
• Equilibrium price remains unchanged (stays at min AC).
• Equilibrium quantity increases by a larger amount (new firms enter to meet the increased demand).
• Number of firms increases.

Comparison Table:

Conclusion: A rightward shift in demand has a larger effect on price and smaller effect on quantity when firms are fixed, compared to free entry/exit where the effect on price is zero but effect on quantity is larger.

Given: Both demand and supply curves shift rightward simultaneously.

Effect on Equilibrium Quantity:
A rightward shift in demand increases quantity; a rightward shift in supply also increases quantity. Both shifts work in the same direction, so equilibrium quantity unambiguously increases.

$$q^* \uparrow \text{ (certain)}$$

Effect on Equilibrium Price:
A rightward shift in demand tends to increase price; a rightward shift in supply tends to decrease price. These two effects work in opposite directions, so the net effect on price is ambiguous and depends on the relative magnitudes of the two shifts.

Three possible outcomes:

1. Demand shift > Supply shift: Price increases.
2. Demand shift < Supply shift: Price decreases.
3. Demand shift = Supply shift: Price remains unchanged.

Diagram Description:

• Draw original demand $D_1$ and supply $S_1$ intersecting at $(p_1^*, q_1^*)$.
• Shift both rightward to $D_2$ and $S_2$.
• New equilibrium at $(p_2^*, q_2^*)$ where $q_2^* > q_1^*$.
• Show three cases for price: $p_2^* > p_1^*$, $p_2^* = p_1^*$, or $p_2^* < p_1^*$ depending on relative shifts.

Conclusion: Rightward shift of both curves → equilibrium quantity definitely increases; equilibrium price change is indeterminate.

(a) Both curves shift in the same direction:

Sub-case (i): Both shift rightward (increase)

• Demand ↑ → price tends to rise, quantity tends to rise.
• Supply ↑ → price tends to fall, quantity tends to rise.
• Equilibrium quantity: Both effects increase quantity → quantity unambiguously increases.
• Equilibrium price: Effects on price are opposite → price change is ambiguous (depends on magnitude of shifts).

Sub-case (ii): Both shift leftward (decrease)

• Equilibrium quantity: Both effects decrease quantity → quantity unambiguously decreases.
• Equilibrium price: Effects on price are opposite → price change is ambiguous.

$$q^* \text{ changes unambiguously; } p^* \text{ is indeterminate}$$

(b) Demand and supply curves shift in opposite directions:

Sub-case (i): Demand increases (rightward), Supply decreases (leftward)

• Both effects tend to increase price → price unambiguously increases.
• Demand ↑ increases quantity; Supply ↓ decreases quantity → quantity change is ambiguous.

Sub-case (ii): Demand decreases (leftward), Supply increases (rightward)

• Both effects tend to decrease price → price unambiguously decreases.
• Quantity change is ambiguous.

$$p^* \text{ changes unambiguously; } q^* \text{ is indeterminate}$$

Summary:

• Same direction shifts → quantity change certain, price change uncertain.
• Opposite direction shifts → price change certain, quantity change uncertain.

Differences between Labour Market and Goods Market curves:

1. Demand Curve:

2. Supply Curve:

3. Key Concept:

• In the goods market, the firm is the supplier and the consumer is the demander.
• In the labour market, the firm is the demander and the household/worker is the supplier.
• The demand for labour is determined by the Value of Marginal Product of Labour (VMP$_L$) = $p \times MP_L$, where $p$ is the price of the good produced.

Given: A perfectly competitive market where firms are price-takers in both the goods market and the labour market.

Concept: A profit-maximising firm will hire labour up to the point where the additional revenue generated by employing one more unit of labour equals the additional cost of hiring that unit.

Step 1 — Marginal Revenue Product of Labour (MRP$_L$):
In a perfectly competitive market, the price of the good ($p$) is constant. The additional revenue from hiring one more unit of labour is:
$$MRP_L = p \times MP_L$$
where $MP_L$ is the marginal product of labour. This is also called the Value of Marginal Product of Labour (VMP$_L$).

Step 2 — Marginal Cost of Labour:
In a competitive labour market, the wage rate ($w$) is given (constant). The marginal cost of hiring one more unit of labour = $w$.

Step 3 — Optimality Condition:
The firm maximises profit by hiring labour up to the point where:
$$MRP_L = w$$
$$p \times MP_L = w$$

• If $MRP_L > w$: hiring more labour adds more to revenue than cost → hire more.
• If $MRP_L < w$: hiring more labour adds more to cost than revenue → hire less.
• If $MRP_L = w$: optimal level of employment.

Conclusion: The optimal amount of labour is determined where $p \times MP_L = w$, i.e., where the value of marginal product of labour equals the wage rate.

Given: A perfectly competitive labour market.

Step 1 — Labour Demand Curve:
The market demand for labour is derived from firms' profit maximisation. Each firm demands labour up to the point where $VMP_L = w$. Since $VMP_L = p \times MP_L$ and $MP_L$ diminishes as more labour is hired, the labour demand curve is downward sloping — firms demand more labour at lower wage rates.

The market demand for labour is the horizontal summation of all individual firms' labour demand curves.

Step 2 — Labour Supply Curve:
The market supply of labour comes from households. Workers supply more labour at higher wage rates (generally). The labour supply curve is upward sloping.

Step 3 — Equilibrium Wage Determination:
The equilibrium wage rate ($w^*$) is determined at the intersection of the market labour demand curve and the market labour supply curve:

$$L_D(w^*) = L_S(w^*)$$

At this wage rate, the number of workers firms want to hire exactly equals the number of workers willing to work.

Step 4 — Stability:

• If $w > w^*$: excess supply of labour → wage falls to $w^*$.
• If $w < w^*$: excess demand for labour → wage rises to $w^*$.

Conclusion: In a perfectly competitive labour market, the wage rate is determined by the intersection of market demand for labour and market supply of labour.

Examples of Price Ceiling in India:

• Essential food items such as wheat, rice, sugar, and kerosene distributed through the Public Distribution System (PDS/ration shops) at prices below market rates.
• Drugs and medicines — the government fixes maximum retail prices (MRP) for essential medicines under the Drug Price Control Order (DPCO).
• Rent control in some cities.

Consequences of Price Ceiling:

A price ceiling is set below the equilibrium price ($p_c < p^*$), which leads to:

1. Excess Demand:
$$Q_D(p_c) > Q_S(p_c)$$
At the lower controlled price, consumers demand more but producers supply less, creating a shortage.

2. Long Queues:
Since the good is available at a lower price but in limited quantity, consumers have to stand in long queues at ration shops to obtain the good.

3. Black Market:
Since not all consumers can obtain the good at the controlled price, some are willing to pay higher prices. This creates a black market where the good is sold illegally at prices above the ceiling.

4. Reduced Quality:
Producers, receiving a lower price, may reduce the quality of the good to cut costs.

5. Under-supply:
Lower prices reduce the incentive for producers to supply the good, worsening the shortage over time.

Conclusion: While price ceilings aim to make goods affordable, they often lead to shortages, black markets, and rationing.

Case 1: Fixed Number of Firms

• The market supply curve is upward sloping (positively sloped).
• When demand shifts rightward (increases), the new equilibrium is at the intersection of the new demand curve and the upward-sloping supply curve.
• Result: Both price and quantity increase, but the price increase is significant because the supply curve is not flat — to induce existing firms to produce more, price must rise.
• The quantity increase is limited because existing firms face rising marginal costs and can only expand output to a limited extent.

Case 2: Free Entry and Exit

• The long-run market supply curve is perfectly elastic (horizontal) at $p =$ min AC.
• When demand shifts rightward, the new equilibrium is at the same price (min AC) but higher quantity.
• Result: Price does not change at all (the horizontal supply curve means any increase in demand is met by new firms entering at the same price).
• The quantity increase is larger because new firms enter the market, adding to total supply without raising price.

Comparison:

Conclusion: With fixed firms, the upward-sloping supply curve means a demand increase raises price substantially but quantity only moderately. With free entry/exit, the perfectly elastic supply curve means price is unchanged but quantity rises by the full extent of the demand increase. Hence, the effect on price is larger and on quantity is smaller with fixed firms compared to free entry/exit.

Part 1: Why is market supply zero for $p < 15$?

The supply is zero for $p < 15$ because Rs 15 is the minimum average variable cost (or minimum average cost / shut-down price) of the firms. In a perfectly competitive market, a firm will not supply any output if the price is below its minimum average variable cost, since it cannot even cover its variable costs. Therefore, at any price below Rs 15, no firm finds it profitable to produce, and hence market supply is zero.

Part 2: Equilibrium Price

At equilibrium: $Q_D = Q_S$

$$700 - p = 500 + 3p$$

$$700 - 500 = 3p + p$$

$$200 = 4p$$

$$p^* = \frac{200}{4} = 50$$

Since $p^* = 50 \geq 15$, the supply function $q^S = 500 + 3p$ is applicable. ✓

Equilibrium price = Rs 50

Part 3: Equilibrium Quantity

Substituting $p^* = 50$ in the demand equation:
$$q^* = 700 - 50 = 650$$

Verification using supply: $q^S = 500 + 3(50) = 500 + 150 = 650$ ✓

Equilibrium quantity = 650 units

(a) Significance of $p = 20$:

$p = 20$ is the minimum average cost (min AC) of each individual firm. It is the price below which no firm will supply any output (shut-down point). At $p = 20$, firms earn only normal profits (zero economic profit). This is the price at which firms are just willing to operate in the long run.

With free entry and exit, $p = 20$ is the long-run equilibrium price because:

• If $p > 20$: firms earn supernormal profits → new firms enter → price falls to 20.
• If $p < 20$: firms incur losses → firms exit → price rises to 20.

(b) Equilibrium Price:

With free entry and exit, the equilibrium price equals the minimum average cost of the firms:

$$\boxed{p^* = Rs\; 20}$$

Reason: At $p = 20$, firms earn zero economic (normal) profit. There is no incentive for new firms to enter or existing firms to exit. The market is in long-run equilibrium.

(c) Equilibrium Quantity and Number of Firms:

Equilibrium Quantity:
Using the demand curve $q^D = 700 - p$ at $p^* = 20$:
$$q^* = 700 - 20 = 680 \text{ units}$$

Output per firm at $p = 20$:
$$q_f^* = 8 + 3(20) = 8 + 60 = 68 \text{ units per firm}$$

Number of firms:
$$n^* = \frac{q^*}{q_f^*} = \frac{680}{68} = 10 \text{ firms}$$

Conclusion:

• Equilibrium price = Rs 20
• Equilibrium quantity = 680 units
• Number of firms = 10 firms

(a) Original Equilibrium:

At equilibrium: $Q_D = Q_S$

$$1000 - p = 700 + 2p$$

$$1000 - 700 = 2p + p$$

$$300 = 3p$$

$$p_1^* = 100$$

$$q_1^* = 1000 - 100 = 900 \text{ units}$$

Equilibrium price = Rs 100; Equilibrium quantity = 900 units

(b) New supply curve after input price rise: $q^S = 400 + 2p$

At new equilibrium: $Q_D = Q_S$

$$1000 - p = 400 + 2p$$

$$1000 - 400 = 2p + p$$

$$600 = 3p$$

$$p_2^* = 200$$

$$q_2^* = 1000 - 200 = 800 \text{ units}$$

New equilibrium price = Rs 200; New equilibrium quantity = 800 units

Change: Price increased from Rs 100 to Rs 200 (↑); Quantity decreased from 900 to 800 units (↓).

Does it conform to expectation? YES. A rise in input price increases production cost → supply curve shifts leftward (from $700 + 2p$ to $400 + 2p$, the intercept decreased by 300, indicating leftward shift) → equilibrium price rises and equilibrium quantity falls. This is exactly what we expect.

(c) Effect of a tax of Rs 3 per unit:

A tax of Rs 3 per unit on sellers increases their cost of production by Rs 3 per unit. This shifts the supply curve leftward. The new supply curve is obtained by replacing $p$ with $(p - 3)$ in the original supply function (sellers receive $p - 3$ after paying tax):

$$q^S_{\text{new}} = 700 + 2(p - 3) = 700 + 2p - 6 = 694 + 2p$$

At new equilibrium: $Q_D = Q_S$

$$1000 - p = 694 + 2p$$

$$1000 - 694 = 3p$$

$$306 = 3p$$

$$p_3^* = 102$$

$$q_3^* = 1000 - 102 = 898 \text{ units}$$

Effect of tax:

• Equilibrium price increases from Rs 100 to Rs 102 (rises by Rs 2, not the full Rs 3 — the burden is shared between buyers and sellers).
• Equilibrium quantity decreases from 900 to 898 units.

Note: The price rises by Rs 2 (buyers bear Rs 2 of the tax) and sellers bear Rs 1 of the tax (they receive Rs 102 − Rs 3 = Rs 99, compared to Rs 100 earlier).

Given: Market equilibrium rent $r^*$ is too high; government imposes a rent ceiling $r_c < r^*$ (price ceiling on rent).

Impact of Rent Control (Price Ceiling) on the Apartment Market:

Step 1 — Excess Demand:
At the controlled rent $r_c$ (which is below equilibrium rent $r^*$):

• Quantity demanded of apartments increases (more people want to rent at lower rent).
• Quantity supplied of apartments decreases (landlords are less willing to rent out at lower rent).
• This creates excess demand (shortage of apartments):

$$Q_D(r_c) > Q_S(r_c)$$

Step 2 — Consequences:

1. Shortage of apartments: The number of people seeking apartments exceeds the number of apartments available for rent.

2. Long queues/waiting lists: People seeking apartments have to wait for long periods to get one.

3. Black market: Since many people cannot get apartments at the controlled rent, some may be willing to pay more than $r_c$. This may lead to illegal subletting or under-the-table payments above the controlled rent.

4. Deterioration in quality: Landlords, receiving lower rent, have less incentive to maintain or improve the quality of apartments.

5. Reduced supply in the long run: New construction of rental apartments may slow down as it becomes less profitable, worsening the shortage over time.

Conclusion: While rent control aims to make housing affordable for common people, it leads to a shortage of apartments, long waiting lists, possible black markets, and deterioration in housing quality. The policy helps existing tenants who get apartments at lower rent but harms those who cannot find apartments at all.