Market Equilibrium — NCERT Solutions

With a fixed number of firms, a shift in demand changes both equilibrium price and equilibrium quantity. A rightward demand shift raises both; a leftward shift lowers both.

With free entry and exit, the equilibrium price stays fixed at minimum average cost. So a demand shift affects only the equilibrium quantity and the number of firms:

• rightward demand shift: quantity and number of firms increase,
• leftward demand shift: quantity and number of firms decrease.

Thus, the impact on quantity is more pronounced with free entry and exit, while price does not change.

If both demand and supply curves shift rightward, then:

• the equilibrium quantity increases definitely,
• the equilibrium price may increase, decrease, or remain unchanged depending on the magnitude of the shifts.

So the exact outcome for price cannot be fixed without knowing which shift is larger.

Graphically, the new equilibrium is found at the intersection of the new demand and new supply curves to the right of the original equilibrium.

When both demand and supply curves shift in the same direction:

• If both shift rightward, the equilibrium quantity increases. The equilibrium price may increase, decrease, or remain unchanged depending on the size of the shifts.
• If both shift leftward, the equilibrium quantity decreases. The equilibrium price may increase, decrease, or remain unchanged depending on the size of the shifts.

When demand and supply curves shift in opposite directions:

• If demand shifts right and supply shifts left, the equilibrium price increases. The effect on quantity may be increase, decrease, or no change depending on the magnitude of shifts.
• If demand shifts left and supply shifts right, the equilibrium price decreases. The effect on quantity may be increase, decrease, or no change depending on the magnitude of shifts.

So, with same-direction shifts, quantity change is certain but price is uncertain; with opposite-direction shifts, price change is certain but quantity is uncertain.

The supply and demand curves in the labour market differ from those in the goods market in the following way:

• In the goods market, households demand goods and firms supply them.
• In the labour market, the roles are reversed: firms demand labour and households supply labour.

Also, labour means the hours of work supplied, not the number of workers.

In a perfectly competitive market, a firm hires labour up to the point where the extra cost of hiring one more unit of labour equals the extra benefit from that labour.

• Extra cost = wage rate $w$
• Extra benefit = marginal revenue product of labour $MRP_L$

So the optimal amount of labour is determined where

$$w = MRP_L$$

For a perfectly competitive firm, $MR = price$, so

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

Hence the firm hires labour up to the point where $w = VMP_L$.

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

• The demand for labour comes from firms.
• The supply of labour comes from households.

At the equilibrium wage, the amount of labour households wish to supply equals the amount firms wish to hire.

Yes. The chapter mentions goods like wheat, rice, kerosene and sugar as common examples where price ceiling may be imposed in India.

A price ceiling set below the equilibrium price causes excess demand or shortage. Its possible consequences are:

• long queues at ration shops,
• rationing of the commodity,
• possible black market because some consumers are willing to pay more to get the good.

With a fixed number of firms, a shift in demand changes both price and quantity more strongly because the supply side cannot adjust by changing the number of firms. So when demand rises, both price and quantity rise, and when demand falls, both fall.

With free entry and exit, firms can enter when demand rises and exit when demand falls. Because of this adjustment, the price is pinned down at minimum average cost. So the main effect of a demand shift is on quantity and number of firms, not on price.

Therefore, compared to free entry and exit, a demand shift under fixed firms has a larger effect on price and a smaller effect on quantity.

Given
$$q^D = 700 - p, \qquad q^S = 500 + 3p \text{ for } p \ge 15$$
and supply is zero for prices below Rs 15.

The supply is zero below Rs 15 because Rs 15 is the minimum price at which firms are willing to supply; below this price, production is not profitable for them.

To find equilibrium, set demand equal to supply:
$$700 - p = 500 + 3p$$
$$200 = 4p$$
$$p = 50$$
So the equilibrium price is Rs 50.

Now substitute in demand or supply:
$$q = 700 - 50 = 650$$
or
$$q = 500 + 3(50) = 650$$
So the equilibrium quantity is 650 units.

For a perfectly competitive market with free entry and exit, the equilibrium price equals the minimum average cost of the firms.

From the single-firm supply curve
$$q^s = 8 + 3p \text{ for } p \ge 20,$$
the price Rs 20 is significant because it is the minimum average cost level, so firms earn normal profit there.

Therefore, the market equilibrium price is
$$p_0 = 20.$$

Using the demand curve
$$q^D = 700 - p,$$
at $p=20$:
$$q_0 = 700 - 20 = 680.$$

For one firm at $p=20$:
$$q_{0j} = 8 + 3(20) = 68.$$

So the number of firms is
$$n_0 = \frac{q_0}{q_{0j}} = \frac{680}{68} = 10.$$

Thus, equilibrium price = Rs 20, equilibrium quantity = 680 units, and number of firms = 10.

Given
$$q^D = 1000 - p, \qquad q^S = 700 + 2p$$

(a) Equilibrium price and quantity

At equilibrium, demand equals supply:
$$1000 - p = 700 + 2p$$
$$300 = 3p$$
$$p = 100$$
So equilibrium price is Rs 100.

Equilibrium quantity:
$$q = 1000 - 100 = 900$$
or
$$q = 700 + 2(100) = 900$$
So equilibrium quantity is 900 units.

(b) New supply curve after input price increase

New supply:
$$q^S = 400 + 2p$$
Set equal to demand:
$$1000 - p = 400 + 2p$$
$$600 = 3p$$
$$p = 200$$
So the new equilibrium price is Rs 200.

New quantity:
$$q = 1000 - 200 = 800$$
So equilibrium quantity becomes 800 units.

The change does conform to expectation: when input price rises, supply shifts left, price rises, and quantity falls.

(c) Tax of Rs 3 per unit

A tax on sale reduces the effective supply available at each market price, so the supply curve shifts left. Let the price received by sellers be $p-3$. Then
$$q^S = 700 + 2(p-3) = 694 + 2p$$
Now equate with demand:
$$1000 - p = 694 + 2p$$
$$306 = 3p$$
$$p = 102$$
So the market price paid by buyers becomes Rs 102.

Quantity:
$$q = 1000 - 102 = 898$$
So the equilibrium quantity becomes 898 units.

If the government imposes rent control on apartments, it is like a price ceiling. If the controlled rent is set below the equilibrium rent, there will be excess demand for apartments because more people will want to rent at the lower price than landlords are willing to supply.

So the market may face:

• shortage of apartments,
• long waiting lists or queues,
• possible black market dealings or under-the-table payments,
• and rationing in the allocation of apartments.

Thus, while rent control is meant to help tenants, it can create shortage and reduce the availability of rented apartments.