Question

Question 1

Assume that: market demand function for a product is: P= 80−q and marginal cost (in dollars) of producing it is: MC= 1q, where P is the price of the product and q is the quantity demanded and/or supplied. Also assume that the government imposes a price control at P= $80/3

a) Find the consumer and producer surplus associated with the price control allocation.

b) How would the price control allocation in (a) differ from the monopoly allocation, if you assume that the market is controlled by a monopoly. Hint: Compute consumer and producer surplus in each case.

Answer 1

Demand is P = 80 -q
Marginal cost : MC = q

Revenue = P * q = 80q - q²
Marginal revenue : MR = 80 - 2q

In equilibrium under monopoly, MR = MC.

Hence 80 - 2q = q
or, 3q = 80
or, q = 80/3= 26.66

Price = 80 - q
= 80 - 26.66
= $53.35

Hence at equilibrium, price = $53.35
quantity = 26.66

a) Price control is imposed. Price = $80/3 = $26.66
Willingness to pay is = 80 (intercept of demand function)
Quantity demanded = 26.66
Consumer surplus = 0.5 * (80 - 26.66) * 26.66
= 0.5 * 53.35 * 26.66
= $711.02

Willingness to sell at = 0 (no intercept in MC)
Quantity supplued at $26.66 = 26.66 (MC = q)
Producer surplus = 0.5 * 26.66 * 26.66
= $355.37

b) Surplus before control :
price = $53.35
quantity = 26.66

Willingness to pay is = 80 (intercept of demand function)
Willingness to sell at = 0 (no intercept in MC)

Consumer surplus = 0.5 * (80 - 53.35) * 26.66
= 0.5 * 26.66*26.66
= $355.37

Producer surplus = 0.5 * 53.35 * 26.66
= $1422.311

Hence due to price control , consumer surplus has increased, but producer surplus has decreased.