Question

Suppose the inverse demand for a product produced by a single firm is given by:

P = 76 – 4(Q)

and this firm has a marginal cost of production of:

MC = 10

1.  If the firm cannot price-discriminate , what is the profit-maximizing

a)price?   

b)and level of output?    

2. If the firm cannot price-discriminate , what is :

a)the consumer surplus?   

b)the producer surplus?   

c)the dead-weight loss?   

3. If the firm can practice perfect price discrmination, what output level will it choose?   

a)the consumer surplus?   

b)the producer surplus?   

c)the dead-weight loss?

Answer 1

(1)

P = 76 - 4Q

Total revenue (TR) = PQ = 76Q - 4Q²

Marginal revenue (MR) = dTR/dQ = 76 - 8Q

Equating MR and MC,

76 - 8Q = 10

8Q = 66

Q = 8.25

P = 76 - (4 x 8.25) = 76 - 33 = 43

(2)

(a)

From demand function, when Q = 0, P = 76 (Vertical intercept of demand curve)

Consumer surplus (CS) = Area between demand curve and price = (1/2) x (76 - 43) x 8.25 = (1/2) x 33 x 8.25 = 136.125

(b)

Producer surplus (PS) = Area between MC curve and price = (43 - 10) x 8.25 = 33 x 8.25 = 272.25

(c)

At efficient outcome, P = MC.

76 - 4Q = 10

4Q = 66

Q = 16.5

P = MC = 10

Deadweight loss = (1/2) x Difference in P x Difference in Q = (1/2) x (43 - 10) x (16.5 - 8.25) = (1/2) x 33 x 8.25 = 136.125

(3)

With perfect price discrimination, firm equates Price with MC, therefore P = 10 and Q = 16.5 [From Part 2(c)].

(a)

CS = (1/2) x (76 - 10) x 16.5 = (1/2) x 66 x 16.5 = 544.5

(b)

PS = 0 (since MC = P = 0)

(c)

Deadweight loss is zero, since P = MC.