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

P=76-4Q

MR=76-8Q

MC=10

1) Set MC=MR

76-8Q=10

Q = 66/8 = 8.25

P = 76-4(8.25) = 43

2) When the firm cannot price discriminate, it sets MR=MC

CS = 0.5*8.25*(76-43) = 136.125

PS = 8.25*(43-10) = 272.25

Setting P=MC, the firm will produce Q= 66/4 = 16.5 at P=10

DWL = 0.5*(16.5-8.25)*(43-10) = 136.125

3) When the firm perfectly price discriminates, it sets P=MC and captures all the consumer surplus and the deadweight loss

so, CS=0

PS = 0.5*16.5*(76-10) = 544.5

DWL = 0