Question

Suppose the demand equation facing a firm is Q=1000-5Q, MR=200-0.4Q, and MC=$20.

A. Compute the maximum profit the firm can earn.

B. Suppose the firm is considering a quantity discount. It offers the first 400 units at a price of $120, and further units at a price of $80. How many units will the consumer buy in total?

C. Compute the profit if the quantity discount is implemented.

D. If the firm implemented a two part pricing strategy, what would be the fixed fee, variable fee, total revenue, and the total variable cost?

Answer 1

A).

Consider the given problem here the demand is given by, => Q = 1,000 – 5*P, => P = 200 – 0.2*Q. The associated MR is “MR = 200 – 0.4*Q”. At the equilibrium the MR must be eqal to MC.

=> MR = MC, => 200 – 0.4*Q = 20, => Q = 180/0.4 = 450, => Q* = 450.

The profit maximizing price is “P = 110”. So, the maximum profit is given by.

=> A = TR-TC = P*Q - MC*Q = (110-20)*450 = $40,500.

B).

Let’s assume the firm is considering a quantity discounting, it offer the 1^st 400 units at price of P1=$120 and further units at price of $80. Consider the following fig.

Here under the quantity discounting the associated MR is step function, => the profit maximizing production if “Q=600”

c).

So, the profit of the producer if the quantity discounting is implemented is given by.

=> A = (P1-MC)*Q1 + (P2-MC)*(Q2-Q1) = (120-20)*400 + (80-20)*(600-400).

=> A = 100*400 + 60*200 = $52,000.

d).

If the firm implement a two part tariff price strategy then the variable fee should be exactly equal to MC=$20. So, the total quantity sold will be “P=MC”, => 200 – 0.2*Q = 20, => Q=(200-20)/0.2 = 900, => Q = 900.

The fixed fee will be the consumer surplus.

=> CS = 0.5*(200-MC)*Q = 0.5*180*900 = $81,000. So, the total revenue is given by.

=> TR = Total Fixed fee + Variable fee = $81,000 + $MC*Q = $81,000 + $20*900 = $99,000.

The total variable cost is “TVC = MC*Q = 20*900 = $18,000”.