Consider a firm with market power. There are N1 = 200 customers with demand P =

Question

Consider a firm with market power. There are N1 = 200 customers with demand P = 10 - Q1 and N2 = 300 with demand P = 15 - Q2 . The firm has zero fixed costs and constant marginal cost C = $4. The firm wants to use a two-part pricing strategy (T,P). Hint: Recall that if P = a1 - Q1 and P = a2 - Q2 , with a2 > a1 , then the derivative of ( N1 + N2 )*T(P) + (P-C)*[ N1 *( a1 - P) + N2 *( a2 - P)] with respect to P, whereT(P) = (a1 - P)2 / 2, is given by -( N1 + N2 )*( a1 - P) + N1 * ( a1 - P) + N2 *( a2 - P) - (P-C)*( N1 + N2 ). If the firm wants to sell to both groups then

a) It will set T = $18 and P = $4

b) It will set T = $4.5 and P = $7

c) It will make more profits than if it sells to just one group

d) None of the above

Explanation / Answer

In two part tariff, the price charged by the firm is equal to the marginal cost of thr firm sSo, price charged = $4.

The membership fee = Consumer surplus of the consumer whose consumer surplus is less.

In this case consumer surplus of the consumer with demand function 10 - Q1 is less than the other consumer. So, memebership fee= 1/2 * (10 - 4) * ^ = $18.

So. option A.

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