Question

Consider the monopolistic competition model developed in class. The demand function faced by a producer of differentiated varieties is given by: Q S. (1) n where n is the number of firms, b is the sensitivity of each firm's sales, (Q ) to its price (P), and (P) is the average price of the other firms in the industry. Each firm has a fixed cost of production equal to A and a constant marginal cost equal to d 1. Use Expression (1) to derive the expression of the marginal revenue (MR) of the firm, while assuming that its sales (O) have an impact on its price (P), i.e., P= PQ). (10 points) 2. Write the expressions of the total cost (C) and the average cost ( AC) of the firm in terms of A, d andQ. (5 points)

Answer 1

9= S-6 0P-P fc= A, Mc=d h MR Let dd funch q= A-BP, then PPIB-91A Total Revenue TR- P. B MA- AB-22 B B So MA- P- % [A- Sln-SbF B= Sb] MB= P- 8 So

2) C = FC + MC*Q

C = A+ dQ

AC = C/Q = A/Q + d

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