Question

7. Consider a monopolistically competitive industry where demands and costs are all mc function is the same for all firms and the demand symmetric across firms (the parameters are the same for all firms).The demand for an individual firm is 1 1 P S = 0 500 4-a 5-5- where S is the size of the industry, n is the number of firms, P is the firm's own price, and P is the average price of the competitors. The size of the Home and Foreign markets are S 20,000 and S* = 30,000. All firms have the same total cost function C 400000 + 200Q 200 The marginal cost of production is constant and equal to mc = (a) What is the average cost function for an individual firm (Average cost as a function of output level). Show this in a graph that also shows the marginal cost function and explain if there are economies of scale. (b) In equilibrium, all firms will have an between Average Cost and the number of firms in the Home market. equal share of total output. Find the relation (c) Show the graph of this relation (AC(n)) and explain why the slope of this is positive

Answer 1

A) TC = FC + MC*Q

AC = FC/Q + MC

AC = 400,000/Q + 200

As AC is falling continuously , so economies of scale exists.

10000 -8000- -6000 -4000 AC 2000 (0, 200) MC 0 2000 1000 Output Average cost

B) Q = S/n

So AC = (400,000n /S ) + 200

AC = (400,000*n/ 20,000) + 200

AC = 20*n + 200

C)

40000 20000 500 1500 1000 Average cost O Number of firms II

Slope of this function is positive, as number of firms increase, each firm gets less of the market share, so the Production cost increase , gains of internal Economies of scale could not realised.