Given Q =120- 10P and TC = 90 + 2Q for an oligopolistic firm, determine mathemat
ID: 2495182 • Letter: G
Question
Given Q =120- 10P and TC = 90 + 2Q for an oligopolistic firm, determine mathematically the output at which the firm maximizes its (a) total profits, and calculate P, TR. and pi; (b) total revenue, and calculate P. TR. and pi; and (c) total revenue, and calculate P. TR, and pi if the firm faces the total profit for constraint of $155. Journal of Economic Literature (December 1998), pp. 1947-1982. Shepherd. William G., The Economics of Industrial Organization (Upper Saddle River, N.J.: Prentice-Hall. 2004). Global corporations and their strategic behavior are examined in:Explanation / Answer
Demand function
Q = 120 - 10P
& TC = 90+2Q
10P = 120 - Q
P = 12 - 0.1Q
Profit = Revenue - total cost
Revenue = Price X quantity
R = (12-0.10Q)Q
R = 12Q - 0.1Q2
Marginal revenue = 12 - 0.2Q
The profit maximzing output is found by equating marginal revenue = marginal cost
TC = 90+2Q
MC = 2
12 - 0.2Q = 2
0.2Q = 10
Q = 50 units
Profit maximizing price = 12 - 0.1Q
Price = $ 7
Profit = $ 7 x 50 - [ 90+2X50]
Profit = $ 160
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If the firm faces a profit constraint of $ 155
$ 155 = P X 50 - [ 90 + 2 X 50]
$ 155 = 50P - 90 - 100
155 = 50P - 190
50P = 345
P = $ 6.90
Total revenue = $ 6.90 X 50
TR = $ 345
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