. Assume that two companies (A and B) are duopolists who produce identical produ
ID: 1244195 • Letter: #
Question
. Assume that two companies (A and B) are duopolists who produce identical products. Demand for the products is given by the following linear demand function: P = 200 Qa - Qb Where Qa and Qb are the quantities sold by the respective firms and P is the selling price. Total cost functions for the two companies are: TCa = 1,500 + 55Qa + Q^2a TCb = 1,200 + 20Qb + 2Q^2b . Assume that the firms act independently as in the Cournot model (i.e., each firm assumes that the other firm s output will not change). B. Determine Firm A, Firm B, and total industry profits at equilibrium solution found in Part (a). the price established in part (a) is $145Explanation / Answer
Answer: TCa = 1,500 + 55Qa + Q^2a , and , TCb = 1,200 + 20Qb + 2Q^2b Let us solve it out now: 1500 + 55Q + Q^2 = 1200 + 20 Q + 2Q^2 2Q^2 - Q^2 + 20 Q - 55Q + 1200 - 1500 Q^2 - 35 - 500 Solve the equation quadratically, and you will get an answer of - 25 & 60 , so the answer is 60 . P: 200 - 60 - 60 = 80 Total profit: 80 * 60 + 80 * 60 = 9600 IF price was 145 then : 145 * 60 * 2 = 17400
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