Question

Joint profit maximizing level of output

Consider two firms facing the demand curve 17 P#90-SQ. where Q Q1+Q2. The firms' cost functions are C1 (91) -10+50, and c2(Q2)#5+10Q2. Suppose that both firms have entered the industry. What is the joint profit-maximizing level of output? How much will each firm produce? Combined, the firms will produce units of output, of which Firm 1 will produce ] units and Firm 2 will produce □ units. (Enter a numeric response using a real number rounded to two decimal places.) 12 3 4567 8 9 10 11 12 13 14 15 16 17 18 Firm 2's output What is each firm's equlibrium output and profit if they behave noncooperativey? Use the Cournot model. If the firms compete, then Firm 1 will produceunits of output and Fim 2 will produce units of output

Answer 1

Given, two firms facing the demand curve P = 90 - 5Q Q = Q_1 + Q_2 The firms cost functions are, C_1(Q_1) = 10 + 5Q_1 C_2(Q_2) = 5 + 10 Q_2 If both firms enter the market, and they collude, they will face a marginal revenue curve with twice the slope of the demand curve. MR = 90 - 5 Q Setting marginal revenue equal to the marginal cost (the marginal cost of firm 1, since it is lower than of the firm 2) to determine the profit- maximizing quantity, Q: 90 - 5 Q = 5 = > 5 Q = 85 Q = 85/5 therefore Q = 17 \r\n Substituting Q = 17 into the demand function to determine the price: P = 90 - 5 Q = 90 - 5(17) = 90 - 85 P = 5 Now the question is how the firm will the total output of 4 among . Since the two firm have different cost functions, it