Consider two firms facing the demand curve P = 90-5Q, where Q = Q1 + Q2. The fir
ID: 1146795 • Letter: C
Question
Consider two firms facing the demand curve P = 90-5Q, where Q = Q1 + Q2. The firms' cost functions are C1 (Q1) = 20 + 15Q1 and C2 (02) -10+3002 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 produceunits. (Enter a numeric response using a real number rounded to two decimal places.) What is each firm's equilibrium output and profit if they behave noncooperatively? Use the Cournot model. If the firms compete, then Firm 1 will produce [ units of output and Firm 2 will produce l-1 units of output. Draw the firms' reaction curves and show the equilibrium.Explanation / Answer
Profit function for Firm 1
1= (90-5Q)×Q1-20-15Q1
=90Q1-5Q1^2-5Q1×Q2-20-15Q1
=75Q1-5Q1^2-5Q1×Q2-20
Finding profit maximising output by calculating FOC
75-10Q1-5Q2=0
7,5-0.5Q2=Q1
Similarly for firm 2
2=P×Q2-C(Q2)=90Q2-5Q2^2-5Q1×Q2-10-30Q2
FoC will be
90-10Q2-5Q1-30=0
60-5Q1=10Q2
6-0.5Q1=Q2
We know 7.5-0.5Q2=Q1 substituting q1 into above equation
6-0.5(7.5-0.5Q2)=Q2
6-3.75+0.25Q2=Q2
2 25=0.75Q2
Q2=3
And Q1=6
Hence they will produced 9 units in total
Firm1 will produce 6 units and Firm 2 will produce 3 units.