Question

Question 13a: On the same graph, draw the typical Best Response Functions (BRF) for two Cournot firms. Question 13b: Draw the effect of a reduction in firm one's marginal costs on its BRF in the above graph.

Answer 1

Answer 13a :-

(4- 0419२) ga (Qu करे।

Latest understand the concept of best response function by looking at the above graph where there are two firms represented by firm 1 and firm 2 and producing Q1 and Q2 quantities respectively . The firms are choosing output simultaneously and neither firm knows the others output before choosing its own.

Max : P*Q -c*q1

Where P = a-b *Q ,

and Q = q1 + q2 and

c = the marginal cost of the specific firm .

So substitute in the equations for P and Q to get :-

Max :( a-b ( q1+q2))q1-cq1

Or Max :(aq1 - bq²₁ - bq1q2 - cq1)

$\\partial$Max /$\\partial$q1 : a-2bq1-bq2-c =0

Best response function :-

q1 = ((a-c)-bq2)/2b

Answer 13b :-

(4-0)

In the above graph there are two firms, firm 1 and firm 2 producing goods Q1 and Q2 respectively . In the cournot's model ,a firm's best response function comes from MR =MC. If MC Falls then the firms best response function will shift. Now let us consider that firm two's marginal cost has been lowered. The best responses to the above situation is that firm one will not change its best response however the firm two's marginal cost curve has decreased ,however its marginal revenue curve remains unaffected .So firm 2 will shift its best response function to the right it as it will want to produce more than before for any given level of firms one's output. This will shift the Nash cournot equilibrium from E1 to E2 As given in the graph above.