Business

Contents

Question 1 2

A. 2

B. 3

C. 3

D. 3

Question 2 4

A. 4

B. 4

C.. 4

D. 5

Question 3 5

A. 5

B. 5

C. 6

Question 4 6

A. 6

B. 7

C. 8

D. 8

Question 5 9

Question 1

Given the two firms (Firm 1 and Firm 2) sell an identical product, compete over output rather than price, and decide simultaneously how much to produce, we can understand their behaviour from the perspective of the Cournot Model.

We also know from the question that the marginal cost is $20 (MC=20) and the fixed cost is 0 (FC=0). What’s more, the linear demand curve is P=a-bQ where a=80 and b= 13

A. Determine the equilibrium output level for each firm

Our duopolists face the following market demand curve:

P = 80 - 13 Q

Where Q is the total production of both firms (i.e., Q=Q1+Q2). Also, suppose that both firms have marginal costs of 20:

MC1=MC2=20

We can determine the reaction curve for Firm 1 as follows. To maximize profit, it sets marginal revenue equal to marginal cost. Its total revenue R1 is given by

TR1=PQ1= (80 - 13 Q) Q1

=80Q1- (Q1+Q2)3Q1

=80Q1- 13Q12- 13Q1Q2

Its marginal revenue MR1 is just the incremental revenue ∆R1 resulting from an incremental change in output ∆Q1:

MR1=∆R1/∆Q1=80 - 23Q1- 13Q2

Now, setting MR1 = MC1 =20(the firm’s marginal cost) and solving for Q1, we find

Firm 1’s reaction curve: Q1=90 - 12Q2

The same calculation applies to Firm 2:

Firm 2’s reaction curve: Q2=90 - 12Q1

Therefore, the equilibrium output levels are the values for Q1 and Q2 at the intersection of the two reaction curves-i.e. the levels that solve the above two equations. By replacing Q2 in Firm 1’s reaction curve by the expression from the Firm 2’s reaction curve, we get:

Q1=90- 12(90 - 12Q1)

Therefore,

Cournot equilibrium (Equilibrium Output Level): Q1=Q2=60

Note that, in this question, we have assumed that the two firms compete with each other; otherwise, the two firms could collude, resulting...