Suppose two firms ( Firm 1 and Firm 2) are competing against each other in a ( d

Question

Suppose two firms ( Firm 1 and Firm 2) are competing against each other in a ( duopoly) market. Suppose further that the demand is given by the equation P= 700-30(q1+q2), where P is the price of the good, q1 is the quantity sold by firm 1, and q2 is the quantity sold by firm 2. Assume that the total cost of production for firm 1 is 100q1, and 100q2 for firm 2 ( meaning that the additional costs to serve one customer is $100 for each firm).

a) Assuming each firm moves simultaneously, find the Nas-Cournot Equilibrium level of output for each firm. Show all of your work.

b) Assuming each firm moves sequentially, find the Nas-Stackelberg Equilibrium level of output for each firm. Show all of your work.

Explanation / Answer

a) Profit for firm1: q1(700-30q1-30q2) - 100q1

Maximize this with respect to q1, differentiating above equation w.r.t q1,

700-60q1-30q2 - 100 =0

2q1+q2=20 ----(1)

profit for firm2: q2(700-30q1-30q2) -100q2

Maximize this with respect to q2, differentiating above equation w.r.t q2,

700-30q1-60q2 -100 =0

q1 + 2q2 =20 - - - -(2)

Solving equations (1) and (2),

q1=20/3

q2=20/3

This is the nash equilibrium.

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