Question

2. Question 2

Consider two firms (A and B) engaging in Cournot Competition. Both firms face an inverse market demand curve P(Q)=700-5Q, where Q=qA+qB. The marginal revenue curve for firm A is MRA=700-10qA-5qB and the marginal revenue curve for firm B is MRB=700-10qB-5qA. The firms have identical cost functions, with constant marginal cost MC=20.

A) Determine the profit function for firm A and firm B.

B) Solve for the best-response functions of both firms.

C) Determine the equilibrium quantities both firms will supply, and the corresponding market price.

D) Suppose both firms could collude. Determine the equilibrium price and quantity produced by both firms (assume both firms split the quantity supplied to the market equally).

E) Find the level of dead-weight loss associated with parts C) and D). Which equilibrium has a larger amount of dead-weight loss? Why?

Answer 1

Q2) answering only first four parts are mandatory

P = 700 - 5Q

A) πA = (P-MC)qA

= (700-5qA- 5qB - 20)qA

= (680-5qB)qA - 5qA²

πB = (680-5qA)qB - 5qB²

B) for BR function

^{dπA/dqA = 0}

^{(680-5qB) = 10qA}

qA= (680-5qB)/10

similarly BR^{​​​​​B}(qA) :

qB = (680-5qA)/10

C) at eqm, two BR curve cuts

qA = 68 -.5(68 - .5qA)

qA = 68- 34 +.25qA

.75qA = 34

qA* = 45.33,

qB* = 45.33

Q= 90.66

P = 700-5*90.66

= 246.667

D) collusion is monopoly outcome

MR = MC

700-10Q = 20

Q* = 68

P* = 700-5*68 = 360