Question

Suppose there are now only two firms in the market, Raleigh and Dawes. The inverse market demand curve for bikes is given by P(Y)=200-2Y. Both firms have the same total cost function as follow: TC(Y)=12Y+6. Suppose this market is a Stackelberg oligopoly and Raleigh is the first mover. Find how much does each firm produce, what is the price on the market and how much profit does each firm earn. Dawes offers to Raleigh to collude and to agree on the quantity to produce and deliver on the market. Study this possibility and find the conditions for the two firms to find an mutually beneficial agreement. In answering the above make sure you fully explain your reasoning

Answer 1

P = 200 - Y

MC = 12

Leader output = ( a-c)/2b

= (200 - 12)/2*2

= 47

Follower output = (a-c)/4b

= 188/8

= 23.5

Total Output = 47 +23.5

= 70.5

P = 200 - 2(70.5)

= 59

Profit of leader = TR - TC

= 59*47 - 12(47) -6

= 2203

Profit of follower = 23.5*70.5 - (23.5)12-6

= 1368.75

Collusive market:

TR = 200Q - 2Q^2

MR = 200 - 4Q

MC =12

MR=MC

200 - 4Q = 12

188 = 4Q

Q = 188/4

= 47

P = 200 - 2(47)

= 106

Profit = 106*47 - 12*47 - 6

= 4412

each firm profit = 2206

Both firms are earning profit larger than Stackbelberg Model. Hence, it is mutually beneficial to form collusion,