Question

Let demand for car batteries be such that Q = 10 − 2P. Assume constant marginal costs of 3. Compute the equilibrium price, quantity, consumer surplus, producer surplus for

(d) Assume one of the two firms has a marginal cost of 4. What is the oligopoly outcome in this case? [Hint you can’t use the trick we used to get a second equation.]

(e) (Hard question) Suppose a discount factor of 0.96 and a duopoly structure on agreements, that is all agreements involve identical output levels from all firms. What is the Pareto frontier of agreements that may form the basis of a cartel?

Answer 1

Quantity	P = AR	TR	MR
1	4.5	4.5	-
2	4	8	4.5
3	3.5	10.5	2.5
4	3	12	1.5
5	2.5	12.5	0.5
6	2	12	(0.5)
7	1.5	10.5	(1.5)
8	1	8	(2.5)
9	0.50	4.50	(3.5)
10	0.25	2.50	(2)

We derive the above table from the demand function.

MC of firm = 3

Equilibrium output will be 2 units because at 2 units MR > MC

Profit of firm will be 8-6. 2

Answer d :-

When they combine production :-

Average marginal cost will be 3+4 /2= 3.5

Total profit = 8-(3.5*2) =1

When they do not combine production :-

Firm 1 profit = 4.5-3=1.5

Firm 2 profit = 4.5-4=1

Total profit =1.5 +1 =2.5

Thus loss of producer welfare = 2.5- 1 = 1.5

Answer e :-

in the above question, the criteria of discounting factor will not work because a firm produces that level of output where it's MR >= MC

In the given question even when firms are producing individually with MC = 3 , 4 or combination MC =3.5

In all three cases the equilibrium output will be when the firm produces less than three units