Question

In: Economics

3. Let demand for car batteries be such that Q = 10 − 2P. Assume constant...

3. 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

(a) A perfectly competitive firm

(b) A monopoly

(c) Two firms engaged in Cournot Competition.

(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?

Expert Solution

The demand function is Q=10-2P.

The marginal cost is given at 3.

Inverse demand function is P=5-(1/2)Q

a. In perfect competition equilibrium takes place at the point where P=MC.

So, price level is $3, quantity is 4 units, consumer surplus is $4 and producer surplus is 0.

b. In monopoly equilibrium is achieved when MR=MC

So,in monopoly price is $4, quantity is 2 units, consumer surplus is $1 and producer surplus is $2.

In duopoly there are two firms A and B. revenue function for both will be different.

Now,

So, quantity of both firms is 1.33 units.

Now, we can find price.

So, in Cournot's duopoly the quantity of both firms is 1.33 units each or total market supply is 2.66 units and the price is $3.67. While the consumer surplus is $1.76 and producer surplus is $1.78.

d. Here, it is duopoly but both firms have different marginal cost. In stackelberg competition when a firm has lower marginal cost it becomes the leader and the other firm is the follower firm. The equilibrium will take place at the point where the best response curve of the follower firm intersects with profit curve of the leader.

Now,

So, quantity of firm A is 3 units while that of firm B is 0 units.

Now, we can find price, consumer surplus and producer surplus.

So, quantity of firm A is 3 units, that of firm B is 0 units and price is $3.5. While consumer surplus is $2.25 and producer surplus is $1.5.

Rahul Sunny answered 2 years ago

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