Doc Brown has decided to manufacture and sell Mr. Fusion home energy reactors. In the present,...

Doc Brown has decided to manufacture and sell Mr. Fusion home energy reactors. In the present, he is the only seller (but in the future, manufacturers are ubiquitous). Doc’s company faces the following demand curve: Q=80-2P

He can produce Mr. Fusions at a constant marginal cost of 5 bitcoins.
a) (5) How many Mr. Fusions will Doc sell and at what price? Circle your answers.

b) (10) Suppose the government puts in a price ceiling at 6 bitcoins. What does the price ceiling do to his marginal revenue curve? What is MR of the 10th, 68th, and 69th units? Circle your answers.

c) (5) How many Mr. Fusions will Doc sell and at what price with the price ceiling in place? Circle your answers.

d) (10) Compare the deadweight loss of the unregulated company with the deadweight loss from the regulated (price ceiling) company. Does the price ceiling increase social welfare?

Solutions

Expert Solution

Ans. Q= 80-2P

Revenue = Q*P = 80P - 2P^2

For max quantity, we differentiate, we get

80- 4P = 0

P = 20 and Q = 40

a) Mr Fusion will sell 40 units at 20 bitcoins per unit.

b) When price ceiling is imposed at 6 bitcoins, then the marginal curve will shift downwards and it will be a horizontal line at P=6

At P= 6, he can sell 68 units, so marginal revenue of 10th and 68th unit will be 6 bitcoins.

But to sell 69 units, he will have to keep price at 5.5/unit, so his marginal revenue will be 5.5 bitcoins.

c) He will sell 68 units at price ceiling as Q = 80-2P

Q= 80 - 2*6 = 68 units

d) Deadweight loss in regulated market is less than that in the unregulated market as in in unregulated market the monopoly tries to maximize it's profit so many consumers can't participate whose utility is less than the price set by monopoly. But when price ceiling is imposed, the Deadweight loss decreases. The Deadweight loss is zero when P= MC.

Rahul Sunny answered 1 year ago

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