Question

As the manager of a monopoly, you face potential government regulation. Your inverse demand is P = 55 - 2Q, and your cost are C(Q) = 11Q.

a. Determine the monopoly price and output.

Monopoly price : $____

Monopoly output: ___ Units

b. Determine the socially efficient price and output.

Socially efficient price: $____

Socially efficient output: ___ units

c. what is the maximum amount your firm should be willing to spend on lobbying efforts to prevent the price from being regulated at the socially optimal level?

$___

Answer 1

Given P=55-2Q

Total Revenue=TR=P*Q=(55-2Q)*Q=55Q-2Q²

Marginal Revenue=MR=dTR/dQ=55-4Q

Total Cost=C(Q)=11Q

Marginal Cost=dTC/dQ=11

a. Determine the monopoly price and output.

Set MR=MC for profit maximization

55-4Q=11

4Q=44

Q=11

P=55-2Q=55-2*11=$33

Monopoly price : $33

Monopoly output: 11 Units

b. Determine the socially efficient price and output.

Socially efficient price is equal to marginal cost

i.e. P=$11

P=55-2Q

11=55-2Q

Q=22

Socially efficient price: $11

Socially efficient output: 22 units

c. What is the maximum amount your firm should be willing to spend on lobbying efforts to prevent the price from being regulated at the socially optimal level?

Let us calculate the profit at monopoly prices

Total Revenue=TR=P*Q=33*11=$363

Total Cost=TC=11*Q=11*11=$121

Profit=TR-TC=363-121=$242

Let us calculate the profit at socially efficient level

Total Revenue=TR=P*Q=11*22=$242

Total Cost=TC=11*Q=11*22=$242

Profit=TR-TC=242-242=$0

Decrease in profit=242-0=$242

Maximum amount that can be spent on lobbying=Decrease in profit=$242