Question

In: Economics

3. Suppose a monopoly firm faces demand for its product of ? = 12 − 2?...

3. Suppose a monopoly firm faces demand for its product of ? = 12 − 2? and has total cost ?? = 8 + 4?. Its

production process, however, generates a pollution side effect that imposes a total cost on all others of 2?.

a. Before any correction for external costs, identify….the total revenue function of the firm.

TR = _________________________________________

b. ... the marginal revenue function of the firm. MR = _________________________________________

c. … the marginal cost function of the firm. MC = ______________________________

d. … the profit-maximizing quantity and price for the firm?

Q = _______________________

P = _______________________

Solutions

Expert Solution

In absence of any correction for external cost,

a)

We are given

P=12-2Q

TR=P*Q=(12-2Q)*Q=12Q-2Q2

TR=12Q-2Q2

b)

Marginal Revenue can be obtained by differentiating TR with respect to Q, we get

MR=dTR/dQ=12-4Q

MR=12-4Q

c)

We are given TC=8+4Q

Marginal Cost can be determined by differentiating TC with respect to Q, we get

MC=dTC/dQ=4

MC=4

d)

Set MR=MC for profit maximization

MR=MC

12-4Q=4

4Q=8

Q=2

P=12-2Q=12-2*2=8

Profit maximizing

Q=2 units

P=8

Rahul Sunny answered 2 years ago
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