Question

In: Economics

1. Assume that a monopolist has T C(Q) = 22Q and the market demand is P(Q)...

1. Assume that a monopolist has T C(Q) = 22Q and the market demand is P(Q) = 50 − 2Q.

(a) What is the firm’s marginal cost?

(b) What is the profit-maximizing price and quantity (P ∗ , Q∗ )?

(d) What is the total cost at (P ∗ , Q∗ )?

(e) What is the profit at (P ∗ , Q∗ )?

(f) What is the consumer surplus at (P ∗ , Q∗ )?

(g) What is the deadweight loss at (P ∗ , Q∗ )?

2. Assume that a monopolists sells a product in the shortrun with a total cost function

STC(Q) =

{125 + 44Q + Q² Q > 0

{108 Q = 0

The market demand curve is given by the equation P(Q) = 80 − 2Q.

(a) Find the marginal cost for the firm.

(b) Find the profit-maximizing output and price (P ∗ , Q∗ ).

(d) Does the monopolist want to stay in business?

3. Assume that a monopolist has TC = 13 + 28Q + Q² and the market demand is P(Q) = 100 − 2Q.

(a) What is the profit-maximizing price and quantity (P ∗ , Q∗ )?

(b) What is the marginal cost at Q∗ ?

(d) Verify that the IEPR holds

Solutions

Expert Solution

Q1)

a) Marginal cost is the addition to the total cost when an additional unit of output is produced. It can be calculated by differentiating the total cost function with respect to quantity produced. So,

Total cost = 22Q

Differentiating this with respect to Q,

Marginal cost = 22 is the answer.

b) A monopolist maximizes its profit at the point where marginal revenue is equal to marginal cost. Marginal revenue is the addition to the total revenue when an additional unit of output is sold. It can be calculated by differentiating the total revenue function with respect to Q.

Total revenue = price x quantity

= (50 - 2Q) x Q

= 50Q - 2Q²

Differentiating this with respect to Q to get the marginal revenue function,

Marginal Revenue = 50 - 4Q

Equating marginal revenue with marginal cost to get the price and quantity,

50 - 4Q = 22

4Q = 50 - 22

4Q = 28

Q = 28/4 = 7 is the answer.

P = 50 - 2Q

P = 50 - 2(7)

P = 50 - 14 = 36 is the answer.

c) Total Revenue = price x quantity

= 36 x 7

= 252 is the answer.

d) Total cost = 22Q

= 22 x 7

= 154 is the answer.

e) Profit = total revenue - total cost

= 252 - 154

= 98 is the answer.

Rahul Sunny answered 1 year ago

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