Question

In: Economics

Scenario A: A monopolist faces the following demand curve, marginal revenue curve, total cost curve for its product:

Q=3500-5p

MR= 250-Q

TC=15Q

MC=100

What level of output maximizes total revenue?
What is the profit maximizing level of output?
What is profit maximizing price?
How much profit does the monopolist earn?
Suppose that a tax of $10 for each unit produced is imposed by state government. What is the profit maximizing level of output.

Solutions

Expert Solution

(a)

P = (3500 - Q)/5 = 700 - 0.2Q

TR = PQ = 700Q - 0.2Q2

Reveue is maximized when MR = dTR/dQ = 0

700 - 0.4Q = 0

Q - 700/0.4 = 1750

(b)

Profit is maximized when MR = MC.

700 - 0.4Q = 100

0.4Q = 600

Q = 1500

(c)

P = 700 - 0.2 x 1500 = 700 - 300 = 400

(d)

TR = 400 x 1500 = 600,000

TC = 15Q = 15 x 1500 = 22,500

Profit = TR - TC = 600,000 - 22,500 = 577,500

(e)

Tax increases MC by $10 and new MC = 10 + 100 = 110

Setting MR = new MC,

700 - 0.4Q = 110

0.4Q = 590

Q = 1475

Rahul Sunny answered 1 year ago

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