Suppose that the monopolist faces a linear demand curve, P(Q) = A – BQ. Further suppose that the monopolist has the marginal cost function: MC = Q. 1. Find the revenue as a function of Q. 2. Find the marginal revenue as a function of Q. 3. Find the quantity that maximizes the monopolist's profit as a function of A and B.

Micro Economics For Today
10th Edition
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Chapter9: Monopoly
Section: Chapter Questions
Problem 15SQ
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Pls solve sub questions 1, 2 and 3 only
Suppose that the monopolist faces a linear
demand curve, P(Q) = A — BQ. Further
suppose that the monopolist has the marginal
cost function: MC = Q.
1. Find the revenue as a function of Q.
2. Find the marginal revenue as a function of Q.
3. Find the quantity that maximizes the
monopolist's profit as a function of A and B.
4. Find the equilibrium price as a function of A
and B.
5. Let's use some numbers. Suppose A
= = 10
and B = 2. Solve for the profit-maximizing
quantity and price.
6. Using A = 10 and B = 2, draw a demand
curve and a marginal revenue function as
well as marginal cost. Shade the deadweight
loss. Also label clearly the profit-maximizing
quantity and price chosen by the monopolist.
7. What would have been the competitive
equilibrium price and quantity (hint: equate
MC and the demand function)? Label the
competitive equilbrium point. Also compute
the size of the deadweight loss due to
inefficiency casued by the monopolist
behavior.
Transcribed Image Text:Suppose that the monopolist faces a linear demand curve, P(Q) = A — BQ. Further suppose that the monopolist has the marginal cost function: MC = Q. 1. Find the revenue as a function of Q. 2. Find the marginal revenue as a function of Q. 3. Find the quantity that maximizes the monopolist's profit as a function of A and B. 4. Find the equilibrium price as a function of A and B. 5. Let's use some numbers. Suppose A = = 10 and B = 2. Solve for the profit-maximizing quantity and price. 6. Using A = 10 and B = 2, draw a demand curve and a marginal revenue function as well as marginal cost. Shade the deadweight loss. Also label clearly the profit-maximizing quantity and price chosen by the monopolist. 7. What would have been the competitive equilibrium price and quantity (hint: equate MC and the demand function)? Label the competitive equilbrium point. Also compute the size of the deadweight loss due to inefficiency casued by the monopolist behavior.
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