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A monopolist faces a market demand curve given by
Demand: Q = 70 - P
such that the marginal revenue curve is MR = 70 - 2Q

The monopolist faces the following cost structure:
C = .25Q^2 - 5Q + 300
such that the marginal cost curve is MC = .5Q - 5

What output level will the monopolist choose in order to maximize profits? What is the price at this output level? What are the monopolist's profits? What is the deadweight loss (in dollars)? Why does deadweight loss arise?

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This solution helps with a microeconomics problem. Concepts covered include profit maximization, output level price, monopolist profits, and deadweight loss.

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Exercise Set 9

1) Monopoly
A monopolist faces a market demand curve given by
Demand: Q = 70 - P
such that the marginal revenue curve is MR = 70 - 2Q

The monopolist faces the following cost structure:
C = .25Q2 - 5Q + 300
such that the marginal cost curve is MC = .5Q - 5

What output level will the monopolist choose in order to maximize profits? What is the price at this output level? What are the monopolist's profits? What is the deadweight loss (in dollars)? Why does deadweight loss arise?

For profit maximization, the rule is MC=MR, doing that we get
70-2Q=0.5Q-5
Solving we get
Q=30 and
P=70-Q= 70-30=40
Profit = Total Revenue (TR) - Total Cost (TC)
TC= 0.25*30^2-5*30+300=375
TR=P*Q=30*40=1200
Profits = 1200-375 =825

Production under perfect competition, MR =MC=P
Thus we have 70-Q=0.5Q-5, Solving we get Q=50, P=20

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