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A Firm with Market Power Faces the Demand Function Q

question 67

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A firm with market power faces the demand function q = 2,000 - 20P. The firm's total cost function is TC(q) = 20q + 0.02q2 + 2,000.
a. If the firm behaves as a single-price monopoly, what are its optimal price and output level?
b. Demonstrate that the single-price monopolist's profit-maximizing choice of price and output also maximize producer surplus.
c. Identify the output level that would maximize total surplus.
d. Identify the output level that a perfectly price-discriminating monopolist would produce.


Definitions:

Semi-Annually

Occurring twice a year, typically every six months.

Face Value

The nominal or dollar value printed on a security or bond, representing the amount that will be paid back at maturity, not including interest.

Coupon Rate

The interest rate a bond pays each year, shown as a percentage of its face value.

Yield To Maturity

The total return expected on a bond if it is held until the date it matures, including both interest payments and the difference between the bond's current market price and its face value.

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