Derive an expression for the monopolist optimal quantity

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1. assume a monopolist faces the market demand function P = a - bQ. Its marginal cost is given by MC = c + eQ. Assume that a > c and 2b + e > O.
a) Derive an expression for the monopolist's optimal quantity and price in terms of a, b, c, and e.
b) Show that an increase in c (which corresponds to an upward parallel shift in marginal cost) or a decrease in a (which corresponds to a leftward parallel shift in demand) must decrease the equilibrium quantity of output.
c) Show that when e 2:: 0, an increase in a must increase the equilibrium price.

2. A monopolist serves a market in which the de¬mand is P = 120 - 2Q. It has a fixed cost of 300. Its marginal cost is 10 for the first 15 units (MC = 10 when 0 ≤ Q ≤ 15). If it wants to produce more than 15 units, it must pay overtime wages to its workers, and its mar¬ginal cost is then 20. What is the maximum amount of profit the firm can earn?

3. Suppose that demand and supply curves in the market for corn are Qd = 20,000 - SOP and QS = 30P. Suppose that the government would like to see the price at $300 per unit and is prepared to artificially increase demand by initiating a government purchase program. How much would the government need to spend to achieve this? What is the total deadweight loss if the government is successful in its objective?

Reference no: EM1369885

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