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Utility maximization. (14 points) GLS Ch4.app P3. Suppose that there are two goods (X and Y). The price of X is $2 per unit, and the price of Y is $1 per unit. There are two consumers (A and B). The utility functions for the consumers are UA(X, Y ) = X 0.5Y 0.5 UB(X, Y ) = X 0.8Y 0.2 Consumer A has an income of $100, and Consumer B has an income of $300.
(a) Solve the constrained utility-maximization problems for Consumer A and Consumer B.
(b) Calculate the marginal rate of substitution for each consumer at his or her optimal consumption bundles. 1
(c) Suppose that there is another consumer (let's call her C). You don't know anything about her utility function or her income. All you know is that she consumes both goods. What do you know about C's marginal rate of substitution at her optimal consumption bundle? Why?
Assume that two companies (C and D) are duopolists that produce identical products. Demand for the products is given by the following linear demand function: P = 600 Â- Qc- Qd Where Qc and Qd are the quantities sold by the respective firms and P i..
Competitive Firm Suppose the competitive market price is $84, and a competitive firm's total costs = 4q2 - 4q + 100 and marginal cost = 8q - 4. a. Solve for the profit-maximizing (or loss minimizing) quantity (q*).
A manufacturer of air-conditioning systems expects to sell 10,000 units next year if the economy recovers from the present recession. If the economy remains at its present state, the firm expects to sell 7,000 units, and if the recession worsens.
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The capital stock of the firm consists of three machines of various vintages, all in excellent condition. All machines can be running at the same time. COST OF PRINTING AND BINDING PER BOOK MAXIMUM TOTAL CAPACITY (BOOKS) PER MONTH MACHINE 1 $1.00 ..
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If Wachovia bank receives a $10,000 deposit, and the required reserve ratio is 0.10 (= 10%), how much can the bank loan out? Assume that Wachovia keeps zero excess reserves and only keeps the required minimum reserves.
The Teenager Company makes and sells skateboards at an average price of $70 each. During the past year, they sold 4,000 of these skateboards. The company believes that the price elasticity for this product is about -2.5. If it decreases the price ..
Is the "immigration issue" one of demographics? Evaluate the chances of a "comprehensive immigration policy" turning away from racial and ethnic quota towards "opportunities not burdens."
Over another range of prices, the price elasticity of demand varies from 1.5 to 0.75. What can you say about total revenue and the total revenue curve over these two ranges of demand curve as price fall
Ford offers a 3-year or 36,000 mile warranty on the Explorer car. Consumers must pay for extended warranties beyond the manufacturer's warranty period. The Auto Club offers an extended warranty for a Ford Explorer in Hanover, New Hampshire, at a p..
Michael Illitch bought the Detroit Tigers in 1992 for $82 million, which amounted to $114.15 million in 2005 dollars. by 2005, the Tigers were worth $292 million. Calculate the real compound annual rate of return on that investment.
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