Exam 5: Demand

Fred has a Cobb-Douglas utility function with exponents that sum to 1. Sally consumes the same two goods, but the two goods are perfect substitutes for her. Despite these differences, Fred and Sally have the same price offer curves.

Let w be the number of whips and j the number of leather jackets. If Kinko's utility function is U(x, y) = min{ 7w, 4w + 12j}, then if the price of whips is $20 and the price of leather jackets is $40, Kinko will demand

Ms. Laura Mussel's preferences between golf and tennis are represented by U(g, t) = gt, where g is the number of rounds of golf and t is the number of tennis matches she plays per week. She has $24 per week to spend on these sports. A round of golf and a tennis match each cost $4. She used to maximize her utility subject to this budget. She decided to limit the time she spends on these sports to 16 hours a week. A round of golf takes 4 hours. A tennis match takes 2 hours. As a result of this additional constraint on her choice,

Alfredo lives on apples and bananas only. His utility function is U(a, b) = min{a + b, 2b}. He maximizes his utility subject to his budget constraint and consumes the bundle (a, b) = (4, 4).

Mickey is considering buying a tape recorder. His utility function is U(x, y, z) = x + f(y)z^.5, where x is the amount of money he spends on other goods, y is the number of tape recorders he buys, and z is the number of tapes he buys. Let f(y) = 0 if y < 1 and f(y) = 8 if y is greater than or equal to 1. The price of tape recorders is $20, the price of tapes is $1, and Mickey can easily afford to buy a tape recorder and several tapes. Will he buy a tape recorder?

A rational consumer spends her entire income. If her income doubles and prices do not change, then she will necessarily choose to consume twice as much of every good as she did before.

Natalie consumes only apples and tomatoes. Her utility function is U(x, y) = x²y⁸, where x is the number of apples consumed and y is the number of tomatoes consumed. Natalie's income is $320, and the prices of apples and tomatoes are $4 and $3, respectively. How many apples will she consume?

An inferior good is less durable than a normal good.

Casper's utility function is 3x + y, where x is his consumption of cocoa and y is his consumption of cheese. If the total cost of x units of cocoa is x², the price of cheese is $10, and Casper's income is $260, how many units of cocoa will he consume?

Katie Kwasi's utility function is U(x₁, x₂) = 5(ln x₁) + x₂. Given her current income and the current relative prices, she consumes 10 units of x₁ and 15 units of x₂. If her income doubles, while prices stay constant, how many units of x₁ will she consume after the change in income?

Miss Muffet insists on consuming 2 units of whey per 1 unit of curds. If the price of curds is $5 and the price of whey is $6, then if Miss Muffet's income is m, her demand for curds will be

Marie's utility function is U(x, y) = min{ 3x + 2y, 2x + 5y}, where x is the number of units of sugar she consumes and y is the number of units of spice she consumes. She is currently consuming 12 units of sugar and 40 units of spice and she is spending all of her income. a. Draw a graph showing her indifference curve through this point. b. The price of spice is $1. In order for this to be her consumption bundle, what must the price of sugar be and what must her income be?

In economic theory, the demand for a good must depend only on income and its own price and not on the prices of other goods.

Is the following statement true or false? "If consumers spend their entire incomes, it is impossible for the income elasticity of demand for every good to be bigger than 1." Write a brief but convincing explanation of your answer.

It is impossible for a person to have a demand curve that slopes upward at all prices.

Define each of the following: a. Inverse demand function b. Engel curve

Daisy received a tape recorder as a birthday gift and is not able to return it. Her utility function is U(x, y, z) = x + z f(y), where z is the number of tapes she buys, y is the number of tape recorders she has, and x is the amount of money she has left to spend. f(y) = 0 if y < 1 and f(y) = 8 if y is 1 or greater. The price of tapes is $1 and she can easily afford to buy dozens of tapes. How many tapes will she buy?

Fred consumes pork chops and lamb chops and nothing else. When the price of pork chops rises with no change in his income or in the price of lamb chops, Fred buys fewer lamb chops and fewer pork chops.

If preferences are homothetic, then the slope of the Engel curve for any good will decrease as income increases.