Exam 4: Choice

Charlie's utility function is U(x_A, x_B) = x_Ax_B. If Charlie's income is $40, the price of apples is $4, and the price of bananas is $2, how many apples are there in the best bundle that Charlie can afford?

Ambrose's utility function is U(x₁, x₂) = . If the price of nuts (good 1) is $1, the price of berries (good 2) is $5, and his income is $145, how many units of nuts will Ambrose choose?

If a consumer maximizes her preferences subject to her budget by choosing a consumption bundle where the ratio of her marginal utilities of shelter and food, , is greater than the ratio of the prices of shelter and food, , then she must

Max Gross has the utility function U(x, y) = max{x, y}. If the price of x is the same as the price of y, Max will buy equal amounts of x and y.

Charlie has a utility function U(x_A, x_B) = x_Ax_B, the price of apples is $1, and the price of bananas is $2. If Charlie's income were $120, how many units of bananas would he consume if he chose the bundle that maximized his utility subject to his budget constraint?

Ambrose's utility function is . The price of x is $1 and the price of y is $2. If his income rises from $100 to $150, his consumption of y increases by more than 10% but less than 50%.

Charlie's utility function is U(x_A, x_B) = x_Ax_B. If Charlie's income is $40, the price of apples is $4, and the price of bananas is $2, how many apples are there in the best bundle that Charlie can afford?

Mary Granola's utility function is U(x, y) = min{x + 2y, y + 2x}. Mary maximizes her utility subject to a budget constraint. If she chooses the bundle (5, 6), then the price of x must be exactly twice the price of y.

Coke and Pepsi are perfect substitutes for Mr. Drinker and the slope of his indifference curves is - 1. One day he bought 2 cans of Coke and 20 cans of Pepsi. (The cans of both drinks are the same size.)

Peter consumes no commodities other than Miller Lite and Bud Light. His annual budget for these two commodities is described by the equation 5x + 30y = 300, where x is sixpacks of Miller Lite and y is cases of Bud Light. Peter considers 2 cases of Bud Light to be perfect substitutes for 6 sixpacks of Miller Lite.

Harold's utility function is U(x, y) = (x + 3)(y + 2). The price of x is $1. The price of y is $2. At all incomes for which Harold consumes positive amounts of both goods, he will consume

Jane's utility function is U(x, y) = x + 2y, where x is her consumption of good X and y is her consumption of good Y. Her income is $2. The price of Y is $2. The cost per unit of X depends on how many units she buys. The total cost of x units of X is the square root of x.

At a boundary optimum, a consumer's indifference curve must be tangent to her budget line.

Charlie has a utility function U(x_A, x_B) = x_Ax_B, the price of apples is $1, and the price of bananas is $2. If Charlie's income were $200, how many units of bananas would he consume if he chose the bundle that maximized his utility subject to his budget constraint?

Casper consumes cocoa and cheese. Cocoa is sold in an unusual way. There is only one supplier, and the more cocoa you buy from him, the higher the price you have to pay per unit. In fact y units of cocoa will cost Casper y² dollars. Cheese is sold in the usual way at a price of 2 dollars per unit. Casper's income is 20 dollars and his utility function is U(x, y) = x + 2y, where x is his consumption of cheese and y is his consumption of cocoa. a. Sketch Casper's budget set and shade it in. b. Sketch some of his indifference curves and label the point that he chooses. c. Calculate the amount of cheese and the amount of cocoa that Casper demands at these prices and this income.

Roger consumes no commodities other than Miller Lite and Bud Light. His annual budget for these two commodities is described by the equation 5x + 25y = 300, where x is sixpacks of Miller Lite and y is cases of Bud Light. Roger considers 2 cases of Bud Light to be perfect substitutes for 6 sixpacks of Miller Lite.

Charlie has a utility function U(x, y) = (x + 3)(y + 4). The price of x is $1 and the price of y is $1. When he maximizes his utility subject to his budget constraint, he consumes positive amounts of both goods. Charlie consumes

Millie's utility function is U(x, y) = min{x, y}. She maximizes her utility subject to a budget constraint. The price of x is the same as the price of y. If the price of x rises and the price of y and her income remain constant, then her consumption of y will certainly decrease.

Clara's utility function is U(x, y) = (x + 2)(y + 1). If her marginal rate of substitution is -4 and she is consuming 14 units of good x, how many units of good y must she be consuming?

Hans has $27 which he decides to spend on x and y. Commodity x costs $16 per unit and commodity y costs $10 per unit. He has the utility function U(x, y) = 5x² + 2y² and he can purchase fractional units of x and y. Hans will choose