Exam 3: Utility

Ike's utility function is U(x, y) = 25xy. He has 12 units of good x and 8 units of good y. Ben's utility function for the same two goods is U(x, y) = 4x + 4y. Ben has 9 units of x and 13 units of y.

Charlie's utility function is U(A, B) = AB, where A and B are the numbers of apples and bananas, respectively, that he consumes. When Charlie is consuming 15 apples and 90 bananas, if we put apples on the horizontal axis and bananas on the vertical axis, the slope of his indifference curve at his current consumption is

Angela has preferences represented by the utility function U(x, y) = 2x + 2y. She consumes 10 units of good x and 6 units of good y. If her consumption of good x is lowered to 4, how many units of y must she have in order to be exactly as well off as before?

Fiery Demon is a rotgut whisky made in Kentucky. Smoothy is an unblended malt whisky imported from Scotland. Ed regards these brands as perfect substitutes. When he goes into a bar, he sometimes buys only Fiery Demon. Other times he buys only Smoothy. This shows that Ed has unstable preferences.

Waldo's utility function is U(x, y) = xy. Waldo consumes 5 units of x and 25 units of y.

The utility function U(x₁, x₂) = 2lnx₁ + 3lnx₂ represents Cobb-Douglas preferences.

Charlie's utility function is U(A, B) = AB, where A and B are the numbers of apples and bananas, respectively, that he consumes. When Charlie is consuming 20 apples and 80 bananas, if we put apples on the horizontal axis and bananas on the vertical axis, the slope of his indifference curve at his current consumption is

Harry Mazzola has the utility function U(x₁, x₂) = min{x₁ + 2x₂, 2x₁ + x₂}. He has $40 to spend on corn chips and french fries. If the price of corn chips is $3 per unit and the price of french fries is $4, then Harry will

Isabella's utility function is U(x, y) = 4min{x, y} + y. If we draw her indifference curves with x on the horizontal axis and y on the vertical axis, these indifference curves are

A person with the utility function U(x₁, x₂) = min{x₁ + 2x₂, 2x₁ + x₂} has convex but not strictly convex preferences.

Emily's utility function is U(x, y) = 3min{x, y} + y. If we draw her indifference curves with x on the horizontal axis and y on the vertical axis, these indifference curves are

Josephine's utility function is U(x, y) = y + 5x^.5. She has 1 unit of x and 2 units of y. If her consumption of x is reduced to zero, how much y must she have in order to be exactly as well off as before?

A person with utility function U(x, y) = 5 + y² + 2x has nonconvex preferences.

Phil Rupp's sister Ethel has the utility function U(x, y) = min{ 5x + y, 6y}. Where x is measured on the horizontal axis and y on the vertical axis, her indifference curves consist of a

Victor Finick likes to have the same amount of x as he has of y. His utility function is U(x, y) = min{2x- y, 2y- x}. a. Draw the indifference curve for Victor that passes through the bundle (0, 0) and the indifference curve that passes through (4, 4). (Hint: Each indifference curve is the intersection of two line segments.) b. If Victor has a bundle that he likes better than (0, 0) and his consumption of both goods is doubled, is Victor better off? c. Does Victor always prefer more of either good to less?

Mark strictly prefers consumption bundle A to consumption bundle B and weakly prefers bundle B to bundle A. These preferences can be represented by a utility function.

Doreen has preferences represented by the utility function U(x, y) = 10x + 5y. She consumes 10 units of good x and 9 units of good y. If her consumption of good x is lowered to 1, how many units of y must she have in order to be exactly as well off as before?