Exam 3: Utility

Jean-Pierre has preferences represented by the utility function U(x, y) = min{ 2x + y, x + 6y}. If x is on the horizontal axis and y is on the vertical axis, what is the slope of his indifference curve at the point (7, 7)?

Joe Bob's cousin Peter consumes goods 1 and 2. Peter thinks that 4 units of good 1 is always a perfect substitute for 2 units of good 2. Which of the following utility functions is the only one that would not represent Peter's preferences?

Charlie has the utility function U(x_A, x_B) = x_Ax_B. His indifference curve passing through 35 apples and 18 bananas will also pass through the point where he consumes 5 apples and

Ernie's utility function is U(x, y) = 32xy. He has 10 units of good x and 8 units of good y. Waldo's utility function for the same two goods is U(x, y) = 3x + 5y. Waldo has 9 units of x and 13 units of y.

Jim's utility function is U(x, y) = xy. Jerry's utility function is U(x, y) = 1,000xy + 2,000. Tammy's utility function is U(x, y) = xy(1 - xy). Oral's utility function is - . Billy's utility function is . Pat's utility function is U(x, y) = -xy.

Wanda Lott has the utility function U(x, y) = max{x, y}. Wanda's preferences are convex.

Raymond's preferences are represented by the utility function U(x, y) = if y > 0 and U(x, y) = 0 if y = 0.

Mr. Surly consumes only two goods and hates them both. His utility function is U(x, y) = 2max{x, y}. Mr. Surly has (weakly) convex preferences.

Molly's utility function is U(x, y) = y + 4x^.5. She has 25 units of x and 12 units of y. If her consumption of x is reduced to 0, how many units of y would she need in order to be exactly as well off as before?

Use separate graphs to draw indifference curves for each of the following utility functions: a. U(x, y) = min{2x + y,2y + x}. b. U(x, y) = max{2x + y,2y + x}. c. U(x, y) = x + min{x, y}. In which of these cases are preferences convex?

If someone has a utility function U = 2 min{x, y}, then x and y are perfect complements for that person.

A person with the utility function U(x, y) = y + x² has convex preferences.

Harmon's utility function is U(x₁, x₂) = x₁x₂. His income is $100. The price of good 2 is p₂ = 4. Good 1 is priced as follows. The first 15 units cost $4 per unit and any additional units cost $2 per unit. What consumption bundle does Harmon choose?

Use separate graphs to sketch two indifference curves for people with each of the following utility functions: a. U(x, y) = x + 2y. b. U(x, y) = min{x,2y}. c. U(x, y) = max{x,2y}.

A person with the utility function U(x, y) = 10 + y² + x has convex preferences.

The absolute value of Mar's MRS at his current consumption bundle is greater than 3. (That is, ). Mars has convex preferences and is currently consuming positive amounts of both goods.

Phil Rupp's sister Ethel has the utility function U(x, y) = min{ 4x + y, 5y}. Where x is measured on the horizontal axis and y on the vertical axis, her indifference curves consist of a

With quasilinear preferences, the slope of indifference curves is constant along all rays through the origin.

A consumer has preferences represented by the utility function U(x₁, x₂) = 10(x²₁ + 2x₁x₂ + x²₂) - 50. For this consumer, goods 1 and 2 are perfect substitutes.

Charlie has the utility function U(x_A, x_B) = x_Ax_B. His indifference curve passing through 32 apples and 8 bananas will also pass through the point where he consumes 4 apples and