Question 8 Note: This question is similar to end-of-chapter problem 3.2 and it is restated here in a multiple choice format. For a utility function for two goods to be strictly quasi-concave (i.e. convex indifference curves), the following condition must hold: UxxU²x - 2UxyUxUy + UyyU²y <0. Use this condition to check the convexity of the indifference curves for following utility function: U(x,y) = xy. You conclude: Because all of the first order partial derivatives are positive, we must only check the second order partial derivatives. Uxx, Uyy < 0 and Uxy > 0: the function is strictly quasi- concave. O Because all of the first order partial derivatives are positive, we must only check the second order partial derivatives. Uxx, Uyy, Uxy > 0: the function is not necessarily strictly quasi-concave. Because all of the first order partial derivatives are positive, we must only check the second order partial derivatives. Uxx = Uyy = 0, Uxy > 0: the function is strictly quasi- concave. O Because all of the first order partial derivatives are positive, we must only check the second order partial derivatives. Uxx = Uyy = 0, Uxy < 0: the function is not strictly quasi-concave.
Question 8 Note: This question is similar to end-of-chapter problem 3.2 and it is restated here in a multiple choice format. For a utility function for two goods to be strictly quasi-concave (i.e. convex indifference curves), the following condition must hold: UxxU²x - 2UxyUxUy + UyyU²y <0. Use this condition to check the convexity of the indifference curves for following utility function: U(x,y) = xy. You conclude: Because all of the first order partial derivatives are positive, we must only check the second order partial derivatives. Uxx, Uyy < 0 and Uxy > 0: the function is strictly quasi- concave. O Because all of the first order partial derivatives are positive, we must only check the second order partial derivatives. Uxx, Uyy, Uxy > 0: the function is not necessarily strictly quasi-concave. Because all of the first order partial derivatives are positive, we must only check the second order partial derivatives. Uxx = Uyy = 0, Uxy > 0: the function is strictly quasi- concave. O Because all of the first order partial derivatives are positive, we must only check the second order partial derivatives. Uxx = Uyy = 0, Uxy < 0: the function is not strictly quasi-concave.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Question 8
Note: This question is similar to end-of-chapter problem 3.2 and it is restated here in a
multiple choice format. For a utility function for two goods to be strictly quasi-concave (i.e.
convex indifference curves), the following condition must hold: UxxU²x - 2UxyUxUy + UyU²
<0. Use this condition to check the convexity of the indifference curves for following utility
function: U(x,y) = xy. You conclude:
Because all of the first order partial derivatives are positive, we must only check the
second order partial derivatives. Uxx, Uyy < 0 and Uxy > 0: the function is strictly quasi-
concave.
O Because all of the first order partial derivatives are positive, we must only check the
second order partial derivatives. Uxx, Uyy, Uxy > 0: the function is not necessarily strictly
quasi-concave.
Because all of the first order partial derivatives are positive, we must only check the
second order partial derivatives. Uxx = Uyy = 0, Uxy > 0: the function is strictly quasi-
concave.
O Because all of the first order partial derivatives are positive, we must only check the
second order partial derivatives. Uxx = Uyy = 0, Uxy < 0: the function is not strictly
quasi-concave.
Question 10
Note: This question is similar to end-of-chapter problem 3.5a and it is restated here in a
multiple choice format. Let x be eggs and y be bagels. If an individual considers that a
complete breakfast is made of 2 eggs and 1 bagel, this individual utility function can be
represented by:
O U(x, y) = min(2x, y)
O U(x, y) = min(x, y)
O U(x, y) = min(x, y)
O none of the above
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