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.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter4: Utility Maximization And Choice

Section: Chapter Questions

Problem 4.13P

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