A consumer with the following utility function U = xy2 faces two constraints. The first is the normal budget constraint where he has GH¢150 and the price of x and y are both GH¢1. Also, the consumer has been issued 200 ration coupons by the government which he must use whenever he buys either x or y. It takes 2 coupons to buy an x and 1 coupon to buy a y (for example: to buy 3 units of x it would require GH¢3 or 6 coupons) (i) Write down the Lagrangian for this problem. (ii) Applying the steps of Kuhn-Tucker, find the optimal x and y. Identify which constraints, if any, are binding.
A consumer with the following utility function U = xy2 faces two constraints. The first is the normal budget constraint where he has GH¢150 and the price of x and y are both GH¢1. Also, the consumer has been issued 200 ration coupons by the government which he must use whenever he buys either x or y. It takes 2 coupons to buy an x and 1 coupon to buy a y (for example: to buy 3 units of x it would require GH¢3 or 6 coupons) (i) Write down the Lagrangian for this problem. (ii) Applying the steps of Kuhn-Tucker, find the optimal x and y. Identify which constraints, if any, are binding.
Economics: Private and Public Choice (MindTap Course List)
16th Edition
ISBN:9781305506725
Author:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson
Publisher:James D. Gwartney, Richard L. Stroup, Russell S. Sobel, David A. Macpherson
Chapter20: Consumer Choice And Elasticity
Section: Chapter Questions
Problem 4CQ
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