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.

ENGR.ECONOMIC ANALYSIS
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A consumer with the following utility function U = xy? 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.
Transcribed Image Text:A consumer with the following utility function U = xy? 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.
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