A consumer has GH¢600 to spend on two commodities, A and B. CommodityA costs GH¢20 per unit and Commodity B costs GH¢30 per unit. Suppose thatthe utility derived by the consumer from x units of Commodity A, and yCommodity B is given by the Cobb-Douglas utility functionU (x, y) = 10x0.6,0.4a. How many units of each commodity should the consumer buy tomaximize utility?b. Is the budget constraint binding?Part CA 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 ofx and y are both GH¢1. Also, the consumer has been issued 200 ration couponsby the government which he must use whenever he buys either x or y. It takes 2coupons to buy an x and 1 coupon to buy a y (for example: to buy 3 units of x itwould 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. Identifywhich constraints, if any, are binding.

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A consumer has GH¢600 to spend on two commodities, A and B. Commodity A costs GH¢20 per unit and Commodity B costs GH¢30 per unit. Suppose that the utility derived by the consumer from x units of Commodity A, and y Commodity B is given by the Cobb-Douglas utility function U (x, y) = 10x060.4 a. How many units of each commodity should the consumer buy to maximize utility? b. Is the budget constraint binding?

A consumer has GH¢600 to spend on two commodities, A and B. Commodity A costs GH¢20 per unit and Commodity B costs GH¢30 per unit. Suppose that the utility derived by the consumer from x units of Commodity A, and y Commodity B is given by the Cobb-Douglas utility function U (x, y) = 10x060.4 a. How many units of each commodity should the consumer buy to maximize utility? b. Is the budget constraint binding?

Economics:

10th Edition

ISBN:9781285859460

Author:BOYES, William

Publisher:BOYES, William

Chapter21: Demand: Consumer Choic

Section: Chapter Questions

Problem 1E

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Question

A consumer has GH¢600 to spend on two commodities, A and B. Commodity
A costs GH¢20 per unit and Commodity B costs GH¢30 per unit. Suppose that
the utility derived by the consumer from x units of Commodity A, and y
Commodity B is given by the Cobb-Douglas utility function
U (x, y) = 10x0.6,0.4
a. How many units of each commodity should the consumer buy to
maximize utility?
b. Is the budget constraint binding?
Part C
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.

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