Please no written by hand solutions Bunter’s preferences over a bundle consisting of x1 units of good 1 and x2 units of good 2 are represented by the utility function U (x1, x2) = 2√x1 + √x2. Bunter faces prices p1 = 4, p2 = p, and he has an income of I = 16. 1. Is Bunter’s utility function quasi-concave? 2. Find Bunter’s demand function for good 1 and good 2 as a function of the price p. 3. What is Bunter’s marginal utility for income? 4. Suppose the price of good 2 increases from p2 = 2 to p2 = 3. What is the income and substitution effect of this price change? If the government wanted to maintain Bunter’s original utility by giving him a cash subsidy, how much should it be?
Please no written by hand solutions
Bunter’s preferences over a bundle consisting of x1 units of good 1 and x2 units of good 2 are represented by the utility function U (x1, x2) = 2√x1 + √x2. Bunter faces prices p1 = 4, p2 = p, and he has an income of I = 16.
1. Is Bunter’s utility function quasi-concave?
2. Find Bunter’s demand function for good 1 and good 2 as a function of the price p.
3. What is Bunter’s
4. Suppose the price of good 2 increases from p2 = 2 to p2 = 3. What is the income and substitution effect of this price change? If the government wanted to maintain Bunter’s original utility by giving him a cash subsidy, how much should it be?
5. Suppose that, as in part (4), the government wanted to maintain Bunter’s utility after the price increase. However, the government does not know Bunter’s preferences. As a consequence, to compensate for the price increase, the government decides to give a cash subsidy just sufficient so that Bunter can still afford the bundle he chose before the price increase. How much should the cash subsidy be? What would Bunter’s demand be after such transfer?
6. Rather than giving a cash subsidy, the government considers compensating Bunter with a per unit subsidy for good 1. For Bunter to be able to afford his initial bundle, how much should the per unit subsidy of good 1 be? What would Bunter’s demand be after such subsidy?
7. Comparing parts (5) and (6), which policy does Bunter prefer? Which policy costs the government less?
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