Minh loves red roses (good 1) and pho (good 2). Her preferences may be represented by...

   
 

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Minh loves red roses (good 1) and pho (good 2). Her preferences may be represented by the Cobb-Douglas utility function u(x1, r2) = x}x2 Minh's income is m = 24 and the price of red roses is pi = 4. Tragically, due to higher tariffs on beef imports, the price of pho is set to rise from p2 to do some parts of this question! Clearly show your approach! 1 to p2 = 8! Note: there are a bunch of different ways (a) Find Minh's Ordinary ("Marshallian") demand functions x(p1; P2, m) and a(P1, P2, m). These are the solutions to the utility-maximization problem, max u(x1, x2) s.t. pie1 + P2æ2 = m. (b) Find Minh's Compensated ("Hicksian") demand functions ri(p1, P2, U) and x(P1, P2, U). These are the solutions to the cost-minimization problem, min p11 + p202 s.t. u(x1, r2) = U. (c) In a budget-line/indifference curve diagram (one is provided on the next page), show the Hicks decomposition of this price change. In particular, draw: • Minh's budget line before and after the price change, labeled BL and BL' • her optimal points before and after the price change, labeled A and C • her tangency conditions before and after the price change, labeled TC and TC" • her Hicks decomposition point, labeled B, showing her cost-minimizing way of achieving her old utility at the new prices • the indifference curves passing through points A, B, and C (d) What is the substitution effect of the price change on her consumption of roses? What is the income effect? What does that imply about whether roses and pho are complements, substitutes, or independent goods? Ex 9.1: Roses and Pho, Part I Minh loves red roses (good 1) and pho (good 2). Her preferences may be represented by the Cobb-Douglas utility function u(x1, x2) = x}x2 4. Tragically, due to higher tariffs on beef to p2 = 8! Note: there are a bunch of different ways Minh's income is m = 24 and the price of red roses is p1 imports, the price of pho is set to rise from p2 to do some parts of this question! Clearly show your approach! %3D Ex 10.1: Roses and Pho, Part II This problem continues Exercise 9.1, to examine Minh's relationship between money and utility, and determine how much she's hurt by the increase in the price of pho. (a) Find Minh's indirect utility function V(p1, P2, m). (b) Find Minh's expenditure function E(p1, p2, U). (c) What is the compensating variation of the price change for Minh? In other words, by how much would her income need to increase in response to the price increase, for her to be as happy as she was before the price change? (d) What is the equivalent variation of the price change for Minh? In other words, how much income would Minh be willing to give up in order for the price not to have changed at all? Minh loves red roses (good 1) and pho (good 2). Her preferences may be represented by the Cobb-Douglas utility function u(x1, r2) = x}x2 Minh's income is m = 24 and the price of red roses is pi = 4. Tragically, due to higher tariffs on beef imports, the price of pho is set to rise from p2 to do some parts of this question! Clearly show your approach! 1 to p2 = 8! Note: there are a bunch of different ways (a) Find Minh's Ordinary ("Marshallian") demand functions x(p1; P2, m) and a(P1, P2, m). These are the solutions to the utility-maximization problem, max u(x1, x2) s.t. pie1 + P2æ2 = m. (b) Find Minh's Compensated ("Hicksian") demand functions ri(p1, P2, U) and x(P1, P2, U). These are the solutions to the cost-minimization problem, min p11 + p202 s.t. u(x1, r2) = U. (c) In a budget-line/indifference curve diagram (one is provided on the next page), show the Hicks decomposition of this price change. In particular, draw: • Minh's budget line before and after the price change, labeled BL and BL' • her optimal points before and after the price change, labeled A and C • her tangency conditions before and after the price change, labeled TC and TC" • her Hicks decomposition point, labeled B, showing her cost-minimizing way of achieving her old utility at the new prices • the indifference curves passing through points A, B, and C (d) What is the substitution effect of the price change on her consumption of roses? What is the income effect? What does that imply about whether roses and pho are complements, substitutes, or independent goods? Ex 9.1: Roses and Pho, Part I Minh loves red roses (good 1) and pho (good 2). Her preferences may be represented by the Cobb-Douglas utility function u(x1, x2) = x}x2 4. Tragically, due to higher tariffs on beef to p2 = 8! Note: there are a bunch of different ways Minh's income is m = 24 and the price of red roses is p1 imports, the price of pho is set to rise from p2 to do some parts of this question! Clearly show your approach! %3D Ex 10.1: Roses and Pho, Part II This problem continues Exercise 9.1, to examine Minh's relationship between money and utility, and determine how much she's hurt by the increase in the price of pho. (a) Find Minh's indirect utility function V(p1, P2, m). (b) Find Minh's expenditure function E(p1, p2, U). (c) What is the compensating variation of the price change for Minh? In other words, by how much would her income need to increase in response to the price increase, for her to be as happy as she was before the price change? (d) What is the equivalent variation of the price change for Minh? In other words, how much income would Minh be willing to give up in order for the price not to have changed at all?