This problem set tells the story of three friends Alice, Bob, who are con- sumers, and...

 

Transcribed Image Text:

This problem set tells the story of three friends Alice, Bob, who are con- sumers, and Carol, who owns a firm. Alice, and Bob have preferences over two goods, Dumplings and Free time. Each of them have T; available hours each day with i = A, B. Carol's firm produces dumplings using two inputs, Labour and Kapital with respective prices w and r. Denote the market price of dumplings as p. 1. [12 points] Alice's preferences over dumplings and free time are repre- sented by the utility function uA (DA, FA) DA + 2ln FA. She has no other income than the one she can obtain by selling part of her available time T, as labour to Carol's company. Find the expression for Alice's budget constraint, with use of income on the one hand and source of in- come on the other. Use the Lagrange method to calculate her demand for dumplings and her labour supply as a function of TA, P and w. Find Alice's optimal consumption of dumplings and labour supply for the case (p, w) = (1, 1) and TA = 16. = 2. [22 points] Suppose that the price of dumplings increases from p = 1 to p = 2, what is Alice's optimal consumption of dumplings and labour supply under the new price? What is the total effect on her dumplings consumption and labour supply of the change in p? Represent both the old and new choices graphically with consumption of dumplings on the vertical axis and free time on the horizontal. Find the number of available hours T under which Alice's optimal choices under (p, w) = (1, 1) would be just affordable under (p, w) (2, 1). Then compute Alice's optimal consumption of dumplings and labour supply if her amount of available hours were replaced by T' and (p, w) = (2, 1). Use this bundle to decom- pose the total change in her dumpling consumption and labour supply into the substitution and the income effects. Are dumplings normal or inferior? This problem set tells the story of three friends Alice, Bob, who are con- sumers, and Carol, who owns a firm. Alice, and Bob have preferences over two goods, Dumplings and Free time. Each of them have T; available hours each day with i = A, B. Carol's firm produces dumplings using two inputs, Labour and Kapital with respective prices w and r. Denote the market price of dumplings as p. 1. [12 points] Alice's preferences over dumplings and free time are repre- sented by the utility function uA (DA, FA) DA + 2ln FA. She has no other income than the one she can obtain by selling part of her available time T, as labour to Carol's company. Find the expression for Alice's budget constraint, with use of income on the one hand and source of in- come on the other. Use the Lagrange method to calculate her demand for dumplings and her labour supply as a function of TA, P and w. Find Alice's optimal consumption of dumplings and labour supply for the case (p, w) = (1, 1) and TA = 16. = 2. [22 points] Suppose that the price of dumplings increases from p = 1 to p = 2, what is Alice's optimal consumption of dumplings and labour supply under the new price? What is the total effect on her dumplings consumption and labour supply of the change in p? Represent both the old and new choices graphically with consumption of dumplings on the vertical axis and free time on the horizontal. Find the number of available hours T under which Alice's optimal choices under (p, w) = (1, 1) would be just affordable under (p, w) (2, 1). Then compute Alice's optimal consumption of dumplings and labour supply if her amount of available hours were replaced by T' and (p, w) = (2, 1). Use this bundle to decom- pose the total change in her dumpling consumption and labour supply into the substitution and the income effects. Are dumplings normal or inferior?

Answer rating: 100% (QA)

1 Alices budget constraint is given by Budget Constraint pDA wFL TA where p is the price of dumplings w is the wage rate DA is the quantity of dumplin... View the full answer