Question

answer e and f only please

Exercise 3. Slutsky (Quasilinear) The utility function is u = x + xy, and the budget constraint is m=P,X, + P2XZ. a) Derive the optimal demand curve for good 1, x,(PP2), and good 2, x2(m, PP.). b) Looking at the cross price effects (@x_/ôp, and Ox_/ôp.) are goods x, and X, substitutes or complements? Looking at income effects (@x,lôm and Ox_lām) are goods x, and X, inferior, normal or neither? c) Assume m=100, =0.5 and p2=1. Using the demand function you derived in part a, what is the consumption of X, and of x ? d) Consider a price drop for only good 1 to p.'=0.25. Calculate the new demands for good 1 and good 2 and label them x,Mand x M. Plot in a graph with p, on the vertical axis the x, you found in part c, and x M. Graph the resulting Marshallian demand curve. e) Assume you are endowed with the amounts x, and x, you found in part c. What is their total worth, given the new prices? Define this as m = p'x, + P2X2. If m was your original budget constraint and you had to maximize your utility, what would be the resulting optimal consumption x, (P'.p.) and X, (mp'.p)? f) Plot the original x, from partc and x, from parte in a graph with p, on the vertical axis. Draw the Slutsky demand curve. How does it differ from the Marshallian demand curve? What is the substitution effect and the income effect of this price change?

Answer 1