Problem
Consider a three-good economy (k = 1; 2; 3) in which every consumer has preferences represented by the utility function U = x1 + g(x2; x3), where the function g(:) is increasing and strictly concave. Suppose that each good is produced with constant returns to scale from good 1, using one unit of good 1 per unit of good k ≠ 1. Let good 1 be the nume´raire and normalize the price of good 1 to equal 1. Let tk denote the (specific) commodity tax on good k so that the consumer price is qk = 1 + tk .Suppose that a tax change is restricted to only good 2 so that t ≠ 2 = t2 + ? with ? > 0.
a. What is the correct measure of the welfare loss arising from this tax increase if t3 = 0?
b. Show that if t3 > 0, then the measure of welfare loss in part a overestimates the welfare loss if good 3 is a substitute for good 2. What is then the correct measure of the welfare change?
c. Show that if t3 > 0, then the measure of welfare loss in part a underestimates the welfare loss if good 3 is a complement for good 2. What is the correct welfare change?
d. Show that if good 3 is subsidized, t3
e. Show that if good 3 is subsidized, t3
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.