Question 1: Slutsky Decomposition, Substitution Effect and Income Effect. 23

(40 pts)

Consider the following utility function: (1, 2) = 15 25 .

(a) Findthedemandforbothgoods,1 =1(1,2,)and2 =2(1,2,).

Hint:usemethod1asseeninclasswiththecondition=1. (6pts) 2

(b) Originally, let = 50 and 1 = 2 = 2. Suppose there is a change 1 such that 1 = 1. Find

the demands for both goods, before the price change and after the price change. Additionally,

in a well-labelled graph, show these optimal points. Name these points: (,) and (,) 12 12

respectively. Make sure to draw the indifference curves and label them. (7 pts)

(c) The goal is now to compute the Slutsky Substitution Effect (SSE). Given the change in price (1),

find the new income level () that makes the original bundle (1, 2) still affordable. Then, find

the optimal point (, ). Include this new budget line and the new optimal point in your graph 12

(include its indifference curve). Hint: 1 requires and 1. Also, your graph should look like the graphs from class. (15 pts)

(d) In your graph, indicate on the horizontal axis, the Slutsky Substitution Effect (SSE), Income Effect (IE) and Total Effect (TE), for good 1. Moreover, calculate the SSE and IE. Which one is larger? Given your answer, what type of good is 1? (6 pts)

(e) In a well-labelled graph, draw the Slutsky decomposition with the Hicks Substitution Effect (HSE)

instead of what you have done previously (the SSE). Call this different intermediate point, . Do

not solve for ( , ), simply draw it. 12

Hint: There is a difference between the two graphs (SSE vs. HSE). (6 pts)