In this question we will decompose a change in price into a substitution and income effect. Suppose there exists a consumer with a Cobb-Douglas utility function.

U(x1, x2) = x1^1/3 x2^2/3

Recall that in this case, the demand equations are given by the following:

x1 = (1/3)(m/p1)

x2 = (2/3) (m/p2)

Suppose that this consumer has an income of $2,400. Suppose that the price of good 1 is p1 =$4 and the price of good 2 is p2 =$10

A) Calculate the amount demanded of both goods at this initial equilibrium. What is this consumer's utility? Graph this result using our standard budget- line/indifference curve diagram. Label this initial point as point A.

B) Suppose the price of good 1 increased to p1 = $10. What will be the new amount demanded of both goods after this price change? What will be the new equilibrium level of utility? Add this new budget line and new equilibrium point to your diagram. Label this new point, B.

C) Following the price change, how much money would we have to com- pensate the consumer to allow him to afford his original bundle that he purchased in part a)? Hint: I'm not looking for you to calculate the equivalent variation or compensating variation, but instead the intermediate step we did when calculating the income and substitution effects.

D) Suppose the consumer faced the following set of prices: p1 = $10 and p2 = $10. Further suppose that the consumer had an income equal to $2,400 plus the value you calculated in part c). Given this situation, what would be the optimal consumption bundle for this consumer? Add this new budget line and new equilibrium point to your diagram. Label this new point, C.

E) Using the values you have calculated above, what is the size of the substitution effect and what is the size of the income effect for this consumer in this scenario?