Question

1. Homer is a deeply committed lover of chocolate. Assume his preferences are Cobb-Douglas over chocolate bars (denoted by C on the x-axis) and a numeraire good (note: we use the notion of a numeraire good to represent spending on all other consumption goods – in this example, that means everything other than chocolate bars – its price is always $1).
a. Homer earns a salary that provides him a monthly income of $360. Last month, when the price of a chocolate bar was $4, he bought 45 chocolate bars. Using what we know about the relationship between the parameters of the Cobb-Douglass utility function and expenditure shares, write down the specific utility function for Homer (i.e. put in the appropriate numbers for ? and 1−?).
b. Use your answer to part (a) to derive Homer’s Marshallian Demand for chocolate bars, his Compensated (Hicksian) Demand for chocolate bars, his Compensated (Hicksian) Demand for the numeraire good, and his expenditure function. Show your work for full credit!
c. Imagine the mayor of the city in which Homer lives sees Homer as representative of the voting public. He is worried about being reelected, given that citizens like Homer are about to be made unhappy by his new regulation on chocolate bar producers, which will increase the market price of chocolate bars from $4 to $ 9. Use the implied change in the Expenditure Function to compute Homer’s Compensating Variation for this potential price increase, that is the amount that Homer would need to be paid to maintain his original utility given the new price for chocolate bars.
d. Draw a rough graph of the Marshallian Demand and show the loss of Consumer Surplus that would be associated with this price increase? Set up the integral that you would use to calculate the loss (no need to actually solve for the area).
e. Now redraw your graph from part (d) and add the Compensated Demand function for chocolate bars. Denote both CV and ΔCS on the graph Identify the difference between CVand ΔCS and clearly label it.
f. Briefly provide intuition, using the Slutsky equation, for why CV and ΔCS diverge. What factors cause the divergence between CV and ΔCS to be large or small? Make sure your answer is no longer than 3 sentences.

I know the Utility function is u=C^.5 * B^.5

I know part a as well, but where I get confused is the math when deriving hicksian demand. i know that B=U^2/c, but I can't seem to substitute it back into the budget constraint. No Larange used.

I can't solve the rest of the problem because I am stuck on part b.

Help!

Answer 1