Part 1

Mira chooses between two goods, x and y, with prices p_x and p_y, respectively. She has an income I and her preferences are represented by the utility function U (x, y) =x + y.

• Assuming that an interior solution exists to the constrained utility maximization problem, derive Mira 's Marshallian demand function for each of the two goods. Are both goods normal? Explain

• Find the indirect utility function,V (p_x, p_y, I).

• Derive Mira's Hicksian demand function for each of the two goods and the expenditure function. Compare the Marshallian demand for goodx and the Hicksian demand for goodx. Are these different functions? If so, why? If not, why not?

• Suppose thatI = 100, p_x= 1 and p_y= 2. How much of goodxand goodywill Mira

optimally choose?

• Now the price of good x rises top_x= 2, while income(I = 100)and the price of goody, p_y= 1, remain unchanged. What quantities does Mira buy and what is her resulting utility? Illustrate graphically

• Find the income and substitution effect for goodxdue to this price change. That is, which change in the consumption ofxis due to pure substitution and which change in the consumption ofxis due to the income effect? Illustrate your answer graphically.

• If the government wants to compensate Mira for the price increase of goodx

from two to four dollars, by giving her some extra income, how much extra

income would be needed to bring her back to the old utility level? In other words,

find the compensating variation for the price change. Show all your calculations

and illustrate graphically.