A consumer consumes only food (X1) and alcohol (X2) and he has a utility function U(X1,X2)=bX1+aInX2
a. Derive the ordinary demand functions for X1 and X2.
b. Derive the Hicksian demand function for good 1 (h1). Show that it is downward sloping in its own price.
c. Using your result for X2 in part a, what can you tell about the income effect on good 2?
d. (Hint) A price change generally includes two effects: Income and substitution effects. Based on your result from part a and c, and given that Hicksian demand captures the substitution effect, what do you think the Hicksian demand for good 2 should be (h2)?
e. Derive the indirect utility function and show that it is homogeneous of degree zero.
f. Using your results from part a, determine whether these goods are complements or substitutes.
g. Write down the budget constraint and drive the consumer’s optimal consumption bundle.
Suppose the government provides a subsidy of $1/unit of food, and collect a tax of $1/unit on alcohol and $10 lump-sum income tax.
h. What is the new budget constraint?
i. What is the consumer’s optimal consumption bundle after this policy?
j. How much does it cost the government to implement this policy?