1. Suppose the utility from consumption of tacos (x) and pad thai (z) is.
a. What are the demand functions (as a function of income and prices) for x and z?
b. Use the demand functions to state the indirect utility function (as a function of income and prices).
c. From the indirect utility function, derive the expenditure function (as a function of utility and prices).
d. What is the compensated demand function for x? What is the compensated demand function for z? (simplify the constants as much as possible)
2. The utility from concerts (x) and music downloads (z) is as in class, with Px=20, Pz=4, and I=100. Suppose the price of music downloads rises to $8. Use the expenditure function (E=pxx+pzz) to calculate the new uncompensated and compensated demands (actual amounts, not a function) for music downloads, and compare it to the original demand for music downloads. Use a graph to show the changes, and indicate the substitution and income effects.
3. In question 1, suppose that the price of a taco is $3 and the price of pad thai is $4. Income is $48.
a. Calculate the optimal x and z.
b. Suppose that a tax of $2 is placed on pad thai, pushing its price to $6. Calculate the new utility-maximizing number of tacos and pad thai, and also utility. How much tax revenue is earned?
Now suppose that instead of the tax on pad thai, the equivalent amount of tax revenue (from b) is raised from taxing income (keeping the prices at the original levels). What is the new utility-maximizing number of tacos and pad thai? What is the new utility in this situation? Explain intuitively why the tax on income generates more utility than a tax on a specific good.