# Optimal Consumption Choice

1. (TOTAL: 5 points). Slutsky Equation. Assume that the function U(x, y) = x 0.2 y 0.7 is the utility function of a person who consumes two goods in quantities x and y, respectively.
The price of x is P x = 3 and the price of y is P y = 5. This person ́s income is m = 160.
a) Find the optimal consumption choice of this person.
b) Assume that the price of x increases to P x = 4. Calculate the person ́s demand for x and y at the new price.
c) Decompose the change in demand for good x into a substitution and an income effect. Show clearly in a graph the pivot effect (substitution) and the shift (income) effect.

2. (TOTAL: 5 points). The wheat market is perfectly competitive, and the market supply and demand curves are given by the following equations:
P = 100 -2 QD
P = 10 + QS
where QD and QS are quantity demanded and quantity supplied measured in bushels, and per bushel.
a. Determine consumer surplus at the equilibrium price and quantity.
b. Determine producer surplus at the equilibrium price and quantity.
c. Assume a per-unit tax of 15 is imposed. You are to find the price the buyers pay (including the tax), the price the sellers receive (net of the tax), and the quantity transacted. Calculate the equilibrium price paid by buyers (including the tax), price received by sellers (net of tax), and quantity. Illustrate the equilibrium on the graph. Show the regions that correspond to (a) producer surplus, (b) consumer surplus, (c) tax revenue, and (d) deadweight loss.

3. (TOTAL: 5 points). Harding Enterprises has developed a new product called the Gillooly shillelagh. The market demand for this product is given as follows:
Q = 240 – 4P
a. If the shillelagh is priced at \$40, what is the point price elasticity of demand? Is demand elastic or inelastic?
b. If the shillelagh price is increased slightly from \$40, what will happen to the total expenditure on the Gillooly shillelagh?

4. (TOTAL: 5 points). Daily demand for gasoline at Billy- Bob’s Mobile Station is described by Q = 980 − 300p, where Q are gallons of gasoline sold and p is the price in dollars. Billy- Bob’s supply is Q = – 2,980 + 3,000p. Suppose the state government places a tax of 18 cents on every gallon of gasoline sold. What is the deadweight loss resulting from this tax?

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