Assignment

Answer the following questions completely and neatly. All answers must be supported by discussions and/or mathematical procedures.

1. An Income Consumption Curve is defined as a set of combinations of goods corresponding to constrained utility maximization solutions for different levels of money income, while holding the prices of the goods constant. Please help Paul with the development of his Income Consumption Curve using the following information. Paul is the third grader who likes only Twinkies (T) and Orange Slice (S), and these provide him a utility of Utility = U(T, S) = T^0.3S^0.7.

Assumption # 1: Twinkies cost $0.10 each and Slice costs $0.35 per can. Paul spends the $1 his mother gives him in order to maximize his utility.

Assumption # 2: Paul's mother increases his allowance to $2 per day.

Assumption # 3: Paul's mother increases his allowance to $3 per day.

Label the graph carefully and mark the optimal quantities of T and S on the graph.

Also, derive an indirect utility function for Paul under the assumption that the school has increased the price of Twinkies to $0.25 each. What is Paul's compensated demand function? Use the minimum expenditure function to determine the minimum cost of keeping Paul as happy as he was under assumption # 1.

All answers must be supported by computations and/or graphs.

In your explanation of each concept, identify the variables that are assumed to be constant and those that vary. In addition, use a hypothetical situation to derive (graph) a Marshallian (uncompensated) demand function and its corresponding Hicksian (compensated) demand function.

2. Suppose that an individual's utility for X and Y are represented by the CES function (for δ = -1).

Utility = U(X, Y) = -(1/X) -(1/Y)

a. Use the Lagrangian Multiplier Method to calculate the uncompensated demand function for X and Y for this function.

b. Show that the demand functions calculated in part (a) are homogeneous of degree zero in P_X, P_Y and I.

c. How do changes in I or P_Y shift the demand for good X?

All answers must be supported by computations and/or graphs.

3. You are given the following information about copper in the United States:

Calculate:

a. The loss to U.S. consumers from the imposition of the tariff.
b. The gain to U.S. producers from the imposition of the tariff.
c. The revenue generated by the imposition of the tariff.
d. The net effect of the imposition of the tariff on the U.S. as a whole.
e. Use two separate graphs (one for the U.S. copper market and one for the world market) to describe the free-trade equilibrium and the restricted-trade equilibrium in the two markets.

All answers must be supported by computations and/or graphs.

4. Val has the following utility function: U = U(X₁, X₂) = 3X₁^0.5X₂^0.5
Let P₁ = $8, P₂ = $6, and I = $120.

Derive the Lagrangian Expression and solve for the first-order conditions. Use the first-order condition to solve for Val's utility-maximizing bundle (consumer equilibrium).