# Assignment Two

Assignment Two

**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 ^{0.3}S^{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).

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:

Situation with Tariff | Situation Without Tariff | |

World Price (delivered in New York) | $0.50 per lb | $0.50 per lb |

Tariff (specific) | $0.15 per lb | 0 |

U.S. Domestic Price | $0.65 per lb | $0.50 per lb |

U.S. Consumption | 200 million lbs | 250 million lbs |

U.S. Production | 160 million lbs | 100 million lbs |

Calculate:

- The loss to U.S. consumers from the imposition of the tariff.
- The gain to U.S. producers from the imposition of the tariff.
- The revenue generated by the imposition of the tariff.
- The net effect of the imposition of the tariff on the U.S. as a whole.
- 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(X_{1}, X_{2}) = 3X_{1}^{0.5}X_{2}^{0.5}

Let P_{1}
= $8, P_{2} = $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).

**All answers must
be supported by computations and/or graphs.
You must show your work neatly and completely.**