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March 31, 2021
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March 31, 2021

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) = T0.3S0.7

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 PX, PY and I.

c. How do
changes in I or PY 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(X1, X2) = 3X10.5X20.5

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).

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

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