# Advanced
Theory 431 Homework Problems Spring 2001

## Assignment Number 1 (January 29)

1. Check the followin gwith respect to **w**
for the following cost functions for linear homogeneity, positive
monotonicity, and concavity:

a. C(y,**w**) = [y(raised to 1/2)][(w1 times
w2)(raised to 3/4)]

b. C(y,**w**) = [y(raised to 1/2]{2[(w1)(raised to
1/2)], [(w2)(raised to 1/2)]}

c. C(y,**w**) = y{w1 + [(w1 times w2)(raised to
1/2)] + w2}

d. C(y,**w**) = y{[w1(e(raised to -w1))] + w2}

e. C(y,**w**) = y{w1 - [(w1 times w2)(raised to
1/2)] + w2}

f. C(y,**w**) = [y + (1/y)][(w1 times w2)(raised to
1/2)]

2. Varian Problem 2.2.

3. Varian Problem 3.4.

## Assignment Number 2 (February 12)

- Show that if one allows "thick" indifference curves,
then expenditure minimization may not coincide with preference maximization
- Show that a good can be a Giffen good only if it is an inferior good.
- Varian Problem 7.4.

## Assignment Number 3 (March 19)

1. Show that a monopolist will never operate at an inelastic portion of
her demand curve.

2. Varian Problem 13.4

3. Varian Problem 16.10.

## Assignment Number 4 (April 2)

- Draw an Edgeworth Box example of a pure exchange economy with multiple
price equilibria, each being locally isolated. Then draw an Edgeworth Box example with
infinite price equilibria.
- Varian Problem 17.4.
- You own a piece of commercial real estate that is currently earning
$10,000 per year net return. Current real rae of interest is 4%. You can sell this
property for $500,00. Discuss all possible explanations. Provide relevant graphs with each
explanation.

## Assignment Number 5 (April 23)

- Suppose demand functions have income included endogenously in the form
x(p,p.w). Show that the marginal utility of income can never be independent of prices.
- Varian Problem 23.4.
- Varian Problem 25.4.