# 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)

1. Show that if one allows "thick" indifference curves, then expenditure minimization may not coincide with preference maximization
2. Show that a good can be a Giffen good only if it is an inferior good.
3. 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)

1. 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.
2. Varian Problem 17.4.
3. 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)

1. 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.
2. Varian Problem 23.4.
3. Varian Problem 25.4.