Problem Set 3

Due 3/10/97


1. Suppose that a consumer's indirect utility function is given as follows:

V(Px,Py,I) = - (Px + sqrt(Px Py)) / I - (Py + sqrt(Px Py)) / I

2. On the last problem set, you analyzed the consumer's problem with U(X,Y)=X^(1/4)Y^(3/4). Now continue this exercise. Let I=16, Px=1, and Py=3.

3. (continued from above; same utility function) We wish to compute the "ideal" change in consumer surplus from a change in the price of good X. Fix Py=3 and I=16. Let the initial price be equal to Px0 = 1, and consider an increase to Px1 = 16.

4. Now suppose that the consumer's utility is U(X,Y)=sqrt(XY).

5. Continuation from #4: U(X,Y)=sqrt(XY). Suppose that initially, prices are Px0 = 1, Py0 = 2, and then they increase Px1 = 2, Py1 = 3. We use different price indices to estimate the change in the cost of living. For each, give the formula for arbitrary prices and income, and then plug in.

Applications: CPI articles

1. The industry commission for Boston puts out a brochure. It announces: "Move your corporation to Boston and make your workers happy. The cost of living is lower than many other cities. We looked at the bundles of goods our citizens purchased, and then computed the cost of buying that bundle in San Francisco. It was more expensive in San Francisco. Furthermore, there are some things you just can't get in San Francisco: you can walk the historical Freedom Trail whenever you like." Does this claim follow sound economic logic? Be very precise about why or why not.

2. How does the presence of different retail outlets lead to bias in the CPI, according to the Boskin report? What is the assumption which is embodied in the CPI calculation that leads to this problem? What evidence is there that the assumption is wrong?

3. Discuss three economic implications of an upward bias in the CPI. How do each of these implications affect which political factions support the CPI?

4. The editorial in the St. Louis Post-Dispatch argues that "if the average family can afford only chicken instead of beef, does this mean inflation is being overstated? Hardly." Does this argument make sense? Explain your answer precisely.

5. The next argument in the editorial says: "if lower quality alternatives no longer exist, the ability of consumers to obtain a given product at all may require more income. Again, that's hardly an argument that inflation is being overstated." Do you find this compelling? Name some examples of quality improvements where this argument fails to apply. Can you think of any where it does apply?

6. Is it possible that the introduction of new products might coincide with a understatement of the change in the cost of living? Explain.

7. What three new products or quality changes improve your life over what it might have been 30 years ago at this same age?