## Problems For Section

1. Roderick Floud consumes only food and clothing, initially in these monthly amounts and at these prices: food: 60 pounds at \$1 per pound; clothing: 20 yards at \$2 per yard.

First, some trivial preparations:

a. What is Floud's money income in dollars?

b. What is the share of food in his total money expenditure (= income)?

c. What is the share in (b) multiplied by -10%, a 10% fall?

Second, the substantive question:

d. Floud's real income in terms of his initial bundle is Y, his money income, divided by PF • (60 pounds) + Pc • (20 yards), a price index with weights on the prices PF and Pc equal to the initial amounts of the two goods (60 pounds and 20 yards). When PF and Pc are at their initial values (namely, PF = \$1 per pound and Pc = \$2 per yard), this quotient is 1.0 (satisfy yourself that this is true). Suppose that PF alone changes, rising by 10% from \$1.00 to \$1.10. If money income is held constant, what happens to the quotient? Calculate it with the new value of PF. What is the percentage change in the quotient?

Third, the interpretation:

e. Notice that the answer to (d) is the same as the answer to (c). What general rule do you suppose holds for small price changes among the percentage change in a price, the share of the item in total expenditure, and the percentage change in real income?

2. A student of economics went one night to Jimmy's Bar where beer and whiskies both cost \$1.00 and drank six beers and four whiskies. The next night, on the eve of the final examination, the student went to the Eagle Bar where beers cost \$0.50 and whiskies \$1.50 and drank two beers and six whiskies. True or false: The student was too irrational to pass the final examination.

° 3. In 1958 underground coal miners in Italy spent 803,000 lire on their purchases and underground coal miners in Germany spent 7330 marks. The Italian bundle would have cost 6270 marks in Germany; the German bundle would have cost 1,139,000 lire in Italy. True or false: With these data one cannot reject the hypothesis that Italian and German coal miners have the same tastes. (Hint: Is one bundle revealed preferred to the other? Now is the other, too?) 4. Consider the following data on purchases of coal miners in France and the Netherlands:

Value of Purchases by Coal Miners at Local and Foreign Prices (local currency units, in thousands)

Bundles (quantities) in:

At Prices in: France Netherlands

France 919 990

### Netherlands 6.84 6.56

True or false: According to these data the French bundle is superior. 5. What are the rankings of bundles in the following data? Is the WARP ever violated? What do you conclude about appealing to differences in national tastes to explain differences in consumption bundles? (Hint: It is possible that some of the bundles will be unranked relative to others: equal, as it were.)

Value Of Consumption at Af prkeg _Value of Bundles Bought in:_

Local and Foreign Prices in: Germany Belgium France Italy Netherlands Saar for Underground Coal -

Miners, Married with Two Germany 7.33 > 9.85 8.99 6.27 9.19 8.43

Children, for Six Localities Belgium 88 107.8 101.8 70.6 104.1 100.4

in the European Coal and France 828 1031 i 980~ , 625 990 925

Steel Community, in 1958 Italy 1139 1462 1246 803 1387 1278

(local currency, in thou- Netherlands 5.59 7.14 6.84 4.87 6.56 6.35

sands) Saar 835 1082 959 649 1023 935

6. Bloomingdale's is an expensive and fashionable department store in New York; Wool-worth's is an inexpensive and unfashionable one. True or false: A rise in the cost of parking in New York would favor Bloomingdale's.