Chapter 10-QC-1 (Page: 242) Using the information in this chapter, label each of the following statements True, false, or uncertain. Explain briefly. a. On a logarithmic scale, a variable that increases at 5% per year will move along an upward-sloping line with a slope of 0.05. TRUE (SEE PAGE 228-FIGURE 10-1) b. The price of food is higher in poor countries than it is in rich countries. FALSE (229) c. Evidence suggests that happiness in rich countries increases with output per person. FALSE (SEE PAGE 231=>SEE FOCUS BOX: Growth and Happiness) d. In virtually all the countries of the world, output per person is converging to the level of output per person in the United States. FALSE (SEE PAGE 236) e. For about 1,000 years after the fall of the Roman Empire, there was essentially no growth in output per person in Europe, because any increase in output led to a proportional increase in population. TRUE (SEE PAGE 235) f. Capital accumulation does not affect the level of output in the long-run; Only technological progress does. FALSE (SEE PAGE 240) g. The aggregate production function is a relation between output on one hand and labor and capital on the other. TRUE (SEE PAGE 237) => Y = F (K, N)
Chapter 10-QC-2 (Page: 242) Assume that the average consumer in Mexico and the average consumer in the United States buy the quantities and pay the prices indicated in the following table: FoodTransportation Services PriceQuantityPriceQuantity Mexico10 pesos80030 pesos300 United States$22,000$33,000 a. Compute U.S. consumption per capita in dollars. b. Compute Mexican consumption per capita in pesos. c. Suppose that 1 dollar is worth 10 pesos. Compute Mexicos consumption per capita in dollars. d. Using the purchasing power parity method and U.S. prices, compute Mexican consumption per capita in dollars. e. Under each method, how much lower is the standard of living in Mexico than in the United States? Does the choice of method make a difference?
Chapter 10-QC-2 (Page: 242) SOLUTION: (SEE PAGES: 228-229) The table should read as follows. FoodTransportation Services PriceQuantityPriceQuantity Mexico10 pesos80030 pesos300 United States$22,000$33,000 a.U.S. consumption per person = $2(2000) + $3(3,000)=$13000 b.Mexican consumption per person=10(800) pesos + 30(300) pesos = 17000 pesos c. From the U.S. point of view, the exchange rate (E)=10 pesos/$. Mexican consumption per person in dollars = 17000 pesos/E=$1700 d. Mexican consumption per person ($PPP)=$2(800)+$3(300)=$2500 e. Mexican standard of living relative to the United States Exchange rate method: 1700/13000 =0.13 PPP method: 2500/13000=0.19
Chapter 10-QC-3 (Page: 242) Consider the production function. a. Compute output when K=49 and N=81. b. If both capital and labor double, what happens to output? c. Is this production function characterized by constant returns to scale? Explain. d. Write this production function as a relation between output per worker and capital per worker. e. Let K/N=4. What is Y/N? Now double K/N to 8. Does Y/N double as a result? f. Does the relation between output per worker and capital per worker exhibit constant returns to scale? g. Is your answer in (f) the same as your answer in (c)? Why or why not? h. Plot the relation between output per worker and capital per worker. Does it have the same general shape as the relation in Figure 10-4? Explain.
Chapter 10-QC-3 (Page: 242) SOLUTION: a.Y=63 b.Y doubles. c.Yes. d.Y/N=(K/N) 1/2 e.K/N=4 implies Y/N=2. K/N=8 implies Y/N=2.83. Output less than doubles. f.No. g.No. In part (f), we are essentially looking at what happens to output when we increase capital only, not capital and labor in equal proportion. There are decreasing returns to capital. h.Yes. SEE PAGE 239-FIGURE 10-4
OUTPUT AND CAPITAL PER WORKER: (SEE PAGE 239-FIGURE 10-4) INCREASES IN CAPITAL PER WORKER LEAD TO SMALLER AND SMALLER INCREASES IN OUTPUT PER WORKER.