On January 1, 2026, each of Boblandia's 100 workers has $2 in physical capital. Over the course of the year, it physical capital depreciates by 8%, and the number of workers increases by 2%. How much does Boblandia have to invest in 2026 to make sure that its capital to labour ratio is the same on January 1, 2027 as it was on January 1, 2026?
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- Would you expect capital deepening to result in diminished1etmns? Why or why not? Would you expect improvements in technology to result in diminished returns? Why or why not?The prime interest rate is the rate that banks charge their best customers. Based on the nominal interest rates and inflation rates in Table 19.10, in which of the years would it have been best to be a lender? Based on the nominal interest rates and inflation rates in Table 19.10, in which of the years given would it have been best to be a borrower?How is the concept of technology, as defined with the aggregate production function, different from our everyday use of the word?
- Say that the average worker in Canada has a productivity level of 30 per hour while the average worker in the United Kingdom has a productivity level of 25 per hour (both measured in U.S. dollars). Over the next five years, say that worker productivity in Canada grows at 1 per year while worker productivity in the UK grows 3 per year. After five years, whiz) will have the higher productivity level, and by how much?Assume there are two countries: South Korea and the United States. South Korea grows at 4 and the United States grows at 1. For the sake of simplicity, assume they both start from the same fictional income level, 10,000. What will the incomes of the United States and South Korea he in 20 years? By how many multiples will each countrys income grow in 20 years?Say that the average worker in the U.S. economy is eight times as productive as an average worker in Mexico. If the productivity of U.S. workers grows at 2 for 25 years and the productivity of Mexicos workers grows at 6 for 25 years, which country will have higher worker productivity at that point?
- Farmland is a developing country with the following production function:Y = 24L2/3K1/3with Y = Output levelL = Quantity of laborK = Quantity of machinesa. Find the real rate of return for labor. Show your calculation. b. Suppose Farmland is granted some extra machines for production.How would this affect the real rate of return for labor? Explain by using theresult in (a).(a) Prove Proposition 20.4. In particular, show that if (20.18) is not satisfied, a CGP cannot exist, and that this condition is sufficient for a unique CGP to exist. (b) Characterize the CGP effective capital-labor ratio k∗. Proposition 20.4 Suppose (20.13) holds. Then in the above-described economy a (unique) CGP exists if and only if1. Country A and B both have the production functionY = F (K, L) = K ½L ½or Y = K0.5 L0.5 a) What is the per-worker production function, y= f (k)? Please make sure to write specificfunctional form of the per-worker production function. b) Assume that neither country experiences population growth nor technological progressand that 4 percent of capital depreciates each year. Assume further that country A saves 24percent of output each year and country B saves 16 percent of output each year. Using youranswer from part a) and the steady-state condition, find the steady-state level of capital perworker for each country. Then find the steady-state levels of income per worker for eachcountry and steady-state level of consumption per worker for each country.
- Assume that Economyland’s production function is Y = F (K, L) = K 0.5 L 0.5Where Y is output level, K is the amount of capital input, and L is the amount of laborinput. a) What is the per-worker production function, y= f (k) for Economyland? b) Assume that 10 percent of capital depreciates each year and savings rate is 20 percent,find the steady-state level of capital per worker for Economyland. Then find the steady-state levelof income per worker and steady-state level of consumption per worker. c) Is it possible to save too much? Why?Ecuador's economy has a production function that is as follows: Y = K2/5L3/5 The men in Ecuador generally stay home performing household chores while women work. Since the Ecuadorian state television stopped airing soap operas, many men decided to join the workforce and thus the labor force increased by 6.5%. However, recent storms have destroyed much of the capital stock of the country and thus the capital stock shrank by 2.5%. A. Assuming there is no change in total factor productivity in Ecuador, how would the output of Ecuador's economy change? B. How would labor productivity (output per worker) be affected by the increase in labor and decrease in capital stock? Explain. C. Assuming instead that Ecuador's economy grew by 4.9%, what would be the change in total factor productivity in the economy?Exercise 4: Growth and capital over-accumulationSuppose two countries, A and B, with the same production function Y = KαL1−α. Thevalue of α is 0.30, the growth rate of population is 2% and the depreciation rate is 5%.a) Show that with price-taking firms the share of labor must be 1 − α.b) Compute the stock of capital, output and consumption per unit of labor in the steadystate if the savings rates were 25% for country A and 35% for country B.c) Compare both economies to the Golden Rule.d) Explain what would happen to both countries if suddenly their savings rate becamethe Golden Rule savings rate.