EC402 MSU Productivity Growth Romer Model & Productivity Improvement Paper

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Economics

EC402

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This is a EC 402 problem set. Please finish this assignment in 20 hours. Thank you .

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For the first 2 questions: Suppose that income (output) grows at 3 percent, capital grows at 2 percent, and labor (employment) grows at 1 percent. Suppose Y = AK®N1-0, with 0 = 1/3. 1. What is productivity growth? A) 3% B) 2% C) 1.67% D) 0.67% 2. What fraction of output growth is contributed by capital? A) 22% B) 50% C) 66% D) 87% 3. What is the growth of output per worker? A) 0% B) 1% C) 2% D) 3% 4. In the Romer model, productivity improvement continues indefinitely if A) Researchers have constant productivity B) Production is subject to perfect competition C) There is no growth in any country D) Old ideas help generate new ideas 5. Which of the following statements about Total Factor Productivity (TFP) is true? 5. Which of the following statements about Total Factor Productivity (TFP) is true? A) TFP is the fraction of output that cannot be explained by factor inputs. B) TFP is the most important factor in accounting for low output per worker in poor countries. C) Resource misallocation across firms can be a reason for low TFP. D) All of the above. 1 6. Read the article "The Productivity Puzzle”. Which one of the following is a reason that the U.S. has experienced a decline in productivity growth since 2014? A) Values of digital products are difficult to measure. B) Low investment demand C) It takes time to translate technological advances into productivity gains. D) All of the above 7. Consider the effect of giving aid to a developing economy in the Romer model with spillovers. Let a be the amount of aid per person given each year. “Total income available” for a country is then Y +aN, where Y is the amount of total output. Describe what happens in a Romer economy with research spillovers (case 2). In particular, assume that the amount spent on purchasing (all) ideas is a fraction of total income available, s(Y+aN), so the value of a patent is PA = 1tr8(Y+aN). At the same time, the total compensation for workers is always (1 - 0)Y. Assume before the start of foreign aid, the economy was in its long-run equilibrium. Describe what happens in the long-run and short-run to (a) the number of researchers versus production workers and (b) the growth rate of productivity. (Hint: For the long run, think about the fact that aid is a constant amount, while output Y is growing.) 8. Consider the model of labor supply that we considered in class. Specifically, an individual who seeks to maximize U(C) + V (leisure) subject to the budget constraint: PC = WL where P is the price of consumption, W is the nominal wage rate, and L is time devoted to work. (a) Argue that if W and P both increase proportionately the optimal choice of how much to work does not change. (b) In class we asked what would happen to optimal labor supply if W were to increase. Ana- lyze what happens to labor supply if P increases. Specifically, does our theory predict what will happen? Explain your answer. If income and substitution effects are roughly offsetting on average, what would you predict would happen to average desired labor supply in the event of an increase in P? (e) Assume that U(C) = log(C) and V(leisure) = log(leisure). Normalize P = 1, and let W = 20. Assume the total available time H for an individual is 3600 hours a year (about 10 hours a day). Therefore, leisure = H - L = 3600 – L. Solve for the optimal labor supply L and consumption C. (Hint: U'(C)= 1 and V'(leisure) = leisure 3600 N (d) Continue from part (c). Now assume W = 10, so the wage rate is cut in half, whereas other parameters remain the same. Solve for the optimal labor supply L and consumption C. Will this individual work more or fewer hours compared to part (c)? What can you say about the income and substitution effects caused by the wage increase? 9. Consider a small modification to the one period labor supply problem that we studied in class. Specifically, assume that the individual seeks to maximize utility, U(C) + V (Leisure) subject to the budget equation PC =WL+D. The only new element in this problem is D, which represents dividend income that the individual receives. The government is going to institute some taxes, and is considering two different options. Option one is a proportional tax on labor income, i.e., a tax on labor income at rate Tl. The second option is a proportional tax on dividend income, i.e., a tax on dividend income at rate Tp. Assume that whichever option is chosen, the tax rate will be set so as to raise the same amount of revenue from this individual. Contrast the implications of these two different tax options for the choices of C and L that the individual makes. In answering this question assume that the values of P, w, and D are not affected by the tax plan.
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Explanation & Answer

Hello fam, please find attached. This is the final copy of all answered questions. The answers and calculations are highlited in red.

For the first 2 questions: Suppose that income (output) grows at 3%, capital grows at 2%, and
labor grows at 1 percent. Suppose

1. What is the productivity growth
Answer: The Solow Residual Model (productivity growth model=
𝑔𝑎 = 𝑔𝑟 − ∅𝑔𝑘 − (1 − ∅)𝑔𝑛
gr= 3%
Ø= 1/3
gn=2%
Thus, ga= 3%-(1/3)*2%- (1-1/3)*1%
Ga=3%-2/3-2/3
=1.67%
Productivity growth=1.675
Correct Answer is option C
2. What fraction of output growth is contributed by capital?
𝑂𝑢𝑡𝑝𝑢𝑡 𝑔𝑟𝑜𝑤𝑡ℎ = 3%
𝐶𝑎𝑝𝑖𝑡𝑎𝑙 = 2%
3−2= 1
½ = 0.5 𝑜𝑟 50%
Answer is 50% option B
3. What is the growth of income per capita (income per worker)
𝑇ℎ𝑒 𝑖𝑛𝑐𝑜𝑚𝑒 𝑔𝑟𝑜𝑤𝑡ℎ 𝑝𝑒𝑟 𝑐𝑎𝑝𝑖𝑡𝑎 𝑖𝑛 𝑡ℎ𝑒 𝑚𝑜𝑑𝑒𝑙 𝑔𝑟 − 𝑔𝑛 = 𝑔𝑎 + ∅𝑔𝑘 − ∅𝑔𝑛
𝑇ℎ𝑒𝑟𝑒𝑓𝑜𝑟𝑒, 1.67% + 1/3(2% − 1%)
= 1.67% + 1.33% = 2%
𝑇ℎ𝑒 𝑔𝑟𝑜𝑤𝑡ℎ 𝑜𝑓 𝑖𝑛𝑐𝑜𝑚𝑒 𝑝𝑒𝑟 𝑐𝑎𝑝𝑖𝑡𝑎 𝑖𝑠 2%

𝑇ℎ𝑒 𝑐𝑜𝑟𝑟𝑒𝑐𝑡 𝑎𝑛𝑠𝑤𝑒𝑟 𝑖𝑠 𝑜𝑝𝑡𝑖𝑜𝑛 𝐶
4. In the Romer Model, productivity improvement continues indefinitely if?
Correct answer is option D-Old ideas help generate new ideas.
5. Which one of the following statements is true about Total Factor Productivity (TFP)
All the options in this question are correct, TFP is the fraction of output that cannot be
explained by factor inputs, TFP is the most important factor in accounting for low
output per worker in poor countries and resource misallocation across firms can be a
reason for low TFP.
Correct Answer is thus option D.
6. Read the article “The Productivity Puzzle”, which one of the following is a reason
that the U.S has experienced a decline in productivity growth since 2014?
Correct answer is C- The article explains that it takes time to translate technological
advances into productivity gains.
7. Consider the effect of giving aid to a developing economy in the Romer model with
spillovers. Let a be the amount of aid per person given each year. “Total income
available” for a country is then Y + aN, where Y is the amount of total output.
Describe what happens in a Romer economy wi...


Anonymous
This is great! Exactly what I wanted.

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