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# Econ 322 Week 2 Notes and Homework Econ 322

USC

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This 9 page Class Notes was uploaded by Tulsi on Wednesday January 20, 2016. The Class Notes belongs to Econ 322 at University of South Carolina taught by Hauk in Spring 2016. Since its upload, it has received 184 views. For similar materials see Intermediate Macroeconomics in Economcs at University of South Carolina.

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Date Created: 01/20/16

Chapter 9 Homework Economic Growth II: Technology, Empirics, and Policy Note: my answers are given in bold-faced, underlined, red font. The values given to me in the question are underlined so if you’re given different numbers, be careful to use them instead. I tried to include as much information as possible about different wording of the questions. 1) Understanding efficiency of labor in the Solow Model Problem: A group of settlers arrive on planet Zars in 2020 with 90 people in their labor force. Their efficiency of labor increases from 1.0 to 1.1. Answer: The average worker is, in effect, as productive as 1.10 workers were at the start of the year, the number of effective workers went from 90 to 99. Explanation: The efficiency of labor increased from 1.0 to 1.1. This means that 1 worker in 2020 is as productive as 1.1 workers in the next year. To calculate number of effective workers: L x E = 90 workers x 1.1 = 99 400 350 300 250 200 150 worker20150 100 Outpu50per effective 0 0 10 20 30 40 50 Capital per effective worker Answer: In 2025, the economy has reached the steady-state shown in the graph above. The capital per effective worker (k) has reached 20. If its capital stock has increased to 3300 units of capital and the efficiency of labor has risen to 1.5, the number of actual workers (L) must be 110, and the number of effective workers has risen to 165. Explanation: The graph shows the intersection of the two curves to be when capital per effective worker is 20. One of the equations from our notes is: k = K/(L x E). Plug in all of the known values to solve for L. 20 = 3300/(L x 1.50) L = 110. Then to solve for effective workers: L x E = 110 x 1.50 = 165 2) The efficiency of labor and the Solow Model If investment in the economy is stopped, capital per effective worker would decline due to the following possible reasons: -increases in the efficiency of labor -depreciation of capital stock -population growth If the population growth rate, worker efficiency rate, or depreciation rate increase, then the break-even curve will have a steeper slope (A). If these rates decrease, then the break-even curve will flatten out (C). A C An increase in any of the rates (population growth, worker efficiency, depreciation) causes a decrease in the steady-state amount of capital per effective worker. A decrease in any of the rates (population growth, worker efficiency, depreciation) causes an increase in the steady-state amount of capital per effective worker. 3) Technological process, steady state, and the Golden Rule Midas’ depreciation rate is 2.0%, its rate of population growth is 2.0%, and its rate of labor- augmenting technological process is 2.5%. In order to graph the break-even investment curve for Midas, we need the slope and y- intercept. The y-intercept is always 0. The slope is the sum of the 3 rates. 2.0+2.0+2.5 = 6.5% (slope = .065) Use the graphing tool to graph a line that has the slope of .065 and y-intercept of 0. Then plot the golden-rule steady state at the point where the break even curve intersects the investment curve. Suppose that Midas’s rate of labor-augmenting technological process increases from 2.5% to 4%. The new break-even curve would have a slope of .08. (2.0+2.0+4.5=8%) The new steady state would be at the intersection of the new break-even curve and the investment curve. Note: if the rate decreases, the new slope will be less than the original slope. The increase in the growth rate of technological process will cause the steady state level of capital per effective worker to decrease. After the increase in the growth rate of technological process, the new Golden Rule steady state level of capital per effective worker will be less than the initial k*gold. Note: if the rate decreased, the steady state level of capital would increase. The new golden rule steady state level of capital would be greater than the initial k*gold. 4) Technological process and growth in output Problem: Suppose that the United States has reached a steady state with a rate of population growth (n) of 1.3% and a rate of labor-augmenting technological process (g) of 1.4%. Answer: The growth rate of output per worker would be 1.4% and the growth rate of output would be 2.7%. Solution: Variable Growth Rate in the Steady State Capital per effective worker 0 Output per effective worker 0 Output per worker g Total Output n + g 5) Balanced growth and convergence What is implied about the relationship between output per worker and capital stock per worker in the steady state? Both output per worker and capital stock per worker are determined by the rate of technological process. Output per worker and capital stock per worker grow at the same rate If the rate of technological progress in Agave is 6% per year and the population grows at 4% per year, then the economy’s real rental price of capital will remain constant. The capital-output ratio will remain constant. Real wage per worker will increase by 6% (g). 6) Determinants of growth The economy of Palladium is English-style common law and the economy of Zirconium if French- style. Which would you prefer to live in if you prefer sustained long term capital growth? Palladium provides protection for shareholders and creditors, has better developed capital markets, and have a more efficient allocation of the nation’s capital. The economy of Yttrium has extremely high levels of productive efficiency compared to the economy of Cadmium. Which would you expect to have the higher levels of physical and human capital? Yttrium The economies of Rhenium and Thorium are identical except Rhenium awards patents to inventors of new technology. Which economy will experience greater technological process? Rhenium NOTE: these are the 3 questions I came across from 3 different attempts. 7) The Golden Rule steady state and saving Problem: Gildonia’s economy has reached a steady state with a rate of depreciation of 10.0%, a rate of population growth of 15.0%, and a rate of labor-augmenting technological process of 12.5%. The formula for MPK is .75/k^.25. Answer: If the steady state has reached the Golden Rule steady state, the marginal product of capital is .375 units of capital and the steady state capital per effective worker would have to be 16 units. Solution: MPK (marginal product of capital) is equal to the sum of the depreciation rate, population growth rate, and rate of labor-augmenting technological process. 10% + 15% + 12.5% = 37.5%. Plug this value into the formula for MPK to solve for k. .375 = .75/k^.25. k = 16. Suppose that Gildonia’s marginal product of capital is greater than what it would be at the Golden Rule steady state. At the GRSS, capital per effective worker would be greater than the current level, which would require the saving rate to increase from its current rate. Suppose that Gildonia’s marginal product of capital is less than what it would be at the Golden Rule steady state. At the GRSS, capital per effective worker would be less than the current level, which would require the saving rate to decrease from its current rate. 8) The basic endogenous growth model This model is more realistic if you interpret knowledge as a form of capital. The economy of Bluso has a capital stock of 2,000 and a yearly output of 1,000. Assuming a constant return to capital, the variable A is equal to .5. If the rate of capital depreciation is .05 a year, determine the change in capital stock in the following year. Savings rate Net change in capital stock 5% -50 10% 0 20% 100 Explanation: Y = AK; solve for A. 1000=A x 2000. A = .5 ∆K = sY –δK. Plug in variables and solve for ∆K. ∆K = .05 x 1000 - .05 x 2000 = -50 ∆K = .1 x 1000 - .05 x 2000 = 0 ∆K = .2 x 1000 - .05 x 2000 = 100 In order to achieve positive output growth, the relationship given by sA > δ must hold. This relationship is interpreted as the rate of savings times the return to capital must be greater than the capital rate of depreciation.

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