1) According to the “Rule of 70" if a variable grows at a constant rate of 5% per year, approximately how many years would it take for the level of that variable to double? A. 14 В. 350 С. 70 D. 65
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A: C(y) = y2 + 1 MC = 2y and, D(p) = 36 - 2y TR = p x y = (36 - 2y)y = 36y - 2y2 MR = 36 -…
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A: C(y) = y2 + 1 MC = 2y and, D(p) = 36 - 2y Now, for long run equilibrium P = MC 36 - 2y = 2y 4y = 36…
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- Country A and country B both have the production function Y = F(K, L) = K1/3L2/3 Does this production function have constant returns to scale? Explain. Find Solow’s production function, y = f (k)? Assume that neither country experiences population growth or technological progress and that 20 percent of capital depreciates each year. Assume further that country A saves 10 percent of output each year and country B saves 30 percent of output each year. Find the steady-state level of capital per worker for each country, then find the steady-state levels of income per worker and consumption per worker. Suppose that both countries start off with a capital stock per worker of 2. What are the levels of income per worker and consumption per worker? Remembering that the change in the capital stock is investment less depreciation, use a calculator (or, better yet, a computer spreadsheet) to show how the capital stock per worker will evolve over time in both countries. For…Suppose that 10 workers were required in 2010 to produce 40,000 bushels of wheat on a 1,000-acre farm. a. What is the average output per acre? Per worker? b. If in 2020 only 8 workers produce 44,000 bushels of wheat on that same 1,000-acre farm, what will be the average output per acre? Per worker? c. By what percentage does productivity (output per worker) increase over those 10 years? Over those 10 years, what is the average annual percentage increase in productivity?A mathematical approximation called the rule of 70 tells us how long it will take for something to double in size if it grows at a constant rate. The doubling time is approximately equal to the number 70 divided by the percentage rate of growth. Thus, if Panama’s real GDP per person is growing at 7 percent per year, it will take about 10 years (= 70/7) to double. Apply the rule of 70 to solve the following problem: Suppose that real GDP per person in Panama in 2017 was about $12,000 per person, while it was about $48,000 per person in the United States. If real GDP per person in Panama grows at the rate of 5 percent per year, about how long will it take Panama’s real GDP per person to reach the level that the United States was at in 2017? (Hint: How many times would Panama’s 2017 real GDP per person have to double to reach the United States’ 2017 real GDP per person?) __________ years
- Suppose that a government wants to reduce its economy’s dependence on coal and decides as a result to tax coal mining companies $1 per ton for every ton of coal that they mine. Assuming that coal mining companies treat this tax as an increase in extraction costs this year, what effect will the tax have on current extraction in the model used in Figure ? Now, think one step ahead. Suppose that the tax will be in place forever, so that it will also affect extraction costs in the future. Will the tax increase or decrease user cost? Does this effect increase or decrease the change in current extraction caused by the shift of the EC curve? Given your finding, should environmental taxes be temporary?16)A mathematical approximation called the rule of 70 tells us that the number of years that it will take something that is growing to double in size is approximately equal to the number 70 divided by its percentage rate of growth. Thus, if Mexico’s real GDP per person is growing at 7 percent per year, it will take about 10 years (= 70/7) to double. Apply the rule of 70 to solve the following problem. Real GDP per person in Mexico in 2005 was about $11,000 per person, while it was about $44,000 per person in the United States. If real GDP per person in Mexico grows at the rate of 4 percent per year, about how long will it take Mexico’s real GDP per person to reach the level that the United States was at in 2005? (Hint: How many times would Mexico’s 2005 real GDP per person have to double to reach the United States’ 2005 real GDP per person?) Instructions: Enter your answer as a whole number.2. Solow-Swan Model (a) You will demonstrate the importance of diminishing returns to capital in the Solow-Swanmodel. Draw a Solow-Swan diagram in which there are constant returns to capital. Thiswould happen if the production function were Yt= AKt, where A = 1. Furthermore,assume that the sum of population growth and the depreciation rate is greater than thesaving rate. Does the economy converge to a steady state in this case? To answer thisquestion, you should draw a Solow-Swan diagram in terms of output per person, as we didin class. Use this diagram to explain why the economy converges to a steady state or doesnot. (b) Assume, instead, that the sum of population growth and the depreciation rate is equal tothe saving rate. In this case, are there any steady states? If yes, describe the steady-statelevels of capital per person. If no, explain why not. (Note: Diagram is not needed for thispart.)
- 9 Based on the production function Y = AKaG1-a (with G representing public expenditure, and the remaining variables and parameters representing usual values), show, using the necessary assumptions the value of the tax amount that maximizes the economic growth rate. Then, represent graphically the situation.Consider an economy’s production function is Y=K^1/3 N^2/3 and that both the saving rate and the depreciation rate are equal to 0.15. A. What is the steady-state level of capital per worker? B. What is the steady-state level of output per worker? Now suppose that the economy has reached its steady-state in period t, and then, in period t+1, the saving rate doubles to 0.30. The depreciation rate remains constant at 0.15. C. Solve for the new steady-state levels of capital per worker and output per worker. D. Calculate the path of capital per worker and output per worker over the first three periods after the change in the saving rate.C I G NX Price Yr1 1000 156 560 52 4 Yr2 1300 159 600 52 5 Yr3 2000 169 690 53 6 Yr4 2900 180 880 53 7 -What will the percent rate of change in real GDP be from year 1 to year 2, from year 2 to year 3, and from year 3 to year 4. (round to the whole number for all calculations and final answers) -State how long it will take for real GDP to double in size.
- Computing growth rates (II): Suppose k, l, and m grow at constant rates givenby g k, gl , and gm. What is the growth rate of y in each of the following cases?(a) y = k 1/3(b) y = k 1/3l 2/3(c) y = mk 1/3l 2/3(d) y = mk 1/4l 3/4(e) y = mk 3/4l 1/4(f ) y = 1klm2 1/2(g) y = 1kl2 1/4 11/m2 3/414)Suppose that the annual rates of growth of real GDP of Econoland over a five-year period are as follows: Year Growth Rate (%) 1 3 2 1 3 – 2 4 4 5 5 Instructions: Round your answers to 2 decimal places. a. What was the average of these growth rates in Econoland over these 5 years? b. What term would economists use to describe what happened in year 3? (Click to select) Expansion Recession c. If the growth rate in year 3 had been a positive 2 percent rather than a negative 2 percent, what would have been the average growth rate?4. Suppose that we have a standard Solow model with a Cobb-Douglas production function. The central equation of the model is as follows:kt+1 = sAkαt + (1 − δ)kt.Consumption per worker is given by:ct = (1 − s)Akαt.(a) Solve for an expression for the steady state capital stock per worker. Indoing so, assume that the level of productivity is fixed at some value A.(b) Use your answer on the previous part to solve for an expression forsteady state consumption per worker.(c) Use calculus to derive an expression for the s which maximizes steadystate consumption per worker.