Consider the following data on two fictional countries:1 and 2.. Country 1 Country 2 Output per worker (y) Physical Capital per Worker, k 120 100 50 100 Human Capital per Worker, h 50 25 If the production function is y = Ak°h'-a, where a = 0.5., then if all differences in output were due to differences in productivity country 1 output would be times greater than in Country 2 O 1.70 O 1.17
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- The “per person” versions of production functions: Write each productionfunction given below in terms of output per person y ; Y/L and capital perperson k ; K/L. Show what these “per person” versions look like in a graphwith k on the horizontal axis and y on the vertical axis. (Assume A is somefxed positive number.)(a) Y = K 1/3L2/3 and Y = K 3/4L1/4 (on the same graph) (b) Y = K(c) Y = K + AL(d) Y = K − ALConsider the following data on two fictional countries: 1 and 2. . Country 1 Country 2 Output per worker (y) Physical Capital per Worker, k Human Capital per Worker, h 120 100 50 100 50 25 If the production function is y = Akºh'-a, where a = 0.5., then if all differences in output were due to differences in factor accumulation then country 1 output would be %3D times greater than in Country 2 1.70 0.59 1.17 1.46QUESTION 37 ROBOTS 60 50 40 30 20 10 0 a 10 b 20 C 30 40 50 BEFR 37. Assuming robots represents capital goods and beer consumer goods, and the growth path of country 1 is from point (a) to (b) to (c), while country 2 goes from points (d) to (e) to (f), what can you conclude about these countries? a) Country 1 has a higher savings rate b) Country 2 starts out with a higher standard of living c) Country 2 has a higher rate of growth d) Both (a) and (b) are correct e) None of the above
- Economics, physical capital represents the uildings or machines used by a business to produce product. The marginal product of physical capital presents the rate of change of output product with spect to physical capital (informally, if you increase e size of your factory a little, how much more Foduct can you create?). articular model tells us that the output product Y is given, a function of capital K, by Y = AKªL'-a ere A is a constant, L is units of labor (assumed to be stant), and a is a constant between 0 and 1. Determine marginal product of physical capital predicted by this del. ned with CamScanner1. O LounchPad • Country A and country B both have the production function Y = F(K, L) = K/³L²/3. a. Does this production function have constant returns to scale? Explain. b. What is the per-worker production function, y = f(k)? c. 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. Using your answer from part (b) and the steady-state condition that investment equals depreciation, find the steady-state level of capital per work- er for each country. Then find the steady-state levels of income per worker and consumption per worker. d. Suppose that both countries start off with a capital stock per worker of 1. What are the levels of income per worker and consumption per worker?The graph below represents per-worker production functions for the same country. Answer the following questions using this graph. Which 1 concept explains that the area between B and C has a flatter slope than the area between A and B? Answer: Law of Diminishing Marginal Returns What has to happen for a country to move from point E to B to D? Answer: The movement through which 3 points (out of 5 given) would indicate the largest increase in productivity? Answer:
- Question 1 The Mankiw-Romer-Weil (1992) model. Assume the production function is given by Y = KaH³(AL)¹-a-B where a and B are constants between zero and one whose sum is also between zero and one. Physical capital is accumulated as K = SKY dk where SK is the constant share of output invested in physical capital. And human capital is accumulated just like physical capital: Н = SHY dH where SH is the constant share of output invested in human capital. The labor force grows at rate n, and the technological progress occurs at rate g. Solve the model for the path of output per worker y=Y/L along the balanced growth path as a function of SK SH, n, g, d, a and B. (Hint: Define state variables such as y/A, h/A, and k/A.)1. 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.The following table provides data on output per worker, physical capital per worker, and human capital per worker, for three countries. Consider the following data on two countries, where α = 0.4. 1)Calculate the countries’ relative levels of output with respect to country III if all differences in output were the result of FOPs. For Country X it would be 1.034, For County Y it would be 0.362 For Country X it would be 193.85, For County Y it would be 67.87 For Country X it would be 67.87, For County Y it would be 187.41 For Country X it would be 0.362, For County Y it would be 1.034 2)Calculate the countries’ relative levels of output with respect to country Z if all differences in output were the result of productivity. For Country X it would be 1.116, For County Y it would be 0.651 For Country X it would be 0.896, For County Y it would be 1.535 For Country X it would be 1.29, For County Y it would be 2.21 For Country X it would be 0.77, For County Y it would be 67.87 3)The…
- Suppose the per-worker production function is: y = A(1-ga) Where ga is the fraction of all workers that produce technologies. Further, suppose the growth of technology is given by the following equation growth of A = (ga/m)(L) Suppose L = 1 and m = 7, and that initially ga = 0.7. If g, fell to 0.8 the level of output per worker would: Impossible to say fall stay the same O riseShow graphically on the same x and y axis what happens to this production function if there is a technological advancement in this economy. Don,t copy from anywhere.e here to search ? 2 2 3 S 1. Consider the following production function: Y=F(K, L) = A(2K + 3L) Does this production function exhibit constant returns to scale? 2. Suppose the table represents the production function of both Mexico and Spain. Use the following information to answer the next question. K = Capital (trillions) Y = Output (trillions) Country L = Population (millions) Mexico 3 Spain E D 105 3. Calculate per capita income for both countries. 4 45 2. Calculate total factor productivity for both countries using Equation 3. Equation 3: Y = F(KL) = AK0.3 L0.7 R 4. Explain the difference in per capita income. % 0.18 0.74 5 6 hip & T Y 1 G H a 00 1.0 W 1.7 39 Focus