Consider a hypothetical economy that has the production function Y = F(K, LE) = K¹/3 (LE) 2/3, where Y is output, K is capital, and LE is the number of effective workers. Suppose the saving rate is 20%, the capital depreciates by 3%, the population grows at the rate of 1%, and the rate of labor-augmenting technological change is 1%. a. Solve for the per-effective-worker production function. b. At what rate (%) do the following grow in the steady state? i. Total output ii. Output per worker iii. Output per effective worker iv. Real rental price V. Real wage
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- 6. Consider a hypothetical economy that has the production function Y = = F (K, LE) = K¹/3 (LE) 2/3, where Y is output, K is capital, and LE is the number of effective workers. Suppose the saving rate is 20%, the capital depreciates by 3%, the population grows at the rate of 1%, and the rate of labor-augmenting technological change is 1%. a. Solve for the per-effective-worker production function.0.5 0.5 Given a production function: Y = AK N If output grows at 5%, capital grows at 2% and the number of workers grows at 4%, then technology (or total factor productivity) grows at % ? (Answer in integer only, no decimal place.) Your Answer: Answer Given a production function: Y = AK0.5 N0.5. If output grows at 5%, capital grows at 2% and the number of workers grows at 4%, then technology (or total factor productivity) grows at %? (Answer in integer only, no decimal place.) Your Answer: AnswerSuppose a country has a population of 120 people, a working-age population of 100 people, its labor force participation rate is 0.5 (50%), and the quantity of output is 60 units. Suppose that the production function of the economy is given by Y=2N, where Y represents the quantity of output and N represents the number of workers needed to produce the output. I know the answer is 0.4 but I don't understand how to get it. Thank you!
- Give only typing answer with explanation and conclusion The production function in an economy is given by Y = K0.4L0.6, where Y is output level, K is capital input, and L is labour input. The saving rate is 24%, the annual population growth rate is 4%, and annual depreciation rate is 2%.The table below shows various values of labour (L), capital (K), and technology (T) for Economies A, B, and C. In each case, the aggregate production function takes the following form: Y = T x KL Economy A Economy B Economy C L. K LK I L K T on 100 50 100 50 100 50 2 110 50 110 55 110 55 4 120 50 2 120 60 120 60 130 50 130 65 2 130 65 8. 140 50 2. 140 70 140 70 10 150 50 150 75 150 75 12 TABLE 25-4 Refer to Table 25-4. The production function that applies to Economies A, B, and C displays Select one: O a. constant returns to scale. O b. diminishing marginal returns to capital. O c increasing returns to scale. O d. increasing marginal returns to capital. O e. Both C and D are correct. 6 2.The economy of Ouratricot has 50 units of labor and 30 units of capital. Ouratricot has a production unit that produces knitted goods with a technology described by the production function QT=min{2KT,LT} where QT is the quantity of knitted goods produced, KT is the quantity of capital used in the knitted goods production unit, and LT is the quantity of labor used in the knitted goods production unit. Ouratricot has a production unit that produces Ouras with a technology described by the production functionQO=min{KO,LO} where QO is the quantity of Ouras produced, KO is the quantity of capital used in the production unit of Ouras, and LO is the quantity of labor used in the production unit of Ouras. Find all of the capital and wage allocations between the two production units that are likely to be part of an optimal allocation in the sense of Pareto in the economy of Ouratricot. Justify your answer with precision and clarity.
- Suppose the economy of Utopia has a labor force of 600 workers, 100 units of capital and 400 hectares of land. It produces manufactured goods (M) which use labor (LM) and capital (K) in production and agricultural goods (A) which use labor (LA) and land (T) in production. The production functions are given by: QM = VR/LM %3D And Ly + LA = L = 600 In autarky, PA = PM = 10. %3D Suppose Utopia engages in trade and the price of manufactured goods, PM = 20. What happens to: 1. The workforce and output of manufactured goods? Of agricultural goods? 2. The nominal and real wage in Utopia? 3. The real return to capital and to land in Utopia? 4. Will everyone support trade?Suppose that the economy's production function is given by Y=K²N¹-a where Y is output, K is capital, and N is labor. Assume that a = 1/3. The production function transformed into output per worker is (Property format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a superscript can be created with N character.)A firm's production function is initially Q = KL . Over time, the production function changes to Q = K?L² (Assume that L > 1 and K > 1) Which one is correct for the situation? No technological progress, only change of function Technological progress Cannot comment on progress
- 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[The following scenario applies to the next two questions.] An economy has a Cobb-Douglas production function: Y = AK L(1-a). A is the technology level, K is capital; L is labor; and Y is income. ● In 20X1, the technology level A is 139, capital K = 245, labor L = 458, income Y = 8,155 In 20X2, the technology level A is 144.96, capital K = 259.26, labor L = 474.12, income Y = 8,945.71 In 20X3, the technology level A is 152.02, capital K = 273.31, labor L = 489.20 Question 1.6: Elasticity of income with respect to labor What is the elasticity of income with respect to labor? A. 18% B. 20% C. 22% D. 24% E. 26% Question 1.7: Income What is income in 20X3? A. 9,240.34 B. 9,535.25 C. 9,830.15 D. 10,125.06 E. 10,419.96Consider an economy described by the aggregate production function: Y = F(K,L)= K0.510.5, the per-worker production function in this economy should be: (The production function may not be entirely displayed on your laptops. The complete production function should be Y-K^0.5L^0.5. It means that we have a CD production function with alpha= 0.5.) Y=K⁰.5 y = 40.510.5 Ⓒy=k0.5 O Per-worker production function is not available.