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.
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- 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: AnswerConsider 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[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. 10,419.96
- 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 FocusGive 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 aggregate production function is y=3KL. If they are 30 units of capital and 40 units of labor, what is aggregate output? What is labor productivity? What is capital productivity?
- 14. If output is described by the production function Y = AK0.2L0.8, then the production function has: Select one: A. Constant returns to scale and the share of labor in GDP is 0.2. B. increasing returns to scale and the share of labor in GDP is 0.2. C. Decreasing returns to scale and the share of labor in GDP is 0.8. D. constant returns to scale and the share of labor in GDP is 0.8.Suppose 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!Indicate whether the following statement is TRUE or FALSE and explain your answer: ‘Consider threeinputs of production: labour, physical capital and natural resources, and an economy with decreasingreturns to scale. If you increase all three inputs x times then the total gross domestic product (GDP) inthe economy will increase exactly x times, but GDP per capita will decrease.’
- True or False A production function in "economics" summarizes the technological relationship between inputs and outputs.Assume that we have a Cobb-Douglas type aggregate production function in the form: Y = Ka.Lb a. Find output per labor; capital per labor (y=Y/ L and k= K/L ). b. Briefly define what is derivative of y with respect to k or or y' or dy/dk ? c. Briefly explain why y'>0 or dy/dk > 0 . Is it possible that dy/dk < 0 ? Why? d. Briefly explain why y'' ≤ 0 . e. Find the elasticity of substitution between K and L. What does expansion path look like?10. As an alternative to the story of Robinson Crusoe, macroeconomists use the "aggregate production function," written as Y = AF(L,K,H,N), to link economy-wide output Y to the number of workers L, the stock of physical capital K, the stock of human capital H, the stock of natural resources N, and stock of technological knowledge A. With reference to this aggregate production function, please indicate whether each of the following statements is true or false. (a) The aggregate production function exhibits "constant returns to scale" if doubling the four inputs - workers L, physical capital K, human capital H, and natural resources N – while holding the stock of technological knowledge A fixed leads to a doubling of output. (b) The aggregate production function exhibits "constant returns to scale" if tripling the four inputs - workers L, physical capital K, human capital H, and natural resources N – while holding the stock of technological knowledge A fixed leads to a tripling of…