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 − AL
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The “per person” versions of production functions: Write each production
function given below in terms of output per person y ; Y/L and capital per
person k ; K/L. Show what these “per person” versions look like in a graph
with k on the horizontal axis and y on the vertical axis. (Assume A is some
fxed 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 − AL
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Please address use above problem to the following equation:
(d) Y = K − AL
- Problem 3: Write each production function given below in terms of output per person y = Y/L and capital per person k = K/L. Plot these per person versions in a graph with y on the vertical axis and k on the horizontal axis. (You can assume à is a constant positive number). (a) Y=AK 1/3 L2/3 and Y = AK3/4L1/4 (plot them on the same graph). (b) Y = K. (c) Y = KL (d) YK-ALThe 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:Table 1 for the Production Function. 1. Capital per hour of work (k/l) 10 20 30 40 50 Show Transcribed Text 2 C Output per hour of work (Y/L) 14 22 28 32 34 Plot the above production function information. What is the equilibrium if capital per hour Hour of work (K/L) =40. Thank You!!
- 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. 10,419.96The graph below shows three production functions. PFO shows the current production function for the economy, and capital per worker is currently (K/L)o; thus ouput per worker is (Y/L)o. Suppose that there is a decrease in capital per worker. Which of the points on the graph could show the new capital per worker and output per worker? A. 3 O C. 1 Click to select your answer. B. 2 D. 4 Real GDP per hour worked, Y/L (Y/L)o 2 0 3 (K/L)o Capital per hour worked, K/L PF1 PF0 PF₂
- Assume that a country's production function is Y= AKº³Lº7. The ratio of capital to output is 3, the growth rate of output is 3 percent, and the depreciation rate is 4 percent. Capital is paid its marginal product. a. What is the marginal product of capital in this situation? (Hint: The marginal product of capital may be computed using calculus by differentiating the production function and using the capital-output ratio or by using the fact that capital's share equals MPK multiplied by K divided by Y.) b. If the economy is in a steady state, what must be the saving rate? (Hint: The saving rate multiplied by Y must provide for gross growth of (8 + n + g)K, where 8 is the depreciation rate.) c. If the economy decides to achieve the Golden Rule level of capital and actually reaches it, what will be the marginal product of capital? d. What must the saving rate be to achieve the Golden Rule level of capital?Suppose an economy uses only two inputs in production: capital and labour. The following table describes a production function, where y stands for output per worker and k is capital per worker.Suppose there are two countries, A and B. The economies of the two countries can be described by this production function. If Country A has initially a capital–labour ratio k = 0.167 and Country B has k = 0.412, show that an equal increase in capital produces more extra output in country A than in Country B. Explain with words (computations) + graph y k 0.000 0.000 0.173 0.030 0.302 0.091 0.408 0.167 0.480 0.231 0.535 0.286 0.577 0.333 0.612 0.375 0.642 0.412 0.667 0.444 0.688 0.474 0.707 0.500 0.724 0.524 0.739 0.545Assume the production function takes the general form (as in lecture notes) Y = z xF(K,L, A) Z X where all marginal products are positive. Which 3 of the following statements are correct? Select one or more: O a. If A is fixed, then population growth acts as a drag on growth of output per person. b. If A is fixed, then population growth acts as a drag on growth, and so Malthus was correct that population growth will always reverse the impact of technological improvements. Both rises in z and rises in K/L (capital intensity) will boost output per worker. O d. Growth in output per worker can occur due to rises in z (technology) or rises in K/L (capital intensity), or both.
- Assume the production function takes the general form: Y=Z*F (K,L,A)where all marginal products are positive.Which 3 of the following statements are correct?a. If A is fixed, then population growth acts as a drag on growth of output per person.b. If A is fixed, then population growth acts as a drag on growth, and so Malthus was correct that populationgrowth will always reverse the impact of technological improvements.c. Both rises in z and rises in K/L (capital intensity) will boost output per worker.d. Growth in output per worker can occur due to rises in z (technology) or rises in K/L (capital intensity), orboth.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.’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 rise