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- Consider the production function Y = K1/2 N12 a. Compute output when K = 49 and N = 81 %3D b. If both capital and labor double, what happens to output? c. Is this production function characterized by constant returns to scale? Explain. d. Write this production function as a relation between output per worker and capital per worker. e. Let K/N = 4. What is Y/N? Now double K/N to 8. Does Y/N double as a result? f. Does the relation between output per worker and capital per worker exhibit constant returns to scale? g. Is your answer to f. the same as your answer to c.? Why or why not?hello, I need help with my homework 4.7 When to Use the Principle of Diminishing Returns? You are the manager of a firm that produces memory chips for mobile phones. In your decision about how much output to produce this week, would you use the principle of diminishing returns? Explain. In your decision about how much output to produce two years from now, would you use the principle of diminishing returns? Explain. My Textbook: macroeconomics by o’Sullivan 10th addition 978 013 519 6434 thank youQuestion 19 Consider the following graph of a production function when capital is constant. (The following is a description of the figure: it shows a two-axis graph; the horizontal axis measures labor and the vertical axis measures output; for a K fixed, the graph shows that maximal production that the firm can achieve with different levels of labor; the graph starts at cero production for zero labor; then it is increasing in all of its range; three levels of labor are shown as reference; there are L1, L2, and L3; they are related as follows L1<L2<L3; the graph is convex from 0 to L1, that is, its slope is increasing; the graph is concave from L1 on, that is, its slope is decreasing; the line that is tangent to the curve at L2, passes through the origin of the graph.) From the graph we know that for the corresponding K: MPL(L2,K)=MPL(L3,K) MPL(L1,K)>MPL(L2,K) MPL(L1,K)=MPL(L2,K) MPL(L1,K)<MPL(L2,K) MPL(L3,K)>MPL(L2,K)
- c. You are given the following information about an economy. Y = C + I Y = F(K, L) The aggregate production function for this economy exhibits constant returns to scale and the marginal products of labor and capital are both subject to diminishing returns. s = saving rate (assume this is constant) per year δ= depreciation rate (assume this is a constant) per year y = Y/L k = K/L k* = steady state of capital per worker (K/L) and sf(k) < δk. i. What is sf(k) ii. What is δk? iii. Interpret the meaning of sf(k) < δk?Consider the following graph of a production function when capital is constant. (The following is a description of the figure: it shows a two-axis graph; the horizontal axis measures labor and the vertical axis measures output; for a K fixed, the graph shows that maximal production that the firm can achieve with different levels of labor; the graph starts at cero production for zero labor; then it is increasing in all of its range; three levels of labor are shown as reference; there are L1, L2, and L3; they are related as follows L1<L2<L3; the graph is convex from 0 to L1, that is, its slope is increasing; the graph is concave from L1 on, that is, its slope is decreasing; the line that is tangent to the curve at L2, passes through the origin of the graph.) Denote by APL(L,K)=f(L,K)/L the so-called average product of labor (here f is the production function of the firm). From the graph we know that for the corresponding K: APL(L1,K)=MPL(L1,K) APL(L2,K)>MPL(L2,K)…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.
- The production function for an economy can be expressed as Y= F(K,L), where Y is real GDP, K is the quantity of capital in the economy, and L is the quantity of labor in the economy. If Y = K0.5 L0.5, what is real GDP if the quantity of capital is 900 and the quantity of labor is а. 400? b. What is/are the endogenous variable(s) in this model? What is/are the exogenous variable(s) in this model? с.Consider the production function Y=K1/2 N1/2 a. Compute output when K=37 and N=80 b. If both capital and labour double, what happens to output? c. Is this production function characterized by constant returns to scale? Explain. d. Are there decreasing returns to capital? Explain. e. Are there decreasing returns to labour? Explain. f. Write this production function as a relationship between output per worker and capital per worker. Show all your work. g. Let capital per worker be 6. What is output per worker? Now, double capital per worker to 12. Does output per worker more or less than double? h. Does the relation between output per worker and capital per worker exhibit constant returns to scale? Explain/show your workSuppose over time that a firm's production process undergoes capital-saving technological progress. This implies (1) the isoquants corresponding to any particular level of output will shift outward from the origin and the MRTSL,K along any ray from the origin will increase. (2) the isoquants corresponding to any particular level of output will shift outward from the origin and the MRTSL,K along any ray from the origin will decrease. (3) the isoquants corresponding to any particular level of output will shift inward toward the origin and the MRTSL,K along any ray from the origin will increase. (4) the isoquants corresponding to any particular level of output will shift inward toward the origin and the MRTSL,K along any ray from the origin will decrease. When a production function can be expressed as q = min{ak, bL}, the relationship between capital and labour in the production function is that (1) capital and labour are perfect substitutes, and the isoquants are linear. (2) capital and…
- Suppose the production function for widgets is given byq = kl - 0.8k2 - 0.2l2where q represents the annual quantity of widgets produced, k represents annual capital input, and l represents annual labor input.a. Suppose k = 10; graph the total and average productivity of labor curves. At what level of labor input does this average productivity reach a maximum? How many widgets are produced at that point?b. Again assuming that k = 10, graph the MPl curve. At what level of labor input does MPl = 0?c. Suppose capital inputs were increased to k = 20. How would your answers to parts (a) and (b) change?d. Does the widget production function exhibit constant, increasing, or decreasing returns to scale?Assume 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.