In one country, its production function of national output is Y = F(K, L) = A * K(3/4) * L(1/5). Does the production function have a constant return to scale, an increasing return to scale or a decreasing return to scale? And why? (show your work)
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(1) In one country, its production function of national output is Y = F(K, L) = A * K(3/4) * L(1/5). Does the production function have a constant return to scale, an increasing return to scale or a decreasing return to scale? And why? (show your work)
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- 1. Imagine an economy with a constant returns to scale production function. Answer the following: (a) Suppose this economy has 3000 units of physical capital, with workers having 200 years of education, and they work 5000 hours. Their output is worth $10,000. Now imagine the same economy has 6000 units of physical capital, 400 years of education, and the workers work 10000 hours. What is their output now? (b) b) Suppose this economy has 3000 units of physical capital, with workers having 200 years of education, and they work 5000 hours. Their output is worth $10,000. Now, their physical capital grows to 6000 units, but the other two inputs remain the same. Provide a range for what the economy's output might be. That is, what is the lower bound, and what is the upper bound for this economy's output? (c) Suppose this economy has 3000 units of physical capital, with workers having 200 years of education, and they work 5000 hours. Their output is worth $10,000. Call this Country A. Now…3(a) A firm's production function is initially Q=VKL. Over time, the production function changes to Q=KL^2 (Assume that L21 and K21). Verify that this change represents technological progress.Question 5 Which of the following production functions exhibit increasing return to scale? Decreasing return to scale? Constant return to scale? Note: X1 and X2 are inputs a. Y = AX95X? b. Y = 0.5X, + 10 c. Y = AX,X2 d. Y = 3X1 + 7X2
- Country A and Country B both have the production function: Y = F(K,L) = K^(1/3)L^(2/3). a) Does this production function have constant returms to scale? Explain.please answer the following, I have attached an image of the question for better format. Thanks! 2. Suppose that the production function of a country is given by Y=K3L0.7, where Y is output, L is labour, and K is capital. a)What is the return to scale property of the production function? B)What will happen to output if we double the use of capital and labour? C)Write the production function as a relationship between output per worker and capital per worker.Assuming that the production function [Y=A(K, L, N, H)] exhibits constant returns to scale we can derive productivity in the following way A.) Y/L = A(K, 1, H, N) B.) Y/L = A(K/L, 1, H/L, N/L) C.) Y/L = AK, AL, AH, AN D.) Y/L = C+I=G=NX
- 4.3 Under what conditions do the following production functions exhibit decreasing, constant, or increasing returns to scale? a. q = L + K b. q = L + LaKb + K5. Proving constant returns to scale A production function expresses the relationship between inputs, such as capital (K) and labor (L), and output (q). The following equation represents the functional form for a production function: q= f (K, L). If a production function exhibits constant returns to scale, this means that if you double the amount of capital and labor used, output is twice its original amount. Suppose the production function is as follows: ƒ (K, L) = 4K +9L. Prove that this production function exhibits constant returns to scale by completing the following algebraic equations. Assume that z is a positive number. f (zK, zL) 111. = 2q Which of the following production functions exhibit constant returns to scale? Check all that apply. f (K, L) = KL f (K, L) 7K0.5 10.5 □ f (K, L) = 3K0.5 L0.1QUESTION 1 For the production function Qs = K0.6L0.7 find the returns to scale, recall that a doubling of inputs that doulbes output is a CONSTANT returns to scale = 1.0 Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 = 1.2, 1.14 = 1.1).
- 1. Suppose the production function for trucks is given by: q = kl + 612 –13 where q represents the weekly quantity of trucks produced, k represents weekly capital input, and I represents weekly labor input. a. Suppose k = 45; at what level of labor input does this average productivity reach a maximum? How many trucks are produced at that point? b. Again assuming that k = 45, at what level of labor input does the total production reach a maximum? How many trucks are produced at that point?Question 24 Consider the following production function when K is fixed. (This is a description of the figure: it shows a two-axis graph; in the horizontal axis we measure labor and in the vertical axis we measure output, in this case articles as in the production function of a newspaper; the graph of the production function, for the given level of capital K fixed, is composed of two line segments; the first goes from the origin to the point (10,30); the second, starting from 10 on, is a horizontal line; it is also shown that the production for five units of labor is 15). Can we say that the production function satisfies the law of decreasing marginal returns of labor?True FalseConsider the Solow-Swan growth model, with a savings rate, s, a depreciation rate, ô, and a population growth rate, n. The production function is given by Y = AK + BK3/4L1/4 where A and B are positive constants. Note that this production is a mixture of Romer's AK model and the neoclassical Cobb- Douglas production function.