Based on the notations and assumptions used in class, which of the following is/are TRUE regarding the production function y = ka, where 0 < a < 1? (i) It is expressed in per capita form. (ii) The function exhibits constant returns to scale. (iii) Production per worker depends on the amount of capital per worker.
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- Based on the notations and assumptions used in class, which of the following is/are TRU regarding the production function y=k, where 0 < a <1? (i) It is expressed in per capita form. (ii) The function exhibits constant returns to scale. (iii) Production per worker depends on the amount of capital per worker. O a. (i), (ii), and (iii) O b. Only (1) O c. Only (iii) Od. Only (ii)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?Which of the following production functions exhibits increasing returns to scale? OA. AY=k1/2 1/2 O B. Y=K°L1-a O.Y=k1/3L 2/3 O D. Y=K1/2L 3/4 O E. Y=K1/3L 1/3
- With the Cobb-Douglas production function Y=zK1/4nd3/4, if both capital and labour increase by 20%, what will happen to output? O Output will increase by exactly 20% O Since the average value of the exponents in the production function is 1/2, output will only increase by 10%. Because the production function exhibits diminishing returns, output will increase by less than 20%.QUESTION 25 Which of the following production functions exhibits constant returns to scale? OA Y=KL O B. Y=KªL1-a ocY=K!/3_ 1/3 O D. Y=K1/4_ 1/2 O E. V=K2/3Output Y is produced according to Y = F(K, L), where K is the capital stock and Lis the number of workers. The production function F(K, L) has constant returns toscale and diminishing marginal returns to capital and labour individually. The levelof technology is assumed to be constant over time. Capital per worker is denotedby k = K/L and output per worker by y = Y/L, and the two are related according toy = f(k), where f(k) = F(k, 1) is the per-worker production function. Investment is equal to saving, which is a constant fraction s of income Y. Capitaldepreciates at rate δ and the number of workers grows at rate n. The change incapital per worker over time is ∆k = sf(k) − (δ + n)k. Consider a country that has reached its steady-state capital per worker. Then, inone year, the country suffers severe flooding that destroys part of its capital stock.Assume this is treated as a one-off event that is not expected to reoccur. explain what happens to incomeper worker in the short run and the…
- Please, assume that At is a technological variable, as reflected in the production functions where capital and labor factors are used tooReturns to scale in production: Do the following production functions exhibitincreasing, constant, or decreasing returns to scale in K and L? (Assume Ais some fxed positive number.)(a) Y = K1/2L1/2(b) Y = K2/3L2/3(c) Y = K1/3L1/2(d) Y = K + L(e) Y = K + K1/3L1/3 (f ) Y = K 1/3L2/3 + A (g) Y = K 1/3L2/3 − AWhich of the following production functions does NOT exhibit constant returns to scale? O a. Y = (L^1/2)*(K^1/2) O b. Y=KL O c. All of the other choices exhibit constant returns to scale. O d. Y = 2K + 2L
- The Cobb-Douglas production function is a classic model from economics used to model output as a function of capital and labor. It has the form f(L, C)=²1C²2 where co. ₁, and care constants. The variable L represents the units of input of labor and the variable C represents the units of input of capital. (a) In this example, assume co5, c, 0.25, and c₂-0.75. Assume sach unit of labor costs $25 and each unit of capital costs $75. With $70,000 available in the budget, devalop an optimization model for determining how the budgeted amount should be allocated between capital and labor in order to maximize output. Max s.t. L, CZO € 70,000 (b) Find the optimal solution to the model you formulated in part (a). What is the optimal solution value (in units)? (Hint: When using Excel Solver, use the bounds 0S LS 3,000 and 0 s Cs 1,000. Round your answers to the nearest integer when necessary.) units at (L. C)=(Which of the following production function exhibits Economies of Scale? Q = K1/2L1/3 %3D Q = K'/²L!/2 %3D O Q = K² + L Q = K'/2 + Lcost data:Assembly: Total cost of production = 400Earnings of High-Skilled Labor = 100Earnings of Low-Skilled Labor = 200Earnings of Capital = 100R&D: Total cost of production = 400Earnings of High-Skilled Labor = 175Earnings of Low-Skilled Labor = 125Earnings of Capital = 100A) In which factor is assembly intensive? In which factor is R&D intensive? Suppose that due to the opening of trade, the price of assembly falls by −20%, the price of R&Dremains unchanged, 0%, and capital’s share earnings remains constant. What has happened to the relative wage of high-skilled/low-skilled labor? Does this match the predictions of the offshoring model?