Suppose that the production function of a company is given by q = qL^2 · qC and that the amount of labour qL and the amount of capital qC are functions of time t. At time t = 2, we know that qL = 9 andqC =8 and that the growth rateof qL is equal to 2 and the growth rate of qC is equal to 8. Find the growth rate of the production q at that moment.
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Suppose that the production function of a company is given by q = qL^2 · qC and that the amount of labour qL and the amount of capital qC are functions of time t. At time t = 2, we know that qL = 9 andqC =8 and that the growth rateof qL is equal to 2 and the growth rate of qC is equal to 8.
Find the growth rate of the production q at that moment.
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- 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.The aggregate production function is Y = 3KL. If there are 20 units of capital and 50 units of labor, what is capital productivity? Group of answer choices 300 1000 600 150Assume that a country's production function is Y = K/2*L/2 and there is no population growth or technological change. a. What is the per-worker production function y = f (k)? b. Assume that the country possesses 40,000 units of capital and 10,000 units of labor. What is Y? What is labor productivity computed from the per-worker production function? Is this value the same as labor productivity computed from the original production function? c. Assume that 10 percent of capital depreciates each year. What gross saving rate is necessary to make the given capital-labor ratio the steady-state capital-labor ratio? (Hint: In a steady state with no population growth or technological change, the saving rate multiplied by per-worker output must equal the depreciation rate multiplied by the capital- labor ratio.)
- 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 production function Y = AK0.2L 0.8 . Suppose the capital growth is 20%, labor growth is 10%, and output growth is 50%. a. Does the production function satisfy diminishing return property? Does it reveal a decreasing return 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.
- A firm's production function is initially Q = KL . Over time, the production function changes to Q = K?L² (Assume that L > 1 and K > 1) Which one is correct for the situation? No technological progress, only change of function Technological progress Cannot comment on progressEconomies production function is Y = AK0.3N0.7. If K = 2000, N = 100, and A= 1, then Y = ?A firm's production function is initially Q = VKL I| Over time, the production function changes to Q = KVL (Assume that L =>1 and K=>1) - a) Verify that this change represents technological progress. - b) Is this change labor saving, capital saving, or neutral?
- Assume that a country's production function is Y = K1/2L1/2 and there is no population growthor technological change.a. What is the per-worker production function y = f (k)?b. Assume that the country possesses 40,000 units of capital and 10,000 units of labor. What isY? What is labor productivity computed from the per-worker production function? Is thisvalue the same as labor productivity computed from the original production function?c. Assume that 10 percent of capital depreciates each year. What gross saving rate isnecessary to make the given capital–labor ratio the steady-state capital–labor ratio? (Hint:In a steady state with no population growth or technological change, the saving ratemultiplied by per-worker output must equal the depreciation rate multiplied by the capital–labor ratio.)d. If the saving rate equals the steady-state level, what is consumption per worker?Assume that a country's production function is Y = K1/2L1/2 and there is no population growthor technological change.a. What is the per-worker production function y = f (k)?b. Assume that the country possesses 40,000 units of capital and 10,000 units of labor. What isY? What is labor productivity computed from the per-worker production function? Is thisvalue the same as labor productivity computed from the original production function?c. Assume that 10 percent of capital depreciates each year. What gross saving rate isnecessary to make the given capital–labor ratio the steady-state capital–labor ratio? (Hint:In a steady state with no population growth or technological change, the saving ratemultiplied by per-worker output must equal the depreciation rate multiplied by the capital–labor ratio.)d. If the saving rate equals the steady-state level, what is consumption per worker? Only D, other option answeredIn Wonderland production per worker (y) depends on capital per worker (3) such the y=10√k. Every year 15% of the capital stock depreciates, while workers in Wonderland save 10% of their income. Every year the population grows at as e of 3% a) How might Wonderland and Neverland achieve economic growth in the long run?