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 progress
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- 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?Microeconomics - Production FunctionFind the returns to scale of the following production functions:F(K,L) = K1/2 * L1/2F(K,L) = A* K3/4 * L1/2F(K,L) = 3K + 2LA farmer has 1 acre of land. If he uses X pounds of fertilizer he can harvest √x tons of wheat. What is his production function if he has A acres of land and can just replicate the same production process on each piece of land? XXX A * A VXA √XA
- 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=K2/3State how is the law of diminishing returns reflected in the shape of total product curve? What is the relationship between diminishing returns and the stages of production?Is it possible to increase the labor productivity (output per unit of labor) in a given production process which exhibits diminishing returns to labor? If so, how? Explain with a graph. NOTE = PLEASE EXPLAIN IN DETAIL EVERYTHING
- Is it possible to increase the labor productivity (output per unit of labor) in a given production process which exhibits diminishing returns to labor? If so, how? Explain with a graph. NOTE = PLEASE EXPLAIN IN DETAIL EVERYTHING. EXPLANATION DOES NOT MEAN DESCRIPTION. EXPLAIN EVERY DETAIL LONG.Please, assume that At is a technological variable, as reflected in the production functions where capital and labor factors are used too3. Imagine we live in a classical world. Suppose that the production function is Y = L²K², where L is the amount of labor and K is the amount of capital. The economy has 100 units of labor and 100 units of capital. a. Does the production function show Constant Returns to Scale? Why? b. Derive an expression for the marginal product of labor. Is the marginal product of labor diminishing? How does an increase in the amount of capital affect the marginal product of labor? Explain. What are the real wage and rental price of capital? d. What is the income share paid to labor? What is the income share paid to capital? C.
- 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…Prof. Smith and Prof. Jones are going to produce a new textbook. The production function for the book is: ?=?1/2?1/2?= is the number of pages in the finished book?= is the number of working hours spent by Smith?= is the number of working hours spent by JonesSmith's labor is valued at 3 TL per working hour and Jones's labor is valued at 12 TL per working hour. After having spent 900 hours preparing the first draft, Smith cannot contribute any more to the book. Jones will revise the Smith's draft to complete the book.a) How many hours will Jones have to spend to produce a finished book of 300 pages?b) What is the marginal cost of the 300th page of the finished book?Give only typing answer with explanation and conclusion Consider a production function with two inputs: f(x1,x2) = (x1)a(x2)b Suppose that a = 0.7 and b = 0.7. What type of returns to scale does this production function exhibit? Type 1 for increasing, 0 for constant, and -1 for decreasing.
