Given the following Cobb-Douglas production function, how much more output is produced by adding one more unit of capital (keeping labour constant) when K=100 and L=25? Y=4K0.5 L0.5 a.1 b.2 c.3 d.4
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Given the following Cobb-Douglas production function, how much more output is produced by adding one more unit of capital (keeping labour constant) when K=100 and L=25?
Y=4K0.5 L0.5
a.1
b.2
c.3
d.4
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- 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?1. Assume that a firm has the following production function: q = L0.5K0.6 a. Calculate output when L = 64 K = 32. b. What returns to scale does this production function exhibit? c. Calculate output if technology utilized by the firm increases by 25%. d. Determine, both, the marginal product of labour and capital functions (ignore c.). e. Calculate, both, the marginal product of labour and capital when L = 64, K = 32 and interpret your answers. f. Calculate the marginal rate of technical substitution when L = 64, K = 32 and interpret your answer.9-100L0.8 K0.4 Given the production function above assume that capital is fixed at 20 units. Calculate the cost minimizing quantity of labor. L=80 L=40 L=20 L=10 k
- Suppose the production function is given by O = 5K - 2L What is the marginal product of the 6th capital when 5 units of capital and 10 units of labor are employed? A5 b. 4 C. 11 d. 45Consider 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.Suppose the production function for widgets is given by q=kl -0.8k²-0.21² where q represents the annual quantity of widgets produced, k represents annual capital input, and I represents annual labor input. Suppose k = 10; at what level of labor input does this average productivity reach maximum? (please put your answer in numerical values with no comma or decimal place). How many widgets are produced at that point? (please put your answer in numerical values with no comma or decimal place). If k = 10, at what level of labor input does MPL = 0? Suppose capital inputs were increased to k = 20, at what level of labor input does this average productivity reach maximum? widgets are produced at that point? (please put your answer in numerical values with no comma or decimal place). If k = 20, at what level of labor input does MPL = 0? answer in numerical values with no comma or decimal place). Does the widget production function exhibit constant, increasing, or decreasing returns to scale?…
- In Example 6.4, wheat is produced according to the production function: | = 100 (K°-$L05). Beginning with a capital input of 4 and a labor input of 49, show that the marginal product of labor and the marginal product of capital are both decreasing. (Round your responses to two decimal places.) The MPK at 5 units of capital is 156.52. The MPK at 6 units of capital is 142.89 The MP, at 50 units of labor is 14.14. The MP, at 51 units of labor is 14. Does this production function exhibit increasing, decreasing, or constant returns to scale? A. Decreasing returns to scale because the inputs exhibit diminishing marginal returns. B. Increasing returns to scale because the inputs exhibit diminishing marginal returns. C. Constant returns to scale because a proportionate increase in all inputs results in the same proportionate increase in output.Show that the following production function has constant returns to scale. It can be through a particular example or by demonstrating the general case. 1/21/2 y = 5x;"x;2Q2: Suppose that a firm's production function of output Q is a function of only two inputs, L and K and can be written Q = L+ 4K. Let w = 5 and r = 25. If the firm produces 100 units of output, how many units of capital will it use? Q3: Suppose that a firm's production function of output Q is a function of only two inputs, L and K, and can be written Q = = min ( K , 2L). Let w 5 and r = 10. If the firm produces 20 units of output, how many units of capital will it use?
- Which of the following production functions exhibits increasing returns to scale in the factors of production K and L? a. y = ĀK0.3 L0.75 b. y = Kª(ĀL)-e,0 < a < 1 c. y = ĀKO.3L0.3 d. y = ĀK/4 + L³/4The production function for a product is given by q=100KL. Its marginal product functions are MPL=100K and MPK=100L. If the price of capital, r, is $200 per day and the price of labor, w, is $400 per day, what is the minimum cost of producing 1,000 units of output? The minimum cost of producing 1,000 units of output is ______? (Round all intermediate results to 3 decimal places and enter your response rounded to two decimal places.)Economic1. For each of the following production functions, determine whether there areincreasing, constant or decreasing returns to scale. a)Q = 3K + 4L b)Q = K + L + KL c)Q = 18K^ 0.6 L^0.3
