# Consider a firm, that has production function, f(L,K)=3L^2/3K^1/3. Does this production function...

## Question:

Consider a firm, that has production function, f(L,K)=3L{eq}^{2/3} {/eq}K{eq}^{1/3} {/eq}. Does this production function satisfy the law of decreasing marginal returns of capital?

## Law of Marginal Returns to Input:

The law of diminishing returns to input states that the marginal output of a production process decreases as the amount of a single factor of production is increased incrementally keeping all other factors of production constant.

## Answer and Explanation: 1

Become a Study.com member to unlock this answer! Create your account

View this answer- The marginal product of capital is given by : {eq}\frac{\partial f}{\partial K} = L^{\dfrac{2}{3}} K^{\dfrac{-2}{3}} {/eq}.

- The marginal product of...

See full answer below.

#### Ask a question

Our experts can answer your tough homework and study questions.

Ask a question Ask a question#### Search Answers

#### Learn more about this topic:

from

Chapter 1 / Lesson 7Learn the definition of a production function in economics, understand the definition of a Cobb-Douglas production function and its formula, and explore some examples of Cobb-Douglas production function.

#### Related to this Question

- Consider the Production Function, Y = 25K1/3L2/3 (a) Calculate the marginal product of labor and capital (b) Does this production function exhibit constant/increasing/decreasing returns to scale? (
- Suppose that a firm's technology is given by the following production function: f(k,l) = 6k^{1/6} L^{1/6 } a. Prove that this production function exhibits diminishing marginal product in both k and l. This is not the same thing as decreasing returns
- Consider the linear production function q=f(K,L)=2L+K . a. What is the short-run production function given that capital is fixed at K=100? b. What is the marginal product of labor?
- Suppose that a firm has a production function given by q = 10L0.5K0.6. The firm has 10 units of capital in the short run. Which of the following will describe the marginal product of labor (MPL) for this production function? a. increasing marginal returns
- Consider an economy that is described by the production function Y = K^0.25L^0.75. Moreover, the depreciation rate of capital is delta = 0.2. What is the per-worker production function, that is y = Y/L? What is the marginal product of capital, that is par
- Consider the production function: f(L;K) =L+K(LK)^2= 1 f(L;K)has diminishing MPL and diminishing MPk, but does not have diminishing MRTS. Provide the evidence for this function. Consider the isoquant
- Consider the following production function F(K, L) = { KL } / {K + L } (a) Does it satisfy the Constant Returns to Scale Assumption? Explain. (b) Are marginal products diminishing? Explain. (If you can't find marginal products mathematically, you can com
- Suppose the production function is given by Y=AK^{1/3}L^{2/3} (a) What is the marginal product of capital given the production function? (b) Given your answer to part (a), why might an investor exp
- Assume a production function can exhibit increasing, constant or decreasing returns to scale. Describe the meaning of this statement using a simple production function Y = F (K, L), where K is capital
- Consider a firm with production function f(L,K) = 2L + 6K. Assume that capital is fixed at K = 6. Also assume that the price of capital r = 10 and the price of labor w = 2. Then, what is the marginal
- Consider a production function of the form: q = L^.5 K^.6 Determine the elasticity of output with respect to labor and the elasticity of output with respect to capital. Show that marginal products
- For each production function below, determine: (1) Whether there are diminishing marginal returns to labor in the short run, and (2) the returns to scale. 1. f(L, K) = 2L + 3K 2. f(L, K) = 4LK 3. f(L, K) = min{L, K}
- A firm's production is given by: q = 5L^{2/3} K^{1/3} (a) Calculate APL and MPL. Determine if the production function exhibits the law of diminishing marginal returns. Calculate the output (production) elasticity with respect to labor. (b) Calculate MRTS.
- Consider the production function: Q = K^(1/3) L^(2/3) where Q is quantity of output, K is capital, and L is labor. Does this function exhibit increasing, diminishing, or constant returns to scale?
- Suppose a firm's production function is given by f(k,l) = kl - 0.8k^2 - 0.2l^2 1. Fixing capital at k = 10, graph the marginal physical product of labour (MP_l), as a function of l. At what l does MP
- A firm has the production function f(x, y) = x^1.40y^1. This firm has: a. decreasing returns to scale and diminishing marginal products for factor x. b. increasing returns to scale and decreasing marginal product of factor x. c. decreasing returns to scal
- Suppose the production function for a firm is given by: q=4L^{0.5}K^{0.25}. In the short run, the firm has 16 units of capital. Find the Marginal Product of Labor (MP_L). (Round to the nearest 2 decimal places if necessary.)
- Suppose that a firm has a production function given by: q= 10 L^{0.4}K^{0.6}. The firm has 10 units of capital in the short run. Which of the following will describe the marginal product of labor (MP_L) for this production function? Select one: a. Decr
- Suppose a firm's production function is given by Q = L1/2*K1/2. The Marginal Product of Labor and the Marginal Product of Capital are given by: MPL = (K^1/2)/(2L^1/2), and MPK =(L^1/2)/(2K^1/2). a) S
- The production function takes the following formY = F(K,N) = zK^0.3N^0.7 (a) Write the expressions for marginal product of labor and marginal product of capital.
- A production function may exhibit _____. a. constant returns to scale and diminishing marginal productivities. b. increasing returns to scale and diminishing marginal productivities. c. decreasing returns to scale and diminishing marginal productivities.
- Consider a firm that has a production function f(L, K) = 3L^{2/3}K^{1/3}. What is the expression for this firm's Marginal Product of capital? A. MP_K(L, K) = 3L^{2/3}/K^{2/3} B. MP_K(L, K) = 2L^{2/3}/K^{1/3} C. MP_K(L, K) = 3L^{2/3}/K^{1/3} D. MP_K(L, K)
- Suppose a firm's production function is given by Q = L^{1/2}*K^{1/2}. The Marginal Product of Labor and the Marginal Product of Capital are given by: MP_L = 1/2L^{-1/2}K^{1/2} and MP_K = 1/2L^{1/2}K
- If the production function for a certain good exhibits constant returns to scale, does this mean that the law of diminishing marginal returns does not apply?
- Consider the following short-run production function: q = 4L2 - (2/3)L3. a. At what level of L do diminishing marginal returns begin? Show your derivation. b. At what level of L do diminishing returns begin? Show your derivation.
- According to the law of diminishing returns, over some range of output: a. Every production function exhibits diminishing returns to scale. b. Total product will decrease as the quantity of variable input employed increases. c. Marginal product will event
- Suppose a firm's production function is given by Q = L^(1/2)K^(1/2). The Marginal Product of Labor and the Marginal Product of Capital are given by: MP_(L) = K^(1/2)/(2L^(1/2)), and MP_(K) = L^(1/2)/(
- Given the production function f (xl, x2) = min{x1, x2), calculate the profit-maximizing demand and supply functions, and the profit function. What restriction must it satisfy?
- Consider a firm with two inputs, capital (K) and labor (L), with the price of capital Pk and the price of labor PL. The firm's production function is q(K, L) = 25KL. a. Write the firm's cost (as a function of K, L, Pk, PL). b. From the production function
- A production function can exhibit increasing, constant or decreasing returns to scale. Describe the meaning of this statement using a simple production function Y = F (K, L) , where K is capital and L
- Suppose that a firms fixed proportion production function is given by: q = min (5K, 10L), and that r = 1, and w = 3. a. Does this function exhibit decreasing, constant, or increasing returns to scale
- Consider the following production function: *Q=100K.4L.6 a) Derive expression for the marginal product of capital, and for the marginal product of capital. b) Compute the marginal products of capit
- Determine whether the following production function exhibits constant increasing or decreasing returns to scale in capital and labor. A). Y = AK^\frac{3}{4} L^\frac{3}{4}
- The production function of an economy is: Y = A * K^{0.3} * H^{0.7} a. What is real output when K = 20, H = 50 and A = 2? b. Does this production function exhibit diminishing marginal productivity of capital? Calculate MPK if K increases from 50 to 60 a
- Diminishing marginal returns means that: a. as more capital is used in production, but the labour input is held constant, MPK falls. b. as labour increases and capital decreases for a given level of output, the marginal product of labour divided by the
- Consider an economy that is described by the production function Y = K^0.25L^0.75. Moreover, the depreciation rate of capital is delta = 0.2. Find the golden rule of capital per worker kg^*, i.e. the steady state level of capital per worker that yields th
- Consider a production function of the form with marginal products MP_K = 2KL^2 and MP_L = 2K^2L. What is the marginal rate of technical substitution of labor for capital at the point where K = 25 and L = 5? A. 5 B. 25 C. 15 D. 1
- Give an example of a production function that exhibits increasing returns to scale and diminishing marginal product of labor at the same time. Prove that the function has these properties.
- Suppose two firms have the respective production functions: Firm 1: q=LK Firm 2: q=0.9LK a. Find the marginal product of labor and capital for each firm. b. For a particular level of labor and capit
- Consider a Cobb-Douglas production function: f(L,K)=0.5K^0.5L^0.5. Using this production function, solve a short-run profit maximization problem for a fixed capital stock K=4, output price p=8, wage rate w=2, and capital rental rate r=4.
- consider a firm that operates with the following production function: q = 2K^2L a. calculate the marginal products of labor and capital (MP_L AND MP_k) b. calculate the marginal rate of technical substitution of labor for capital, MRTS_{LK} Firm faces m
- Consider the following production function: Q = 10L2K, where Q is the amount of production, L is the amount of labor, and K is the amount of capital. a. Does this production function exhibit the law of diminishing returns? Explain. b. Does this production
- Suppose that the production function is Q = L^{2 / 3} K^{1 / 2}. a. What is the average product of labour, holding capital fixed? b. What is the marginal product of labour? c. Determine whether the production function exhibits diminishing marginal product
- Suppose a firm has a production function given by Q = L*K. Does this production function exhibit increasing, constant or decreasing returns to scale?
- Show that increasing returns to scale can co-exist with diminishing marginal productivity. To do so, provide an example of a production function with IRTS and diminishing marginal returns.
- The concept of the production function implies that a firm using resources inefficiently will: A. obtain more output than the theoretical production function shows. B. not be subject to diminishing marginal product. C. obtain exactly the amount that the
- Consider a firm which produces according to the following production function by using labor and capital: f(l,k) = k1/2 * l1/2 (a) Solve the cost minimization problem of this firm for the given wage
- Suppose a firm's production function is Q = 2K0.5L0.5. If the level of capital is fixed at 25 units, then what is the firm's short-run production function?
- A firm's production function is given by f(L, K) = LK^1/2. The prices of labor and capital are w = 20 and r = 10, respectively. Suppose the firm's capital is fixed at 25. Find, as functions of output
- The law of diminishing marginal returns (a) does not hold when the marginal product is always positive (b) has to hold when an additional unit of capital produces more extra output than an additional unit of labor (c) has to hold when increasing capital
- Assume that production is a function of capital and labor, and that the rate of savings and depreciation are constant. Furthermore, assume that the production function can be described by the function
- What happens with no diminishing returns? Consider a Solow model where the production function no longer exhibits diminishing returns to capital accumulation. More specifically assume that the product
- Consider two goods, x and y, each produced using two inputs, labor l and capital k. Which of the following statements is correct? a. If production functions exhibit diminishing returns to scale, the
- Suppose there is a fixed amount of capital K=20. Find a short run cost function CFK(q) when the wage is 6 and the rental rate of capital is 3 for a firm whose production function is F(K,L)=3^3/5L^2/5
- Suppose a firm's production function is given by Q = LK^2. Suppose the firm is producing 16 units of output by using 1 units of Labor and 4 units of Capital. What is the slope of the isoquant at this
- Consider the production function Y=\frac{X-500}{20}, where Y is output and X represents inputs. Graph this production function. Does it display decreasing, constant, or increasing returns to scale?
- Suppose that a firm's production function is given by Q = K^0.33L^0.67, where MPK = 0.33K - 0.67L^0.67 and MPL = 0.67K^0.33L - 0.33. As L increases, what happens to the marginal product of labor? What
- Consider a profit-maximizing firm with the following production function: f(x_1,x_2) = x_1 x_2. The prices of the two inputs are equal to w_1 = 4 and w_2 = 2, respectively. a) What are the returns-to
- The production function for a product is given by q = K1/2L1/4 where K is capital, L is labor and q is output. a. Find the marginal products of labor and capital. b. Is the marginal product of labor increasing or decreasing with labor? Is the marginal p
- Determine whether this production function exhibits increasing, decreasing, or constant returns to scale.
- Consider the following production function and marginal products: q = L^{0.8}K^{0.2} MP_L = 0.8K^{0.2}/L^{0.2} MP_K = 0.2L^{0.8}/K^{0.8} The wage is $4.80 and the rental rate of capital is $2.00.
- The production function for a firm is given by q = L^{.75} K^{.25} where q denotes output; Land K labor and capital inputs. (a) Determine marginal product of labor. Show whether or not the above production function exhibits diminishing marginal produ
- Suppose output is produced according to the production function: Q = M^0.5 K^0.5 L^0.5, where M is materials, K is capital and L is labor (inputs) used for the production. Does this production function exhibit decreasing, increasing, or constant returns t
- Consider the following production function. q = 100L^{0.8}K^{0.4} Currently, the wage rate (w) is $15.00 and the price of capital (r) is $5.00. If the firm is using 100 units of capital in production, how much should be employed to minimize costs?
- Suppose a Leontief production function is given by a. What does this production function tell you? b. Suppose the firm is currently employing 10 workers and 5 units of capital. What is output? c. Supp
- Given that the production function relating output to capital becomes flatter moving from the left to the right means that: A) The marginal product of capital is positive. B) There is diminishing marginal productivity of labor. C) There is diminishing mar
- 1. Consider the case of neoclassical production function : Y= 0.75X + 0.0042X^2 - 0.000023X^3 a. State down the corresponding profit function b. State the profit maximizing condition c. Assume P (p
- As its capital stock increases, a nation will: A. move rightward along a fixed production function. B. move leftward along a fixed production function. C. find its production function shifting upward. D. find its production function shifting downward. E.
- This firm doesn't use capital (K). They only use labor (L). Suppose the firm's production function is Y = L^(x). Furthermore, r = rental rate of capital and w = wage. Find the profit function and solv
- Suppose we know that output in the economy is given by the production function: Y_t = A_t K_t^(1/4) L_t^(3/4) a) Use partial derivative techniques to solve for the marginal product of capital (Remembe
- Suppose the production for good q is given by q=3k+2l, where k and l are capital and labor inputs. Consider three statements function about this function: I. the function exhibits constant returns to scale. II. the function exhibits diminishing marginal p
- In Neoclassical growth theory, when labour increases for a fixed level of capital, the aggregate production function exhibits: a. Diminishing output b. Diminishing marginal returns c. Increasing marginal returns d. Constant marginal returns
- The production function q=100k^0.4L^0.8 exhibits: a. increasing returns to scale but diminishing marginal products for both k and l. b. decreasing returns to scale and diminishing marginal products for both k and l. c. increasing returns to scale but dim
- Consider the production function q= sqrt(L) + 8K^3. Starting from the input combination (5,10), does the production function exhibit increasing, constant or decreasing returns to scale if inputs doubl
- A firm's production function is given by q = f(L, K) = LK + 2L^2 K - L^3. Suppose the firm is operating in the short-run with K = 9. A) What is the marginal product of labor function? B) For what values of labor does increasing marginal product exist? C)
- Suppose a firm's production function is given by Q = 2L + K. Also, the price of Labor, w = 10, and the price of Capital, r = 4. If the firm minimizes the cost of production, how much will it cost the
- Assume that an economy's production function is Y = 1000L^1/2, so that when the marginal product of capital is equated to the real wage the labor demand curve is L = 250, 000 (P/W)^2. The labor supply
- Consider an economy described by the production function: Y = F(K, L) = K^(1/2)L^(1/2). Find the per worker production function. Find the steady-state capital stock per worker as a function of the sav
- Suppose firms have the following production function This production function exhibits a. Increasing returns to scale b. Decreasing returns to scale. c. Constant returns to scale. d. The returns to sc
- Consider an economy described by the production function: Y = F (K, L ) = K1/2L1/2 where the depreciation rate is ? and the population growth rate is n. a) Find the per worker production function. b)
- A firm has the production function q = f (L, K) = L + K2 This firm has: a) Decreasing returns to scale. b) Increasing returns to scale. c) Constant returns to scale. d) Increasing marginal product. e) None of the above.
- Suppose you have a firm whose production function is given by Q=K^0.3L^0.7. Wages=3, Rental rates=6, Price of product = $10 a) In the short run, capital is fixed at 5. What is the optimal labor demand in the short run? b) What is the optimal ratio of c
- The law of diminishing returns implies that, with the use of capital fixed, as the use of labor rises, A. the marginal product of labor will fall eventually. B. total product will fall eventually. C. the production process will become technologically inef
- A firm has the production function f(k, l) = 2k sqrt l. Let the price of capital be r = 1, the price labor be w = 2, and the price of output be p. Find the marginal products of capital and labor. Does the firm have constant returns to scale?
- If a firm has a production function f(k,l) = 3k^{0.3}l^{0.5} where r = 8, w = 9, and the price of output = 17, What is profit maximizing level of capital? For this question both the level of capital
- Consider a production function given by: Q = 27K^{2}L^{0.5} - 2K^{4} A. Let L = 16. Find the level of K at which the marginal product of capital reaches a maximum B. Let L = 16. Find the level of K
- Why is it sensible to assume that the production function exhibits constant returns to scale and diminishing returns to capital?
- Consider a firm with the production function f(L,K)=L^{1/5}K^{4/5}. Assume that the price of capital r=3 and the price of labor w=2. If L^* and K^* are the amounts used by the firm to produce q units of output when both L and K are variable, then what is
- Consider the following production function: q = 4LK. Which term describes this production function's returns to scale? A. increasing returns to scale B. decreasing returns to scale C. constant returns to scale
- Consider a production economy with 10 units of capital, K, and 10 unitsof labor, L. Capital and Labor can be used to produce the goods, x and y. The production functions of x and y are x = Min{K,L} y
- The production function of a firm is y = min {2l, k} where y, l and k rest denote output, labor, and capital. The firm has to produce 10 units of output and the wage rate is 2 and the price of capital
- A firm's production function is Q = 5L2/3K1/3. a) Does this production function exhibit constant, increasing, or decreasing returns to scale, and why? b) What is the marginal rate of technical substitution of L for K for this production function? c) Wh
- A production function shows a firm how to: a. maximize profit b. maximize output c. minimize losses d. minimize output
- Suppose a production function is given by Q = 4K + 3L. What is the marginal product of capital when 10 units of capital and 10 units of labor are employed?
- Suppose the production function is given by Q = 3K + 4L. What is the marginal product of capital when 5 units of capital and 10 units of labor are employed?
- Suppose that the production function of a firm is given by the equation Q = 2K1/2L1/2, where Q represents units of output, K units of capital, and L units of labor. What is the marginal product of labor and the marginal product of capital at K = 40 and L
- Deriving short-run and long-run cost functions: Suppose a firm's production function is: y = K2L 2 The wage rate is w = 2 and the rental rate is r = 4. If the firm's capital is fixed at \bar{K} = 10 i
- Assume Knappy Knickers has the following production function and marginal product of labor: Y = L^{1/3} and MPL= 1/3L^{2/3} Use levels of labor equal to 10, 11 and 12 to show that this function exhibits diminishing marginal returns to labor. Clearly use