# Given the production function q = 1.37LK, what is the marginal product of capital? A) 1.37 B) 0...

## Question:

Given the production function q = 1.37LK, what is the marginal product of capital?

A) 1.37

B) 0

C) 1.37K

D) 1.37L

E) Cannot be determined with the information given.

## Marginal Product of Capital:

The term Marginal Product of Capital can be abbreviated as MPk that measures the extra amount of output that a firm can receive by adding one additional unit of capital, keeping the other variable inputs constant.

## Answer and Explanation:

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

View this answerSee 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 4 / Lesson 2In Economics, there are three factors involved in the theory of production: total product, average product, and marginal product. Explore this theory and learn how to maximize the efficiency of these production tools.

#### Related to this Question

- Given the production function q = 1.37LK, what is the marginal product of capital? A. 1.37 B. 0 C. 1.37K D. 1.37L E. Cannot be determined with the information given.
- Given the production function q = 6L + 2K, what is the marginal product of labor when capital is fixed at 15?
- 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 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 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
- Suppose the production function is given by Q = 2K + 5L. What is the marginal product of labor when 15 units of capital and 10 units of labor are employed?
- 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
- 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
- Given the Production Function Q = 72X + 15X^2 - X^3, where Q = output and X = Input a. What is the Marginal Product (MP) when X = 8? b. What is the Average Product (AP) when X = 6? c. At what value of
- 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
- The production function is given by Q = K^1/4L^1/4. a. Derive the marginal product of capital. Consider a production manager who must produce 200 units. b. Given this, express labor in terms of the needed output (200) and capital (K). c. From this, derive
- 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
- If the production function is Q = K^(1/2) L^(1/2) and capital is fixed at 100 units, then the marginal product of labor (MPL) will be?
- Consider the production function is q = L^0.6 + 4K. A) Starting from the input combination (10,10), calculate the marginal product of adding one worker. B) What is the marginal product of adding anoth
- 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)/(
- 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
- Suppose a firm's short-run production function is given by Q = 16L0.80. What is the marginal product of the fourth worker?
- 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 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
- 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
- Suppose the production function is Q = 20(K^0.5 L^0.5) and the value of capital is 100. A.) Calculate the total product for the following values of labour input: 1, 5, 10, 20, 40, 50, 80, 100, 150, 2
- Suppose the production function is Q = 20(K^0.5 L^0.5) and the value of capital is 100. A.) Calculate the total product for the following values of labor input: 1, 5, 10, 20, 40, 50, 80, 100, 150, 200
- How do you find the marginal product given a production function?
- The production function for the Gwilmo Firm can be written as Q = 9K^{1/2}L^{1/2}. 1. Graph the isoquant for Q = 1,350. 2. Assume K = 1,600 and L = 225. Calculate the marginal product of L. 3. Assume K = 1,600 and L = 225. Now, decrease L by one unit. By
- the question is based on the following table, which provides information on the production that requires one variable input. Marginal product is zero when the total product is _
- Write the equation for an isoquant for the production function q = f(K, L) = α*ln(K) + β*ln(L). Make sure to state it in an explicit form where K represents a function of L for a fixed level of output, q0. Hint: requires the knowledge of the e
- Suppose that a company produces output according to the following production function: Q = 0.5L^2 a) Define and calculate the marginal product of labor. b) Define and calculate the average product of
- 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
- A firm uses two inputs, X and Y and its production function is Q = radical(xy), where here we are using x and y to represent the quantities of the two inputs. (a) Calculate the marginal products of X
- Write the equations for the marginal product of capital, marginal product of labor, and marginal rate of technical substitution for the long-run production function q = K^2 L.
- Write the equations for the marginal product of capital, marginal product of labor, and marginal rate of technical substitution for the long-run production function q = 10L + K.
- For the production function, Q = K^{0.5}L^{0. 5}, the slope of the Q = 100 isoquant when L = 16 is: a. -39.06 b. -4 c. -25 d. -6.25
- Suppose a firm's short-run production function is given by Q = 4L^{0.8}. If the production function is Q = L^{0.8} K^{0.2}, how many units of capital is it using?
- Which of the following production functions exhibit constant marginal product of capital, K? In each case y is output and K and L are inputs. a. y=K*L^{2/3} b. y=3K^{1/2}*L^{1/2} c. y=K^{1/2}+L^{1/2} d. y=2K+3L
- Write the equations for the marginal product of capital, marginal product of labor, and marginal rate of technical substitution for the long-run production function q = 5L^0.5K.
- What is the marginal product of labor for this production function: Y=k^0 6L^0 4+ k^0 5L^0 5?
- If AVC = Q 2 - 10Q + 120 and MC = 6Q 2 - 40Q + 120, then the quantity at which AVC is minimized is: a. 11 b. 5 c. 1 d. 6 A firm's production function is Q = 2KL. Its marginal product of capital is
- You estimate a short-run production function to be Q = 16L^{0.8} which gives a Marginal Product of Labor function MPL = 0.8*16L^{-0.2} = 12.8/L^{0.2}. If the product made by the labor sells at a price of P=$8 per unit, then the Marginal Revenue Product of
- 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 function is q = 12L0.25K0.75. Determine the long-run capital-to-labor ratio \frac{K}{L} if the cost of a unit of capital ''(r)'' is three times the cost of a unit of labor ''(w)''.
- Suppose the production function is q = 12 L^{0.25} K^{0.75}. Determine the long-run capital-to-labor ratio (K/L) if the cost a unit of capital (r) is three times the cost of a unit of labor (w).
- From a long-run production function (e.g., Q = 4K + 2L or Q = K0.5L0.5), which of the following may be determined? i. the quantity of output resulting from all combinations of inputs (e.g., capital a
- Suppose that the production function for iPods is Q = 20K^0.5L^0.5. The marginal product of labor is 10(K/L)^0.5, and the marginal product of capital is 10(L/K)^0.5. Suppose that labor can be hired fo
- What is the equation for k* based on the values given below? Its per-worker production function is y = f(k) = 5k1/2. The marginal product of capital What is the equation for k* based on the values giv
- For the production function Q = K^{0.5}L ^{0.5}, the slope at any point on any isoquant will be: a. -2. b. -1 c. \frac{-K}{L} d. \frac{-3K}{2L}
- 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
- Suppose the following production function: Q = 10 (K)^{1/3} (L)^{2/3} subject to; W *L + r * K = Cost. a. Suppose that K the amount of capital is K = 8. If this company hires 64 workers (L), calculate the value of Q. b. Determine if this production func
- List whether each of the following production function functions has diminishing marginal returns to labor (Y or N). a. Q = 50K + 30L - .5L2, MPL.= 30- L b. Q = L.5K.8 MPL = .5K.8/L.5 c. Q = 2L + K
- Suppose that a firm's production function is given by Q = K^{2/3}L^{1/3} , where MP_L = w = 6 MP_K = r = 8 (a) As L increases, what happens to the marginal product of labor? (b) As K increases, w
- Assume that the following production function is given by: Q = 5 K0.8 L0.8 Pk = 10 Pl = 3 A) what is the value of the elasticity of the labor factor (L)? B) what is the value of the elasticity of th
- In the production function, Q = 10L1/2 K1/2. Calculate the slope of the isoquant when the entrepreneur is producing efficiently with 9 laborers and 16 units of capital. (Hint: The slope of the isoquant = the ratio of the marginal product of labor to the m
- A production function Q = 100 L 0.4 K ? 0.6 relates to output, Q, to the number of labour units, L, and capital units K. A) Derive the equation for the marginal and the average products of labour an
- Suppose the production function for a firm is given by q = 5L0.5K0.25. In the short run, the firm has 16 units of capital. Find the marginal product of labor (MPL). Round to 2 decimal places.
- A firm produces quantity Q of breakfast cereal using labor L and material M with the production function Q = 50 (ML)1/ 2 +M + L . a) Find out the marginal products of M and L. b) Are the returns to scale increasing, constant, or decreasing for this produc
- A firm produces output according to a production function: Q = F(K,L) = min {3K,6L}, where K is capital, and L is labor. a) How much output is produced when K = 2 and L = 3? b) If the wage rate is $55
- 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
- How much labor does a firm require to produce q = 1000 when capital is fixed at 5 and they have a production function equal to q = 200L0.5K0.5? a. L = 200 b. L = 2.5 c. L = 5 d. L = 2.25
- A more general form of the Cobb Douglas production function is q = f(L, K) = AL^aK^b where A, a, b > 0 are constants. Use calculus to solve for the marginal product of capital (MPK).
- Use the production function below to answer the following questions: A) Calculate marginal productivity (MP) and put this in the table. B) At what level of employment does diminishing marginal product
- Suppose the production function for widgets is given by: Q = f (K, L) = KL - 0.6 K^2 - 0.2 L^2. (a) Suppose L = 25 (is fixed), derive an expression for and graph the total product of capital curve (the production function for a fixed level of labor) and t
- Solve for the marginal product of labor for the following production function. Does the marginal product of labor increase, decrease, or remain constant with increases in Q? Q = (aL^{\rho} + bK^{\rho})^{\delta/\rho}
- Suppose that the production function takes the form Q = L - 0.9L^2. In addition, marginal revenue is $10 and marginal cost is $1. The optimal number of hours of labor is (blank).
- Consider the production function: Q = 12L - 2L^2 where Q is quantity of output, and L is labor. What is the average product?
- Suppose the empirical production function given is: Q = aK_{fixed}^3L^2 + bK_{fixed}^2L^3, then Q = AL^2 + BL^3, where A = aK_{fixed}^3, and B = bK_{fixed}^2 for simplicity. a. Derive the average product of labor, AP_L. b. Derive the marginal product
- Question 18 Consider a firm that has production function f(L,K)=4L2/3K1/3. What is the expression for this firm's Marginal Product of labor?
- Explain how a firm's production function is related to its marginal product of labor.
- Suppose the production function for good q is given by q=3k+2l where k and l are capital and labor inputs. a. What is the return to scale for this function? b. What is the RTS of this function?
- A firm has carefully estimated its production function to be: Q = K^0.4L^ 0.6 , where Q = units of output, K = units of capital, and L = units of labor. If both capital and labor were increases by 10%,
- A firm has the following weekly production function: Q = 20KL - 0.025KL^2. Suppose the firm is in the short-run with K fixed at 20. a. What is the equation for the marginal product? Explain whether the production function is consistent with the Law of Di
- A firm has the production function q = 0.2LK + 5L^2K - 0.1L^3K. Assume that K is fixed at 10 in the short run. A. What is the short-run production function? B. What is the marginal product of labor and the average product of labor in the short run? C. Whe
- The marginal product of capital depends on how many units of: a. labor is used. b. capital is used. c. labor and capital are used. d. None of the statements associated with this question are correct.
- A firm has the production function: Q = 30 + 10 L + 5 K^2 - 5 K. If the firm has 4 units of capital (K) they plan to use, how much labor is needed to produce 300 units of output?
- Suppose the production function is q = 20K^0.5L^0.5. Calculate the RTS (-MPL/MPK) when: a) K = 200, L = 300 b) K = 50, L = 400
- Suppose capital is fixed at 4 units in the production function Q = KL. Draw the total, marginal, and average product curves for the labor input.
- The sole producer of a product has determined that the marginal-revenue function is dr/dq = 190 - 1.2q - 0.21q^2, where r represents revenue and q represents the number of units sold. Determine the po
- Assume that a firm's production function Q = K1/2L1/2. Assume that the firm currently employs 200 units of capital and 100 units of labor. Determine the Average Product of Capital, Average Product of Labor, Marginal Product of Capital, and Marginal Produ
- A firm's production process uses labor, L, and capital, K, and materials, M, to produce an output, Q according to the function Q= KLM, where the marginal products of the three inputs are MP_L= KM, MP_K = LM, and MP_M= KL. The wage rate for labor is w = 2
- The production function is Q = K^.6L^.4. What is the marginal rate of substitution of L for K? What is the numerical MRS when K = 5 and L = 10? What is MRS if K = 10 and L = 5?
- An economist estimated that the cost function of a single-product firm is: C(Q) = 50 + 25 Q + 30 Q^2 + 5 Q^3. Based on this information, determine the following: a. The fixed cost of producing 10 units of output. b. The variable cost of producing 10 units
- Wheat is produced according to the production function q = 100(K^{0.8}L^{0.2}) a. Beginning with a capital input of 4 and a labor input of 49, show that the marginal product of labor and the marginal
- 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 is given by: MPL= K^1/2 /2L^1/2 and MPk= L^1/2/2K^ 1/2. Suppose the price of labor is w = 24 and the price of capital is r
- Consider the production function expressed in the following table: 1) What is the marginal product of the 4th unit of labor when K = 2? When K = 4? 2) What is the slope of the production isoquant (wit
- The marginal product of labor, MPL, for production function q = 25 KL^2 is [{Blank}]
- A firm has a production function of y = f(L, k) = ( sqrtL + sqrtk)^2 a) Find expressions for the marginal product of labor and capital (b) Find the cost function
- What is the cost function of production function y= \sqrt {min(x,y)} + z^3? Input prices are w1 , w2 ,w3 respectively.
- Assume that demand equation is given by q = 6000 - 100p. Find the marginal revenue for the given production levels (values of q). a. 1000 units b. 3000 units c. 6000 units
- Suppose the production function of automobiles is given by Q = K^(1/4)L^(1/4) a. Show that the marginal product of any given quantity of labor increases as capital is increased. b. Suppose Japanese a
- If a price taking firm's production function is given by q=2\sqrt l, its supply function is given by: a. q = 2pw b. q = p/w c. q = 2p/w d. q = p/2w
- 1. Suppose a firm's short-run production function is given by Q = 16L0.8. What is the marginal product of the fourth worker? a. 36 b. 49 c. 1.85 d. 10
- Suppose a production function is q = K^(1/2)L^(1/3) and in the short run capital (K) is fixed at 100. If the wage is $10 and the rental rate on capital is $20, the short run marginal cost is _____.
- A firm's production function is given by Q = 2L - L^2 + K. The price of labor is w > 0 and the price of capital is r > 0. Assuming the firm uses both labor and capital, derive the long-run total cost function.
- 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
- Suppose the production function for T-shirts can be represented as q = L^(0.25)K^(0.75). When K = 1 and q = 2, what is the slope of the isoquant? If there is insufficient information to answer the que
- 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
- 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 that a firm faces the production function Q = 3K^{0.2}L^{0.3}, where the cost of labor and capital are w and r. What are the demand curves for labor and capital?
- Consider a firm whose production function is Q = 0.4K^0.5L^0.5. Its level of capital is fixed at 100 units, the price of labor is PL = $4 per unit, and the price of capital is PK = $2 per unit. Given this information, the firm s total cost function is A)