A firm has a production function F(L,K), where K is a fixed amount of capital, and L is the...
Question:
A firm has a production function F(L,K), where K is a fixed amount of capital, and L is the variable amount of labor hired. The equation {eq}w= pF_{L}(L,K) {/eq} determines the amount of labor that the firm hires. If L is considered as an implicit function of K, p, and w, then derive an equation for {eq}\displaystyle \frac{\partial{L}}{\partial{w}} {/eq}.
Labor Demand Function:
The labor demand function describes the quantity of labor a firm demands given wage rate in the market. In a competitive market, a firm will hire labor up to a point at which the marginal revenue product of the last unit of labor hired is equal to the market wage rate.
Answer and Explanation: 1
Become a Study.com member to unlock this answer! Create your account
View this answerIn a competitive market, the firms will take prices {eq}w, P{/eq} as given. In addition, we know that the quantity of capital {eq}K{/eq} is fixed. In...
See full answer below.
Ask a question
Our experts can answer your tough homework and study questions.
Ask a question Ask a questionSearch Answers
Learn more about this topic:

from
Chapter 7 / Lesson 4Learn about the labor supply and demand curves in economics. Explore the labor supply and demand curve shifts, and study the factors that impact both curves.
Related to this Question
- A firm production function is given by q(l,k) = l^{0.5}k^{0.5}, where q is number of units of output produced, l the number of units of labor input used and k the number of units of capital input used
- 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
- A firm employs labor L and capital K = 10 to produce using the production function q = 60K^2L^2 - K^3L^3. Derive the total product of labor curve.
- A firm's production function is given by Q=2L^1}/{2+4K^1}/{2 }] where Q, L, and K denote the number of units of output, labor, and capital, respectively. Labor costs are $2 per unit, capital
- Suppose a firm's production function is given by Q = F(L, K) = 5LK where L is the amount of Labor and K is the amount of capital. For this particular Cobb-Douglas production function, MRTS(L,K) = K/L. The wage rate is $100 per unit of labor and the rental
- A firm's production function is given as Q=10L^{1/2}K^{1/2} where L and K are labour and capital. Firm's iso-cost function is C = wL + rK. (a) Using this production function, express the amount of labour employed by the firm as a function of the level of
- A firm uses capital and labor to produce a single output good. The production function is given by F(K, L) = K L^{0.5} where K is the amount of capital and L is the amount of labor employed by the firm. The unit prices of capital and labor are given by, r
- Suppose in the short run, a firm is able to adjust the amount of labor (L) while the amount of capital (K*) is fixed. The production function is: f(K,L) = K^1/3 L^1/3. The price of output is 'p,' the
- A firm's production function is given by the equation Q=10K0.3L0.7 where Q represents units of output, K units of capital, and L units of labor. a. What are the returns to scale? b. What is the output elasticity of labor?
- A firm produces a product with labor and capital. Its production function is described by Q = 2L + 3K. Let w and r be the prices of labor and capital, respectively. (a) Find the equation for the firm's long-run total cost curves as a function of quantity
- 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%,
- The long-run production function for widgets is: Q=L^.6K^.4, where Q is total output, L is the quantity of labor employed, and K is the physical quantity of capital in place. a. Determine the short-run production function, if capital is fixed at 240 units
- Given the following production function: q = 2K ^(1/3)L^(1/2) where K is capital and L is amount of labor used in the process. Price of capital is r, wage is w. Find the firm's long run cost function,
- Capital and labor, denoted by K and L restively, are used to produce output denoted by q, so firm's production function is equal to q = min {K, 2L} The price of capital is $5 and the price of labor is
- A firm produces output according to a production function: Q = F(K,L) = min {6K,6L}. How much output is produced when K = 2 and L = 3? If the wage rate is $60 per hour and the rental rate on capital i
- 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)
- Let Y denote output K is capital stock and L is labor input. A denotes total factor productivity. The production function is the following: Y = AF(K, L) = A(K + L). a. Calculate output and the marginal product of capital (MPK) when A=3, K=1 and L = 1. b
- Let q L 1 3 K 2 3 w and r denote, respectively the production function, the prices of K capital and L labor. Suppose K 8 fixed and L is variable. c. Let FC, VC and MC denote fixed, variable, and ma
- A manufacturing firm's production function is Q = KL + K +L. For this production function, MPL = K + 1 and MPK = L + 1. Suppose that the price r of capital services is equal to 1, and let w denote the price of the labor services. If the firm is required t
- Firm Alpha uses capital K and labor L to produce output q. The firm's production function is F(K,L)= 5K^{0.4}\times L^{0.6}. The prices of capital and labor are r = 4 and w=4, respectively. Moreover,
- Suppose that a production function of a firm is given by Q= min{2L,K}, where Q denotes output, K capital, and L labor. Currently the wage is w=$10, and the rental rate of capital is r=$15. a. What is the cost and method of producing Q=20 units of capital
- Consider a Cobb-Douglas production function of: q(L,K) = 30K^0.3*L^0.7 where q is the production level, K is the quantity of capital, and L is the amount of labor. Suppose that a firm is interested in
- 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?
- Let Y denote output. K is capital stock and L is labor input. The production function is the following: Y = F(K,L) = 4K +2L. a. Calculate output and the marginal product of capital (MPK) when K=1 and L=1. b. Calculate output and the MPK when K=2 and L=1
- Assume that the production function is given by Y A K 0.5, L 0.5 , where Y is GDP, K is capital stock, and L is labor. The parameter A is equal to 10. Assume also that capital is 100, labor is 400, an
- A firm produces output according to the production function: Q = F(K, L) = 4 K + 8 L. a. How much output is produced when K = 2 and L = 3? b. If the wage rate is $60 per hour and the rental rate on capital is $20 per hour, what is the cost-minimizing inpu
- A firm produces according to the following production function: Q = K^{0.5}L^{0.5} where Q = units of output, K = units of capital, and L = units of labor. Suppose that in the short run K = 100. Moreover, wage of labor is W = 5 and price of the product is
- A firm has the following production function: q = 5LK0.5 + 2L2K - L3K, with capital fixed at K = 9 Show that the firm's elasticity of output with respect to labor in the short run is a function of ma
- A firm produces output according to a production function: Q = F(K,L) = min(4K,4L). a. How much output is produced when K = 2 and L = 3? b. If the wage rate is $50 per hour and the rental rate on capi
- A firm produces output, y, by using capital, K, and labor, L 2. A firm produces a good Y, using capital K and labor L. The production technology is described by the following function: F(K,L) = K^{\
- 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
- A competitive firm has a production function of the form Y = 2L + 5K, where 'L' is units of labor and 'K' is units of capital. Design a graph with the capital on the y-axis and labor on the x-axis. Sh
- A firm produces output according to a production function: Q = F(K,L) = min(9K,3L) a. How much output is produced when K = 2 and L = 3? b. If the wage rate is $60 per hour and the rental rate on capit
- A firm produces output according to a production function: Q = F(K,L) = min(6K,6L). a. How much output is produced when K = 2 and L = 3? b. If the wage rate is $35 per hour and the rental rate on capi
- Consider a firm whose production function is f(L, K) = AL^aK^b. For which values of A, L,K, a, and b is the Average Product of Labor for this company equal to the Marginal Product of Labor? a) a = 1 and any values of b, L, and K. b)a+b=1, b greater than
- Consider the following production function: Q=5L + 20K where Q is total output, L is the quantity of labor employed and K is the quantity of capital employed. What is the marginal product of labor? O
- A firm produces output according to a production function: Q = F(K,L) = min [2K,4L]. a) How much output is produced when K = 2 and L = 3? b) If the wage rate is $50 per hour and the rental rate on cap
- A firm produces output according to a production function: Q = F(K,L) = min {2K,2L}. a. How much output is produced when K = 2 and L = 3? b. If the wage rate is $40 per hour and the rental rate on cap
- A firm produces output according to a production function: Q = F(K,L) = min {9K,3L}. a. How much output is produced when K = 2 and L = 3? b. If the wage rate is $60 per hour and the rental rate on cap
- A firm produces output according to a production function: Q = F(K,L) = min {6K,6L}. a. How much output is produced when K = 2 and L = 3? b. If the wage rate is $60 per hour and the rental rate on cap
- 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
- 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
- A firm uses labor, denoted by L, and capital, denoted by K, to produce skateboards, denoted by q. The firm's production function is q = K^{1/2}L^{1/2}. The price of capital and labor are both equal to
- 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.
- A firm produces output according to the production function Q = F (K, L) = K + 10L. If the wage rate is $50 per hour and the rental rate on capital is $4 per hour, what is the cost-minimizing input m
- Here A is total factor productivity, K is capital, and L is labor. Note that A, K, and L, change over time so that A=A(t), K=K(t), L=L(t). a. Determine the marginal product of capital and labor. b. D
- A firm with fixed capital K = 100 sells output at p=200 and hires inputs for w = 100 and r = 100.The production function is q = 2K^{1/2}L^{1/2}. How many workers should this firm hire?
- Suppose a firm's production function is given by the equation Q = 12L^.5K^.5 . This firm operates in the short run where capital (K) is fixed at a quantity of 16. If the price per unit of the good is $1.9 and labor costs $10 per unit. Then the profit-maxi
- (1) A firm has the production function . The price of k is v, and the price of l is w. (a) Solve for the equation describing the k/l ratio that minimizes the total cost of producing a given level of o
- A firm produces output according to a production function: Q = F(K,L) = min\space {2K,2L}. a. How much output is produced when K = 2 and L = 3? b. If the wage rate is $65 per hour and the rental rate on capital is $35 per hour, what is the cost-minimizin
- Firm Omega uses capital K and labor L to produce output q. The firm's production function is F(K,L) = 12K+3L. The prices of capital and labor are r = 40 and w=4, respectively. In the long-run, when th
- A firm has the following production function: Q = 7*K1/2*L1/2a) Calculate the amount of output the firm should expect if it uses 25 units of capital and 50 units of labor. b) Suppose the firm wants to produce the same amount of output from a), but only h
- Suppose f(L, K) = KL^9 w = 1; r = 2: MPL = 9L^8K; MPK = L^9. How much labor and capital should the firm hire if it wants to produce 10 units of output while minimizing its cost of production? Show your work.
- A firm has the following production function: Q = 7*K1/2*L1/2 a) Calculate the amount of output the firm should expect if it uses 25 units of capital and 50 units of labor. b) Suppose the firm wants to produce the same amount of output from a), but only h
- Consider a firm whose production function is given by q(L, K) = LK where MPL = L and K and MPK = L. The per unit price of labour is w = $2 while the per unit price of capital is r = $1. (a)What is th
- Suppose the production function is y = 2K^{0.5}L^{0.5} and in the short-run K is fixed at K = 16. The market wage rate w=1 and price of capital r=4. The total costs C of a firm is: C = 4K + L. a. Find what is the short-run total cost function C (C as a fu
- 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
- 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 that a firm had a production function given by q = 2L0.4K0.8. The rental rate for the firm is $20 and the wage is $15. Solve the optimization condition for K and then fill in the value that appears in front of L.
- Suppose the production function is q=L^{0.75}K^{0.25}. In the short run, K is fixed at K=10. Derive an equation for the (short run) average product of labor and for the short run marginal product of labor. In the long run, capital and labor are both varia
- Suppose a firm's production function is given by F(L,H,K;A), where L, H, and K are the current quantities of labor, human capital, and physical capital employed in production, and A is an index of cur
- Output is produced according to Q = 4LK, where L is the quantity of labor input and K is the quantity of capital input. The price of K is $10 and the price of L is $5. Determine the cost minimizing co
- A firm has a production function given by Q=10K^{0.5}L^{0.5}. Suppose that each unit of capital costs R and each unit of labor costs W. a. Derive the long-run demands for capital and labor. b. Derive the total cost curve for this firm. c. Derive the lon
- A competitive firm produces output y using two inputs, labour L and capital K, The production function is given by F(K,L)=K^(1/3)L^(1/3). The firm takes the input and output prices as given and they a
- A firm produces output according to a production function: Q = F(K,L) = min {2K,2L}. a. How much output is produced when K = 2 and L = 3? b. If the wage rate is $65 per hour and the rental rat
- Suppose in the short run a firm's production function is given by Q = L1/2K1/2, and K is fixed at K = 36. If the price of labor, w = $12 per unit of labor, what is the firm's marginal cost of production when the firm is producing 48 units of output?
- A firm produces output according to a production function: Q = F(K,L) = min {9K,3L}. a. How much output is produced when K = 2 and L = 3?
- The production function for tomboys is f(L,K)=L/4+sqrt(K), where L is the amount of labor service used and K is the amount of capital service used. (a) What are the characteristics of the marginal products of labor (L) and capital (K)(increasing, consta
- Suppose the production function is given by Q = 5 K + 3 L. What is the average product of capital when 10 units of capital and 10 units of labor are employed? a) 5. b) 8. c) 3. d) 30.
- A firm is producing output Q using a mix of capital K and labor L. The production function is given by . A unit of capital costs $3 and a unit of labor costs $9. The firm wants to minimize the total c
- Suppose that a firm had a production function given by q = 2L0.5K0.5. The rental rate for the firm is $10 and the wage is $5. Solve the optimization condition for K and then fill in the value that appears in front of L.
- Suppose a firm with a production function given by Q = 30 K^{0.5}L^{0.5} produces 1,500 units of output. The firm pays a wage of $40 per unit and pays a rental rate of capital of $640 per unit. How many units of labor and capital should the firm employ to
- Suppose a firm with a production function given by Q = 30K^0.5L^0.5 produces 3,000 units of output. The firm pays a wage of $40 per unit and pays a rental rate of capital of $640 per unit. How many units of labor and capital should the firm employ to mini
- A firm produces output according to the production function Q = F (K, L) = K + 10L. How much output is produced when K = 10 and L = 4?
- Starting with the general production function Q=FK,L, which states that output Q is a function of or depends on the quantity of labor L and capital K used in production, derive the expression for the
- A firm has the production function q = k%%(vertical-align: super)0.50%% l%%(vertical-align: super)0.50%%. The price of k is v = 1 and the price of l is w = 1. The amount of k is fixed at k = 4. (a) W
- 1. The production function Y = K^1/3 L^2/3 describes: a. how any amount of capital and labor can be combined to generate output. b. how particular amounts of capital and labor can be combined to gen
- The long-run production function for a firm's product is given by q = f(K; L) = 5 K L. The price of capital is $10 and the price of labor is $15. a. Suppose the firm wishes to produce an output of 500. List 5 combinations of capital and labor that the fi
- A firm's production function is given by the equation Q = 100K0.3L0.8, where Q represents units of output, K units of capital, and L units of labor. a. Does this production function exhibit increasing, decreasing, or constant returns to scale? b. Suppose
- 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
- The production function describes: a. how any amount of capital and labor can be combined to generate output b. how any amount of capital and a particular amount of labor can be combined to generate o
- A firm's production technology is given by the production function q = 0.25LK, where L represents labor hours, K machine hours, and q the amount of output. The market wage and rental rates are w = $16 and r = $256. The firm currently is using 10 labor hou
- 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
- In the mathematical formulation of the short-run production function A. the quantity of capital employed is usually assumed to be fixed. B. the quantity of output is usually assumed to be fixed. C. the quantity of both labor and capital must be allowed to
- The following cubic equation is a long-run production function for a firm: Q= -0.0032K^3L^3 + 8K^2 L^2 where Q is the number of units produced per year. Suppose the firm employs 25 units of capital.
- 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
- 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
- A firm's production technology is given by the production function q = LK, where L represents labor hours, K machine hours and q the amount of output. The rental rates and market wage are, r = $100 and w= $25. The firm is operating in the long run where
- A firm has production function: Q = f ( K , L ) = 0.1 K 1 / 2 L 3 / 4 , where, K has a price w K =1, and L has a price w L =2 a) In the long run, the cheapest way to produce exactly one unit of output ( Q =1) is to use how much L ? (Round to the
- Suppose a firm can use either capital (K) or labor (L) in a production process. The firms production function is given by Q = 5L + 15K. The price of capital is $20 per unit and the price of labor is $8 per unit. a. What is the firm's total cost function?
- 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
- 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
- Suppose an economy's production possibilities are represented by the function Y = A K L where Y represents total output (i.e GDP), K is capital, L is labor, and A is total factor productivity (TFP
- A firm has a production function Q = F(K,L) with constant returns to scale, where K is units of capital and L is units of labour. Input prices are r = $2 per unit of K and w = $1 per unit of L. When i