Consider the following information about how a firm's output Y is related to the amount of labor...
Question:
Consider the following information about how a firm's output {eq}Y {/eq} is related to the amount of labor it hires, {eq}L {/eq} (holding the amount of capital, K, constant).
| L | Y |
|---|---|
| 0 | 0 |
| 1 | 301 |
| 2 | 477 |
| 3 | 602 |
| 4 | 699 |
| 5 | 778 |
| 6 | 845 |
A. Compute the marginal product of labor associated with each additional unit of labor hired.
B. Plot the firm's demand for labor, with {eq}L {/eq} on the horizontal axis and the real wage, {eq}W/P {/eq}, on the vertical axis.
C. Suppose the nominal wage is {eq}W = 237 {/eq}, and the price of output is {eq}P = 3 {/eq}. How many units of labor should the firm hire and why?
D. Suppose the nominal wage rises to {eq}W = 291 {/eq}. How many units of labor should the firm hire now?
Labor demand
The input demand function, or specifically labor demand function, expresses the relationship between the input price (wage rate) and the quantity of inputs (labor) hired. The profit-maximizing input usage is attained at the level where the marginal product equals the real wage rate.
Answer and Explanation: 1
Become a Study.com member to unlock this answer! Create your account
View this answer
A. Compute the marginal product of labor associated with each additional unit of labor hired.
| L | Y | MPL |
|---|---|---|
| 0 | 0 | ...
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:
Get access to this video and our entire Q&A library
Understanding Shifts in Labor Supply and Labor Demand
from
Chapter 7 / Lesson 4
58K
Learn 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
- Consider the following information about how a firm's output Y is related to the amount of capital it hires, K (holding the amount of labor; L, constant). ||K||Y |0|0 |1|30 |2|55 |3|75 |4|90 |5|100 |6
- 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
- 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 = 4\sqrt(LK), where q is the quantity of output produced, and L and K respectively denote the quantity of labor and capital used. Given this production fu
- 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 functions. Y = AK^{0.5}L^{0.5}, Y = AK + L A. Fixing total factor productivity (A) at 10 and capital employment (K) at 4 units, what is the marginal product of labor associated with labor employment of 25, 35, and 45 for
- 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
- Consider the following production function q= f(k, l)= kl, where k is capital and l is labor used. Assume the k is fixed at 2 units. Rental rate of capital is given by r and wage rate of labor is given by w. a) Are we in long run or short run? Why? b) F
- Consider the production function f(L, K) = L + K. Suppose K is fixed at 2. Find algebraic expressions for the total product of labor (TPL), the average product of labor (APL), and the marginal product
- Consider the following production function: Y=0.2L^{0.5}K^{0.5}. Beginning with K=4 and L=49, show the marginal product of labor (MPL) and the marginal product of capital (MPK) are both decreasing by: a. Calculate MPK, when K=4, K=5, and K=6, b. Calcula
- Consider the following table. What is the total output when 1 worker is hired? | Number of Workers | Total Output | Marginal Product | 0 | 0 | -- | 1 | | 30 | 2 | | 45 | 3 | | 60 | 4 | | 50 | 5 | | 40
- 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,
- Consider the following table. What is the total output when 4 workers are hired? | Number of Workers | Total Output | Marginal Product | 0 | 0 | -- | 1 | | 30 | 2 | | 45 | 3 | | 60 | 4 | | 50 | 5 | | 40
- 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? (
- 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 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 w= pF_{L}(L,K) determines the amount of labor that the firm hir
- Consider the following table. At which number of workers does diminishing marginal product begin? | Number of Workers | Total Output | Marginal Product | 0 | 0 | -- | 1 | 300 | | 2 | 500 | | 3 | 600 | | 4 | 650 |
- A firm has the following production function: Q=2K L. Capital is fixed at 16 units. (a) calculate the average product of labor when 16 units of labor are utilized (b) calculate the marginal product
- 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
- Do the following production functions, where Q is total output, L is the quantity of labor employed, and K is the quantity of capital employed, exhibit constant, increasing, or decreasing returns to scale. Explain. a. Q=3LK^2 b. Q=8L+5K
- Consider an economy in which the marginal product of labor MPN is MPN = 309 - 2N, where N is the amount of labor used. The amount of labor supplied, NS, is given by NS = 22 + 12w + 2T, where w is the
- Consider the information in the following table. What is the marginal physical product of the third unit of labor? a. 80 b. 45 c. 35 d. 100 | Labor | Output | 0 | 0 | 1 | 20 | 2 | 45 | 3 | 80 | 4 | 100 | 5 | 110
- Consider the following production function Q=100K.4L.6. The wage rate is $12/hr and rental rate on capital is $8/hr. a) Compute the minimum cost of producing 200 units of output b) Use an isoquant and
- Refer to the table below. What does the marginal physical product equal when the amount of labor goes from 12 to 13 units. a. 58.8 b. 70 c. 760 d. 690 |Labor input (workers/day)|Total physical product (output/day) |10|500 |11|600 |12|690 |13|760 |14|800
- 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
- Consider the following production function y = F(K, L) = TK \alpha L \beta where K and L represent capital and labor inputs respectively. Denote by s the capital-labor ratio (s = K L ). T captures technological progress and is assumed constant here. \al
- 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)
- Consider the following scenario: the firm estimates that currently, its marginal product of labor is 80, while the marginal product of capital is 160. The firm pays $40 in the rental price of capital
- 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
- The following table shows the relationship between workers and output for a small factory in the short run, with capital held constant. Find the marginal product of labor (MP_L).
- 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.
- 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
- Consider the following production function: Y = zK 1/3 N 2/3 If K is fixed, set up the firm's maximization problem and solve for the labor demand in terms of exogenous variables k, w, z.
- 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
- 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
- The following table shows data of a firm that produces watches. If the firm's marginal resource cost of labor is constant at $18 per unit of labor, at the profit-maximizing level of output, the firm will hire _________ of labor. a) five units b) three uni
- Consider the following production function: q = 100 L^(0.5) K^(0.5). Currently the wage rate (w) is $20.00 and the price of capital (r) is $5.00. If the firm is using 100 units of capital in production and the production price is $10, how much labor shoul
- Suppose you have the following production function: Q = L^25 K^75, where Q is production, L is the amount of labor used in production, K is the amount of capital. The marginal product of labor is mathematically defined as: partial Q/ partial L. If K is fi
- Consider the following production function: a. Suppose K=10. Determine the average product of labor function, APL. At what level of labor input does the average product of labor reach a maximum? How m
- Consider a firm that has just built a plant, which costs $1,000. Each worker costs $5.00 per hour. Based on this information, fill in the table below. Number of Worker Hours Output Marginal Product
- 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
- Consider the production function Q = 6L^2 - L^3. a. Find the average product. Find the number of labor (L) that the firm should hire to maximize the average product. b. Find the marginal product. Find the number of labor (L) that the firm should hire to
- 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.
- Consider the following Cobb-Douglas production function Y = 30K1/2L1/2. Calculate de marginal product of labor. Find the numerical value of MPL when K = 32 and L = 4. In the equilibrium, if we consider that the economy employs 8 workers, what would be the
- 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 the following production function: Q = 100K^(0.4)L^(0.6). The wage rate is $12/hr., and the rental rate on capital is $8/hr. A. Compute the minimum cost of producing 200 units of output.
- Consider the following production function: q = 100L^{0.8}k^{0.4} Currently the wage rate (w) is $1.00 and the price of capital (r) is $2.00. If the firm is using 200 units of capital in producti
- Consider a competitive firm with the following profit function \prod = R ? C = PQ ? wL ? rK, where P = Price of the output Q = Output L = Labor input
- Consider a profit-maximizing firm that uses labor, L, as an input to produce its output, Q, according to the production function Q = L^1/2. Labor is paid an hourly wage w. The firm's total revenue is
- Consider the following table. A. Draw the total product curve. B. Find the marginal product (MP) and average product (AP) for each quantity of labor. Draw the graphs for MP and AP curves on the same plane. C. What can be said about the relationship betwee
- Consider labor that is hired for $18 per hour. If the last hour of labor hired produces 8 units of output which sells for $10 per unit, that labor hour's marginal revenue product is: A) $1.20 B) $4.44 C) $64 D) $80 E) $144
- 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?
- Consider the production function f(L,K)=L+K. Suppose K is fixed at 2. (a) Find algebraic expressions for the total product of labor function TP(L), the average product of labor AP(L), and the marginal
- Consider the information in the following table. What is the marginal physical product of the fourth laborer? a. 80 b. 45 c. 35 d. 100 | Labor | Output | 0 | 0 | 1 | 20 | 2 | 45 | 3 | 80 | 4 | 100 | 5 | 110
- 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
- Consider the Cobb-Douglas production function. K is the amount of capital, and L is the amount of labor. The isoquant associated with this function reflects the levels of capital and labor that yield
- Consider a newspaper with production function f(L,K)= 4min(L,K), where L is the units of labor and K the units of capital they use. Denote by APL(L,K)=f(L,K)/L the so-called average product of labor (here f is the production function of the firm). Is 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
- Consider a firm which produces according to the following production function just by using labor f(l)=ln(l) a) Solve the cost minimization problem of this firm for the given wage rate, w. b) Derive t
- Consider a call center with production function f(L,K)=30L+300K, where L is units of labor and K is units of capital. Denote by APL(L,K)=f(L,K)/L the so-called average product of labor (here f is the production function of the firm). Suppose that K=2. For
- 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
- Calculate a firm's labor demand for the following production functions. Assume that output is 100 and the rental cost of capital is 1. In each of the following cases, calculate the amount of labor
- 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)
- This firm has a wage of $100 per worker, according to the following output schedule, the marginal cost when the firm is producing 15 units. Marginal cost is Labor Output 1 5 2 15 3 20 4 24
- Refer to the table below. This firm sells output in a competitive product market at an equilibrium price of $3. If the competitive wage for a unit of labor is $45, how many units of labor will be employed? a. 2 b. 3 c. 8 d. 5 e. 4 |Units of Labor |Margin
- 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
- Scenario 1: A production process has the following input-output relationship using labor (L) and capital (K). The following table provides information on how many outputs can be produced from L and K:
- 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
- In order to hire the least-cost combination of labor and capital, the firm must do which of the following? A. Find the combination of labor and capital where the marginal product of labor is equal to the marginal product of capital. B. Find the combinatio
- If the marginal product of labor is MPL = 100k - L and the marginal product of capital is MPk = 100L - K, what is the maximum combination of labor and capital that would be employed? The producer has
- 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 an economy with the following production function: Y = AK^{.5}L^{.5} The labor force is constant. The rate of depreciation is δ = .1, the savings rate is s = .3. a. Has this production function constant returns to scale? Why? b. Write t
- The marginal product of labor is the change in total product from a one-unit increase in A. the wage rate. B. both the quantity of labor and the quantity of capital employed. C. the quantity of labor employed, holding the quantity of capital constant. D.
- Assume a firm is currently employing 20 units of capital and 100 units of labor in its production process. Assume also that the marginal product of the 20th unit of capital is 40 units of output, the marginal product of the 100th unit of labor is 10 units
- Consider the following production function: Q = 10KL. If w = 25, r = 75, and c = 1200, find the minimum cost combination of capital and labor to produce a given level of output.
- When calculating the marginal product of labor, which are held constant? A. output and capital B. output but not capital C. capital but not output D. neither output nor capital
- Suppose that labor is the only input used by a perfectly competitive firm. The firm's production function is as follows: (TABLE). Calculate the marginal product for each additional worker.
- 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
- Consider the following production function: Q = F(L, K) = L^4 * K^7. A) Does this production function exhibit diminishing or increasing marginal rate of technical substitution of labor for capital? Show your work. B) Find the elasticity of substitution fo
- 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
- 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 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 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
- Refer to the following output for data for a firm in the short run (labor is the variable input and all other factors of production are fixed). Number of workers Units of output 0 0 1 20 2 50 3 70 4 80 5 85 6 87 With the addition of which labor does dimi
- Explain how a firm's production function is related to its marginal product of labor.
- Assume the price of output is p = 10 dollars, the marginal product of labor is given by the equation MPL = 20 - (1/2)L, and the price of labor is wL = 100 dollars. Then, the optimal quantity of labor is: A) 5 Workers B) 10 Workers C) 20 Workers D) 25 Work
- Consider the following information: Q = 14 L + 38 K PL=30, PK=11, P=65 and C=4,891 What is the profit maximizing level of labor?
- Consider a firm where, in the long-run, K and L are imperfect substitutes. The firm is currently production 1000 units of output with K = 10 and L = 2. A this mixture of inputs, the MRTS is 8. The cost of labor is 8 and the cost of capital is 24. (a) Is
- A firm produces output with capital and labor. Suppose currently the marginal product of labor is 21 and the marginal product of capital is 6. Each unit of labor costs $12 and each unit of capital co
- 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?
- For the following Cobb-Douglass production function, q = f ( L , K ) = L 0.45 K 0.7 a. Derive expressions for marginal product of labor and the marginal product of capital, M P L and M P K . b. D
- Suppose a firm finds that the marginal product of capital is 60, and the marginal product of labor is 20. If the price of capital is $6, and the price of labor is $2.50, describe how the firm should adjust its mix of capital and labor. What will be the re
- Suppose that a firm's production function is Q = F(L) = L^3 - 200 L^2 + 10,000 L. Its marginal product of labour is MP_L = 3 L^2 - 400 L + 10,000. At what amount of labor input are the firm's average and the marginal product of labor equal?
- 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
- 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
- Consider a firm that uses labor (L) and capital (K) to produce a general output (q) using the following production function: \\ q = K^{0.9}L^{0.1} \\ The firm seeks to produce q = 60 units for sale and faces prices for labor of w = 5 and capital of r = 6.
- Consider a production function \text Y = \text z \text F(\text K, \text N^d). Which of the following properties we assume for F? 1. Constant returns to scale. 2. Output increases with increase in either the labor input or the capital input. 3. The margina
- 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
- 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
- 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?
Explore our homework questions and answers library
Browse
by subject