Suppose that labor is the only input used by a perfectly competitive firm. The firm s production...
Question:
Suppose that labor is the only input used by a perfectly competitive firm. The firm's production function is as follows:
| Days of Labor | Units of Output |
|---|---|
| 0 days | 0 units |
| 1 | 7 |
| 2 | 13 |
| 3 | 19 |
| 4 | 25 |
| 5 | 28 |
| 6 | 29 |
| 7 | 29 |
a. Calculate the marginal product for each additional worker.
b. Each unit of output sells for $10. Calculate the value of the marginal product of each worker.
c. Compute the demand schedule showing the number of workers hired for all wages from zero to $100 a day.
Input Factors
The factors with the help of which the output level of the firm is produced are called the input factors or the factors of production. The input factor can be labor, land, capital, and many more. The factors can be varied, but what they have in common is that they help to produce the desired output.
Answer and Explanation: 1
Become a Study.com member to unlock this answer! Create your account
View this answer(a) The marginal product of labor is the incremental increase in the value of the total product or output with the employment of a labor into the...
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
Marginal Product of Labor: Definition, Formula & Example
from
Chapter 3 / Lesson 49
81K
Understand the meaning of marginal product of labor. Learn the marginal product of labor (MPL) formula, its significance, and how to calculate MPL with examples.
Related to this Question
- A. Suppose the price of output is $4 per unit. What is the value of the marginal product of labor as the firm moves from using three workers to using four workers? B. If this profit-maximizing firm sells its output in a competitive market for $4 per unit
- 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
- When labor is the only input a firm uses, the marginal cost of a unit of output can be defined as the A. marginal product of labor divided by the wage. B. marginal product of labor multiplied by the
- The value of marginal product of labor equals: A. the marginal product of labor divided by the price of a unit of output. B. the price of a unit of output divided by the marginal product of labor. C. the price of a unit of output multiplied by the margin
- Suppose that the firm's only variable input is labor. When 50 workers are used, the average product of labor is 50 and the marginal product of labor is 75. The wage rate is $80 and the total cost of the fixed input is $500. What is the marginal cost? a) $
- Explain how a firm's production function is related to its marginal product of labor, how a firm's marginal product of labor is related to the value of its marginal product, and how a firm's value of
- Suppose the marginal product of labor is currently equal to the average product of labor. If you were a new worker being hired to the firm, would you prefer to be paid the value of your average product or the value of your marginal product? What would it
- Explain how a firm's production function is related to its marginal product of labor, how a firm's marginal product of labor is related to the value of its marginal product, and how a firm's value of a marginal product is related to its demand for labor.
- Suppose a firm has a constant marginal product of labor, where one additional worker adds four units of output given any initial quantity of workers. What do the average variable and marginal costs look like for this firm? Provide a graph of the MC and AV
- In the table below, calculate the marginal product of labor when each unit of labor is hired. At what unit of labor does diminishing marginal returns set in?
- 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?
- Suppose that a competitive firm's marginal cost of producing output q(MC) is given by: MC(q)=6+2q. Assume that market price (P) of the firm's product is $18. a. What level of output (q) will the firm produce? b. What is the firm's producer surplus? Suppos
- Assume that a competitive firm has the total cost function: TC = q^3 - 40q^2 + 870q + 1500. Suppose the price of the firm's output (sold in integer units) is $700 per unit. How many units should the firm produce to maximize profit?
- Suppose your firm's long-run total cost function (in a perfectly competitive market) is given by: C(q) = 12 + 3q^2 - 2q. a. What is the firm's average cost function? b. What is the firm's marginal cost function? c. What is the firm's profit-maximizing
- a) Suppose the marginal produce of labor is: MPL = 10, the marginal product of capital is: MPK = 20, while the cost of labor is: W = $5 and the cost of capital is: r = $30. Is the firm minimizing cost? If not, what should the firm do to produce the sa
- Suppose the production function is y=x^{2/3}+(1/3)x, and the price of y is p=6. Assume x geq 1. (a) Find the firm's marginal product MP(x) and average product AP(x). (b) Derive the firm's value of ma
- Suppose that a competitive firm has a total cost function of C(q) = 410 + 15q + 2q^2 and a marginal cost function of MC(q) = 15 + 4q. If the market price is P = $131 per unit, find the level of output produced by the firm. Find the level of profit and the
- a. Compute the average Product and the Marginal Product. b. Assuming that each product is sold for $3, find the Marginal Revenue Product. c. Which worker won't be hired by the firm if the wage is $65 per hour? Why? d. Should the firm hire the 5th worker,
- You are the manager of a firm that sells its product in a perfectly competitive market at a price of $60. Your firm's total cost function is C = 33 + 3Q^2 and marginal cost function is MC = 6Q. The profit-maximizing output for your firm is: (a) 3. (b) 5.
- Calculate the marginal revenue product of labor, the marginal revenue product of capital, the ratio of the marginal revenue product of labor to the price of labor, and the ratio of the marginal produc
- Suppose a price taking firm has the cost function C(q) = q3 - 12q + 5. a. What is the firm's marginal cost function? What is the firm's average cost function? b. Calculate the profit function. Be sure to include the shutdown decision.
- Suppose that a firm is currently employing 20 workers, the only variable input, at a wage rate of $250. The average physical product of labor is 25, the last worker added 10 units to total output, and the total cost is $5,000.What is the marginal cost?
- Suppose a firms 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 / {2 L^{1/2 and MP_k = {L^{1/2 / {2K^{1/2. What is the firms marginal cost?
- When the labor market is not perfectly competitive, labor will be hired up to the point where the {Blank} of labor equals the {Blank}. A. marginal revenue product; marginal revenue B. marginal product; market wage C. marginal revenue product; marginal
- Assume that for a perfectly competitive firm marginal revenue equals rising marginal cost at 100 units of output. At this output level, the firm's total fixed cost is $600 and its total variable cost is $400. If the price of the product is $10 per unit, t
- Suppose that capital costs $10 per unit and labour costs $5 per unit. For a profit-maximizing firm operating at its optimal factor mix, if the marginal product of capital is 50, the marginal product of labour must be A) 10 B) 20 C) 25 D) 50 E) 100
- Firm X sells output at a price of $8 per unit and pays labor a wage of $20 per hour. The marginal product of labor is given by MPL = 12 - 0.43L. To maximize profit, the firm should utilize __ units of labor.
- Suppose a perfectly competitive firm has the marginal cost function of MC = 3Q. The market price is given by P = $45. How many units of output will the firm produce? Suppose that at this same firm's profit-maximizing level of output, average costs are ATC
- Suppose the cost function for your firm is: C = 10 +2Q + 5Q^2. If the firm sells output in a perfectly competitive market and other firms in the industry sell output at a price of $35. What level of output should the firm produce to maximize profits or mi
- Suppose that for a particular firm the only variable input into the production process is labor and that output equals zero when no workers are hired. In addition, suppose that the marginal cost of the third worker hired is $40, and the average total cost
- A competitive firm's cost function is: C=0.48Q3-27Q2+418Q+16393. The market price of your outputs $152. Calculate the profit-maximization level of output.
- A competitive firm's cost function is: C = 0.4Q3 - 31Q2 + 495Q + 18,318 The market price of your output is $123. Calculate the profit-maximizing level of output. (Please round answer to the 2nd de
- Assume that a firm has the following short-run production function: q = 10L^0.5 and that the market wage rate is 4. a. Derive the equations for marginal and average product of labor. b. Derive the eq
- Suppose a competitive firm has as its total cost function: TC=26+3q^2 Suppose the firm's output can be sold (in integer units) at $61 per unit. Using calculus and formulas to find a solution, how many units should the firm produce to maximize profit? Sp
- Consider the following production function: q = L1/2. Derive the marginal product of labor, average cost, and marginal cost when L = 9 and wage is $8.
- Consider a widget-producing firm with a total cost function given by: TC = 1,000 + 500Q + 0.05Q^2 a) Calculate the firm's marginal cost function, expressing marginal cost as a function of Q. b) Calcu
- Suppose that at 500 units of output, the marginal revenue is equal to marginal cost. The firm is selling its output at $10 per unit and the average total cost at 500 units of output is $6. On the basis of this information, we: 1 can say that the firm sho
- Suppose that at 500 units of output, marginal revenue is equal to marginal cost. The firm is selling its output at $5 per unit and the average total cost at 500 units of output is $6. On the basis of this information, we A. can say that the firm should cl
- 1. Do you think the diminishing returns principle is applicable to the company/firm where you work? Why or not? 2. Define the concept of marginal revenue product (MRP), or value of the marginal produc
- Assume that a competitive firm has the total cost function: TC = 1q^3 - 40q^2 + 710q + 1700 The price of the firm's output (sold in integer units) is $550 per unit. Using tables (not Calculus) find a solution for total profit at the optimal output level?
- Suppose a competitive firm has as its total cost function: TC = 25 + 3q^2. Suppose the firm's output can be sold (in integer units) at $54 per unit. How many units should the firm produce to maximize profit?
- Assume that a competitive firm has the total cost function: TC=1q3-40q2+810q+1500 Suppose the price of the firm's output is $700 per unit. What is the total profit at the optimal output level?
- If labor is the only variable input, W is the cost of a worker, and MPL is the marginal product of labor, then the cost of producing one more unit of output, the marginal cost (MC), is equal to: a. W/MPL b. W x MPL c. MPL d. W
- Consider a perfectly competitive, profit-maximizing firm facing the following marginal product of labor function and prices. MP_L = 0.5A(K/L)^{1/2}, W = 40, R = 60, P = 10 If the total factor productivity (A) is 50 and the firm is employing 16 units of ca
- Assume that a firm has the following short-run production function: q = 10L0.5 and that the market wage rate is 4. Derive the equations for marginal and average product of labor. Derive the equation
- In order for a firm to determine how much it would save by reducing production by one unit of output per-period (e.g., hourly), it will evaluate its: A. marginal product function B. marginal cost function C. average product function D. average total cost
- Suppose a firms production function is given by, Q = L^{1/2}K^{1/2} and the Marginal Product of Labor and the Marginal Product of Capital are given by MPK= MPL = 1/2 L^{1/2}K^{-1/2}. (a) If the price
- Suppose the marginal product of the second worker hired by a firm is 3 units and the price of the last unit produced is $7. Which of the following is true of the marginal revenue product of the second worker? a. It equals $21. b. It is less than or equa
- The graph below shows the marginal revenue product of labor. a. How many units of labor will the firm hire at a wage of $3? b. What is the marginal revenue product of the 3rd unit of labor? c. Diminishing marginal product begins with the addition of what
- Suppose a firm is hiring 20 workers at a wage rate of $60. The average product of labor is 30, the last worker added 12 units of output, and the total fixed cost is $3,600. a) The average total cost is $ [{Blank}], b) The marginal cost of the last unit
- A profit-maximizing firm will employ more workers until the: a. value of the marginal product of labor is less than wage. b. marginal product of labor is zero. c. value of the marginal product of labor equals wage. d. marginal revenue is zero.
- A competitive firm's cost of production is C(Q) = 16Q-Q^2 + 4Q^3. (a) Calculate and draw the firm's average and marginal cost functions. The firm's problem is to choose the quantity that maximizes pr
- A competitive firm's cost of production is C(Q) = 16Q - Q^2 + 4Q^3. (a) Calculate and draw the firm's average and marginal cost functions. The firm's problem is to choose the quantity that maximizes p
- Assume that a competitive firm has the total cost function: TC=1q^3-40q^2+770q+1700 Suppose the price of the firm's output (sold in integer units) is $600 per unit. Using calculus and formulas to find a solution, how many units should the firm produce t
- Assume that a firm's marginal cost function is MC = 3q and its marginal revenue function is MR = 120 - 3q. At the output level of 18 units, in order to maximize profit, this firm should: a. increase its output by 2 units b. decrease its output by 2 units
- Define marginal product of labor and value of the marginal product of labor.
- Define the marginal product of labor and the value of the marginal product of labor.
- A competitive firm's cost function is: C = 0.38Q3 - 22Q2 + 488Q + 363 The market price of your output is $103. Calculate the profit-maximizing level of output. (Please round answer to the 2nd decima
- In a competitive labor? market, the? profit-maximizing number of workers that a firm will hire occurs where the? ____________. A. marginal product of labor equals zero. B. marginal product of labor
- Suppose a perfectly competitive firm has the marginal cost function of MC = 3Q. The market price is given by P = $45. How many units of output will the firm produce?
- Assume that a competitive firm has the total cost function TC = q^3 - 40q^2 + 740q + 1600. Suppose the price of the firm's output (sold in integer units) is $650 per unit. Using tables (but not calculus) to find a solution, how many units should the firm
- a. Suppose a perfectly competitive firm has the marginal cost function of MC = 4Q. The market price is given by P = $47. How many units of output will the firm produce? b. Suppose that at this same firm's profit-maximizing level of output, average costs a
- Suppose a monopolist can purchase Labor at a price w = 1 and can purchase Capital at a price r = 9. The monopolist s production function is given by Q = L^1/2 K^1/2. The demand facing the monopolist is given by P = 78 - 6Q. What is the monopolist s margin
- Suppose that a competitive firm's marginal cost of producing output q(MC) is given by MC(q) = 6 + 2q. Assume that the market price(P) of the firm's product is $15. What level of output? (q) will t
- Assume that a monopolist sells a product with a total cost function TC=1200+1/2Q2. The market demand is given by the equation P=200-Q. a) Find the profit-maximizing output and price for this monopolis
- You are the manager of a firm that sells its product in a competitive market at a price of $1969. Your firm's cost function is C = 252 + 1Q2. Calculate your firm's maximizing profit Round all calculat
- For the competitive firm in the labor market, the value of the marginal product is equal to the marginal revenue product because marginal: A. revenue equals marginal cost. B. physical product of lab
- Suppose a profit-maximizing monopolist is producing 800 units of output and is charging a price of $40 per unit. a) If the elasticity of demand for the product is -2, find the marginal cost of the last unit produced. b) What is the firm's percentage m
- Suppose that a competitive firm's marginal cost of producing output q is given by MC(q) = 3 + 2q. Assume that the market price of the firm s product is $9. \\ a) What level of output will the firm produce to maximize profit? b) What is the firm's produc
- Consider a production function given by: Q=KL^2-1/3L a. Derive the equation for the average product of labor and the marginal product of labor. b. Let K=5. Find the level of L at which the marginal
- Assume that you are the manager of a perfectly competitive firm. The market price of the output is $60. Your firm's total cost function is Q^2 + 12Q + 60. a) How many units should your firm produce in
- Suppose a firm has some power in the product market and hires labor in a perfectly competitive labor market. If the market wage rate is $20, the marginal product of the last worker hired is 5, and the firm is hiring the profit-maximizing amount of labor,
- Suppose a monopolist has a production function given by Q = L1/2K1/2. Therefore, MPL = , and MPK = The monopolist can purchase labor, L at a price w = 16, and capital, K at a price of r = 9. The dema
- The demand function for a product sold by an oligopolist operating in the short run is given below: Q_D = 370 - P. The firm's marginal cost function is given below: MC = 10 + 4Q. Calculate the profit-maximizing price and quantity, if the firm operates in
- Suppose that a competitive firm has a total cost function of C(q) = 410 + 15q + 2(q^2) and a marginal cost function of MC(q) = 15 - 4q. If the market price is P = $131 per unit, find: a) The level
- Assume a perfectly competitive market. The selling price of a firm is $9 and the profit-maximizing output q* is 80. Producing 80 units cost $800. a. What is the MR for this firm? b. Calculate profi
- 1. A competitive firm's short run total cost function is given by TC=q^3-16q^2+100q+120 (a) Calculate the profit maximizing output and the resulting profit when price is $30. (b) Calculate the profit
- A company has fixed costs of $300 and each worker it hires costs $100 per day. Calculate Marginal product, Total cost, Average total cost, and Marginal cost for each level of output in the table below. ||Workers||Output (Q)||Marginal product||Total cost||
- Assume a certain firm is producing 1,000 units of output (so Q = 1,000). At Q = 1,000, the firm's marginal cost equals $15 and its average total cost equals $11. The firm sells its output for $12 per unit. At Q = 1,000, the firm's profit amounts to: a. $-
- A firm has the following marginal revenue and total cost function: MR= 140-2 (output) TC=50+10 (output) + � (output)2 1. Determine the revenue maximization output and price. Graph the total revenue f
- If a company hires an additional worker and finds that its total output then falls, it must be true that: a. Marginal product is negative, b. Marginal product is minimized and the marginal cost is maximized, c. Average total cost is negative, d. Marginal
- Profit maximization requires that: a. the marginal factor cost of every input equals that input's marginal physical product b. equal amounts of each input are employed c. the amount of one input hired
- A firm operating in a purely competitive market has a total cost function given by c(y)=y2 +10 for y0 and c(0)=0. (i) What is the firm's marginal cost function? (ii) What is the firm's average cost function? (iii) At what quantity is the firm's marginal c
- To compute the level of output that a firm would produce to maximize profits, you must compute the level of output where equals the price of the product. a. marginal cost b. average revenue c. total cost d. average total cost
- The diminishing marginal product explains why, as a firm's output increases [{Blank}] a.) The production function and total-cost curve both get steeper. b.) The production function and total-cost curve both get flatter. c.) The production function gets
- A firm has the following marginal revenue and total cost function: MR = 140 - 2 (output) TC = 50 + 10 (output) + 1/2 (output)squared Determine the revenue maximization output and price. Graph the tota
- Consider a monopoly whose total cost function is TC = 10 + 5Q + 2.5Q^2 and whose marginal cost function is MC = 5 + 5Q. The demand function for the firm's goods is P = 115 - 0.25Q. The firm optimizes by producing the level of output that maximizes profit
- To determine its output quantity, the firm in perfect competition sets: a. marginal cost equal to marginal revenue. b. marginal cost equal to average total cost. c. price equal to marginal cost. d
- Consider a monopolist that only hires one input, labor, to produce output. The monopolist's demand curve is p = 100 - q, its production function is q = L 0.5, and the price of labor is w. (The labor market is competitive, however). Derive the firm's labor
- Diminishing marginal product explains why, as a firm's output increases. a. the production function and total-cost curve both get steeper. b. the production function and total-cost curve both get flatter. c. the production function gets steeper, while the
- A purely competitive firm sells trinkets for $10 each. Fixed costs are $2, and each unit produced adds $2 of variable costs. a. Calculate the total and marginal costs. b. What the is profit-maximizing level of output? c. Suppose instead that the same firm
- 28) Consider a perfectly competitive firm that is producing a level of output such that price equals average total cost and average total cost is less than marginal cost. In order to maximize its profits, the firm should A) reduce output. B) expand output
- Suppose that a price-taker firm has a marginal cost function given by MC = 30 + 0.5q. The firm could join a cartel in its industry and agree to a quota of 5 units. The collusion drives the price of the good from $35.91 to $70.00. Calculate the producer su
- A. Suppose a perfectly competitive firm has the marginal cost function of MC = 3Q. The market price is given by P = $45. How many units of output will the firm produce? B. Suppose that at this same firm's profit-maximizing level of output, average costs a
- Consider a competitive firm. The production function is Q = L^.5, the marginal product of labor is MP_L = 1/L^.5, the price level taken as given is P = 20, and the wage rate taken as given is w = 5. A
- A firm has a production function such that y = KL + 2L. The marginal product of K is L, and the marginal product of L is K+2. a. Find the conditional input demand functions for K and L. b. Find the cost function, given that the price per unit of K is r an
- Explain how a firm's marginal product of labor is related to the value of its marginal product.
- Suppose a single firm produces all of the output in a contestable market. The market inverse demand function is P = 200 - 2Q, and the firm's cost function is C(Q) = 8Q. Determine the firm's equilibrium price and corresponding profits.
- Suppose a single firm produces all of the output in a contestable market. The market inverse demand function is P = 250 - 5Q, and the firm's cost function is C(Q) = 6Q. Determine the firm's equilibrium price and corresponding profits.
- Suppose a perfectly competitive firm is producing a level of output for which price equals average total cost, and the average total cost is less than marginal cost. In order to maximize its profits, the firm should: a) reduce its output. b) expand its ou
Explore our homework questions and answers library
Browse
by subject