# Suppose that in order to produce any positive amount of output, a firm must build an operating...

## Question:

Suppose that in order to produce any positive amount of output, a firm must build an operating facility which costs $40. The Variable Cost of production is equal to 6q, where q is the quantity of output. Therefore the Marginal Cost of production is constant at MC = $6. If the firm decides not to produce, it does not build the operating facility, and so it incurs 0 costs. The demand facing the firm is given by P = 20 - 2q.

a) What is the Average Total Cost of producing 5 units of output?

b) What amount of output should the firm produce in order to maximize its profit?

c) What is the socially optimal level of output?

d) What is the total social welfare of the socially optimal level of output?

## Social Optimal Level of Output

The social optimal level of output is the output for which social welfare maximizes. This is the point of an optimal level of resource allocation. The social optimal level of output is attained when the price of commodities is equal to the marginal cost of commodities, at that output level social welfare will be maximized.

## Answer and Explanation: 1

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

View this answerGiven:

Demand function: P = 20 - 2q

Fixed cost (F) equals to 40.

Variable cost (V) equals to 6q.

Marginal cost (MC) is equal to 6.

a. Total cost...

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 24 / Lesson 6Learn the profit maximization definition, its importance, and explore the profit maximization theory. See how to calculate profit maximization with examples.

#### Related to this Question

- 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
- Suppose that a firm's production function is q = 5x^{0.5} in the short run, where there are fixed costs of $1,000, and x is the variable input whose cost is$1250 per unit. The total cost of producing a level of output q is C(q) = 1,000 + \frac{1250q^2}{25
- 1. Suppose that a firm's production function is q = 10L^{1/2}K^{1/2}. The cost of a unit of labor is $20 and the cost of a unit of capital is $80.a. If the firm wishes to produce 100 units of output,
- Suppose in the short run a firm's production function is given by Q = L^(1/2) x K^(1/2), and that K is fixed at K = 9. 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
- Suppose the production function for a competitive firm is Q = K^.75L^.25. The firm sells its output at a price of $32 and can hire labor at a wage rate of $2. Capital is fixed at 1 unit. a. What is the profit-maximizing quantity of labor? b. If the price
- 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?
- Suppose that a firm's production function is q = 10L^{0.5}K^{0.5} . The cost of a unit of labor is $10/hour and the cost of capital is $40/hour, and the firm is currently producing q=1000 units
- Suppose that a firm's production function is q = 10L1/2K1/2. The cost of a unit of labor is $20 and the cost of a unit of capital is $80. a. Derive the long-run total cost curve function TC(q). b. The firm is currently producing 100 units of output. Find
- Suppose in the short run a firm's production function is given by Q = L^{1/2}K^{1/2}, and that 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 ou
- Suppose a firm has a production function given by Q = L1/2K1/2. The firm can purchase labor, L, at a price w = 8, and capital, K, at a price of r = 2. a) What is the firm's total cost function, TC(Q)? b) What is the firm's marginal cost of production?
- Suppose a firm operates two production facilities within the U.S. Marginal costs of production for each plant are given as follows: MC_1=2q, MC_2=q_2. The firm's marginal revenue is given by MR=800-2q. Calculate the profit-maximization production distribu
- A firm produces a good X. The production function is: Q = 5LK. L is labor in person hours, K is capital in machine hours and Q is quantity produced of good X. The firms's labor cost (w) is $20 per ho
- 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
- 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 product function is Q = 5L^{0.5}K^{0.5}. Labor costs $40 per unit and capital costs $10 per unit. K = 16 in the short run. Suppose the production of a firm is Q = 5 + 2K + L. Which of the following statements is correct? A. The firm's production
- Output is produced according to Q = 4LK, where L is the quantity of labor input and K is the quantity of capital input. If the price of K is $10 and the price of L is $5, then what is the cost minimiz
- 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 a firm with production function f(L,K)=3L1/3K2/3. Assume that capital is fixed at K=1. Assume also that the price of capital r=5 and the price of labor w=3. Then, the variable cost of producing q units is what?
- Suppose that a firm has only one variable input, labor, and firm output is zero when labor is zero. When the firm hires 6 workers the firm produces 90 units of output. Fixed costs of production are $6 and the variable cost per unit of labor is $10. The ma
- 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
- 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
- If output is produced according to Q = 5Lk (L is the quantity of labor and k is the quantity of capital), the price of K is $12, and the price of L is $6, then the cost minimizing combination of K and L capable of producing 4,000 units of output is A. L
- 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
- 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 that a firm's short-run production function has been estimated as Q = 2L + 0.4L2 - 0.002L3, where Q is units of output and L is labor hours. a. What is the firm's marginal product of labor equation? b. What is the firm's average product of labor e
- In the short run, a firm incurs fixed costs: a. Only if it incurs variable costs, b. Only if it produces no output, c. Only if it produces a positive quantity of output, d. Whether it produces an output or not.
- In the short run, a firm incurs fixed costs: A. only if it also incurs variable costs. B. only if it produces no output. C. only if it produces a positive quantity of output. D. whether it produces output or not.
- 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
- Output is produced according to Q = 4LK, where L is the quantity of labor input and K is the quantity of capital input. If the price of K is $10 and the price of L is $5, then the cost-minimizing combination of K and L capable of producing 32 units of out
- 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
- Consider a firm with production function f(L,K)=3L+8K. Assume that capital is fixed at K=12. Assume also that the price of capital r=10 and the price of labor w=3. Then, the average cost of producing q units is what?
- The cost to a firm producing q units of a product is given the cost equation c = 5q(ln q) + 15. Evaluate the cost when q = 12.
- The short-run production function of a profit maximizer firm is given by f(L) = 6L^(2/3), where L is the amount of labor it uses. The cost per labor unit is w = 6, and the price per unit of output is p = 3. 1) How many units of labor will the firm hire?
- Using the production function (ie: q = (K^{1/2} + L^{1/2})^2) suppose that the firm is now operating in the long-run. a) Solve for the long-run cost function (i.e. total costs as a function of input
- A firm's production function is Q = 8L^(1/2) and this firm sells each unit of its product at a price of P = $100. It also pays its workers a wage of w = $10. a. How many workers would this firm hire to maximize its profit if it only has labor costs and no
- Consider a firm with production function f(L,K)=3L1/3K2/3. Assume that capital is fixed at K=1. Assume also that the price of capital r=5 and the price of labor w=3. Then, the average fixed cost of producing q units is what?
- A firm's product function is Q = 5L^{0.5}K^{0.5}. Labor costs $40 per unit and capital costs $10 per unit. K = 16 in the short run. Suppose the production function of a firm is Q = 5 + 2K + L. Which of the following statements is correct? A. The firm's LA
- Suppose a firm produces an output measured in units Q. The cost of producing Q units is given by the cost function C(Q) = aQ^2 + bQ + c, where you can assume a 0,b 0,c 0. In Economics we also think about cost per unit (average cost) given by: AC(Q) = C(
- Let L represent the number of workers hired by a firm, and let Q represent that firm's quantity of output. Assume two points on the firm's production function are (L = 5, Q = 120) and (L = 8, Q = 180). Then the marginal product of the 8th worker is - 20
- 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 a firm's short-run production function is given by Q = F(L) = 10L. L stands for number of workers. If the wage rate is $15 and the firm has sunk costs of $1000 what is the firm's total cost fu
- Assume a firm has a production function Q = 2 S L 5 K 5 and the price of labor is $3 and the price of capital is $12. a) What is the minimum cost of producing 1,250 units of output? b) Now show t
- Assume a firm has a production function Q = 25 L 5 K 5 and the price of labor is $3 and the price of capital is $12. a) What is the minimum cost of producing 1,250 units of output? b) Now show tha
- 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
- Output is produced according to Q = 4 L K, where L is the quantity of labor input and K is the quantity of capital input. If the price of K is $10 and the price of L is $5, then the cost-minimizing combination of K and L capable of producing 32 units of o
- 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
- 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 production function for a firm takes the following algebraic form Q = 4KL - 0.3L^2, where Q is the output of sweaters per day. Now suppose the firm is operating with 7 units of capital (K = 7) and 9 units of labor (L = 9). What is the output of
- A firm's production function Q = 20L^{0.5}K^{0.4}. Labour costs $100 per unit and capital costs $100. The firm sets a production target of 100 units. a. Show or explain whether the production function
- Suppose a firm with a production function given by Q = K^{0.25}L^{0.75} produces 1,500 units of output. The firm pays a wage of $50 per unit and pays a rental rate of the capital of $50 per unit. To produce 1,500 units of output, the firm should use: a. 1
- Suppose that a firm that produced buttons had a production function given by q = 4L^{0.5}K^{0.5}. The firm has 16 units of capital in the short run. Determine the amount of labor required to produce 64 units of output.
- Suppose that a firm's production function is Q = 250 L ? L 2 , where Q represents units of output per week and L represents one worker. Output sells for $10 per unit, and the cost of a worker is $500
- Production A firm has the following short-run production function:Q = 50L + 6L^2 = 0.5L^3 Where Q = Quantity of output per week and L = Labor (number of workers)
- 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
- 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 func
- A firm has the following production function: Q = 50K + 20L. Each unit of capital costs $4 to employ and each unit of labor costs $1 to employ. Labor and capital are this firm's only costs of production. The firm is currently producing 250 units of output
- A firm's product function is Q = 5L^{0.5}K^{0.5}. Labor costs $40 per unit and capital costs $10 per unit. K = 16 in the short run. If K is not fixed, determine the lease cost combination of L and K to produce 1000 units of Q.
- Suppose product price is fixed at $24, MR = MC at Q = 200, AFC = $6, AVC = $25. What do you advise this firm to do? a. Increase output. b. Decrease output. c. Shut down operations. d. Stay at the current output; the firm is earning a profit of $1,400.
- Suppose that a monopolistically competitive firm must build a production facility in order to produce a product. The fixed cost of this facility is FC = $24. Also, the firm has constant marginal cost,
- A firm produces output with the production function F(K,L) = K^{1/2}L^{1/2}. The price of capital is p_K = 10 and the price of labor is p_L = 40. Find the cost-minimizing input bundle for producing Q = 50 in the long run.
- 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 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
- A firm has determined that its variable costs are given by the following relationship: VC = 0.05Q3 - 5Q2 + 500Q, where Q is the quantity of output produced. Determine the output level (Qm) where average variable costs are minimized.
- Let L represent the number of workers hired by a firm, and let Q represent that firm's quantity of output. Assume two points on the firm's production function are (L=6, Q=147) and (L=7, Q=174). The ma
- A firm produces Q = K^{1/2}L^{1/4} units of its output good when it uses K units capital and L units of labor. The firm sells its output at the price of $16 per unit of output; it pays $4 per unit of capital and $2 per unit of labor. a. Is Q homogenous in
- Suppose a short-run production function is described as Q = 1L - (1/800)L2, where L is the number of labor units used each hour. The firm's cost of hiring (additional) labor is $20 per hour, which includes all labor costs. The finished product is sold at
- 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 a firm can use either Capital (K) or Labor (L) in a production process. The firm's Production function is given by Q = 5L+ 15K. The price of Capital is $20 per unit and the price of Labor is
- The production function for a certain firm is given by Q = 20K^(0.7)L^(0.3), where Q is the firm's annual output, K is the firm's capital input and L is the firm's labor input. The price per unit of c
- 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
- Let the fixed cost for production of a good (F) be equal to $1000, the labor requirement to produce one unit, a, be equal to 10 hrs and the wage rate, w, be $10 per hr. Let Q stand for the number of units output. a) The unit cost when q=1 is? b) The uni
- 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).
- 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 a firm's short-run production function is given by Q = 3 sqrt(L) , where L represents the number of hours of labor employed. The firm has a sunk cost of $500 and the wage rate is $18 per hour. What is the firm's short-run cost function?
- A manufacturing firm's production function is Q = KL + K + L. The price of capital services is equal to 1, and let w denote the price of labor services. If the firm is required to produce 5 units of output, for what values of w would a cost-minimizing fi
- In the short run, when a firm is producing quantities that are greater than the quantity which minimizes short-run average costs, the marginal product of labor (MPL) A. will be rising the more the firm is producing. B. will be falling the more the firm is
- A firm produces output according to the production function: Q = F(K,L) = 4K + 8L. b. If the wage rate is $60 per hour and the rental rate on capital is $20 per hour, what is the cost-minimizing input mix for producing 32 units of output? c. If the wage r
- Consider the production function: Q = 12L - 2L^2 where Q is quantity of output, and L is labor. What is the average product?
- 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
- Suppose a firm operates three production facilities within the U.S. Marginal cots for each plant, price, and quantity, are provided in the table below. how many units should be produced at each plant in order to maximize profits? |Quantity|TR|MR|MC1|MC2|M
- 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 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
- 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
- A firm is currently producing their profit maximizing quantity of 600 units of output using 150 hours of labor and 50 hours of capital. The marginal product of labor is 10 units of output per hour and
- You are the manager of a firm that produces output in two plants. The demand for your firm's product is P =120 - 6Q, where Q = Q1 + Q2. The marginal costs associated with producing in the two plants are MC1 = 2Q1 and MC2 = 4Q2. What price should be charg
- Suppose that capital costs $10 per unit and labour costs $4 per unit. If the marginal product of capital is 50 and the marginal product of labour is 50, then in the long run the firm should in order to minimize its costs of producing its output. A) emplo
- A firm produces 1,000 units of output at an average variable cost of production of 50 cents. The firm's total fixed costs equal $700. The total cost of producing 1,000 units of output equals A. $500. B. $800. C. $1,000. D. $1,200. E. $700.
- 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
- Given Q=100K^(0.5)L^(0.5), w = 30, r =30, a) Please find the quantity of labor and capital that the firm should use in order to minimize the cost of producing 1500 units of output. b) What is this min
- 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 $
- Suppose we are given a profit function Q = 12L0.5K0.5. The price of labor (L) is $6 per unit and the price of capital (K) is $6 per unit. The firm is interested in the optimal mix of inputs to minimize the cost of producing any level of output Q. In the o
- 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
- 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
- A firm produces output according to the production function Q = F(K, L) = 4K + 8L. 1. If the wage rate is $60 per hour and the rental rate on capital is $20 per hour, what is the cost-minimizing capital and labor for producing 32 units of output? 2. If th
- 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 firm with a production function f(x_1, x_2). The firm sells its output for a price of p per unit, and pays w_i per unit for input i = (1, 2). In the short run, input 2 is fixed at \bar{x_2}. If the firm has chosen to use a quantity of input 1 s
- Suppose that a firm had a production function given by q = L0.25K0.75. The wage rate (w) is $5 and the rental rate (r) is $10. Calculate the amount of labor the firm would hire when it produces 400 units of output in a cost-minimizing way. (Round to the n
- Suppose we are given a profit function Q = 12L^.5K^.5. The price of labor is $6 per unit and the price of capital (K) is $7 per unit. The firm is interested in the optimal mix of inputs to minimize the cost of producing any level of output Q. In the optim
- Let L represent the amount of labor that a firm employs and let Q represent the quantity of the firm's output. The firm's production function is: Q = f(L) = 100 \ln(2L + 1). a. Let z = 2L + 1. Then Q = 100 \ln(z). Use the chain rule for derivatives to to
- The production function for a firm in the business of calculator assembly is given by \sqrt{q} =2 l where q denotes finished calculator output and l denotes hours of labor input. The firm is a price-t