Show that the quantity of labor(L) and capital(K) that a firm demand decreases with a factor’s own factor price (w for labor and r for capital) and increases with the output price (P) when the production function is a Cobb-Douglas of the form ? = ?????

Show that the quantity of labor(L) and capital(K) that a firm demand decreases with a factor’s own factor price (w for labor and r for capital) and increases with the output price (P) when the production function is a Cobb-Douglas of the form ? = ?????

Exploring Economics

8th Edition

ISBN:9781544336329

Author:Robert L. Sexton

Publisher:Robert L. Sexton

Chapter16: The Markets For Labor, Capital, And Land

Section: Chapter Questions

Problem 16P

See similar textbooks

Related questions

Q: K L Q 10 10 1 15 10 30 10 3 50 10 4 60 10 65 10 6 68 What is the marginal product of labor for the…

A: The marginal product of labor (MPL) refers to increase in total production or output (Q) when one…

Q: Suppose a firm produces according to the production function Q = 2L0.6K0.2, and faces wage rate…

A: *Answer:

Q: Suppose a firm produces according to the production function Q=3K/3L/3 and faces a wage rate of $5…

A: The Production function Q = 3K1/3L1/3 Wage rate(w) = $5 Rental rate of capital(r) = $2 Output price…

Q: c) Given Y = 10K0.5L0.5 and that w and r are the prices for Labour and Capital i) Derive the…

A: Given information q=10L0.5K0.5 Price of labor=W Price of capital=r

Q: Consider a production function: Q = f (L), where Q represents the output and L is the factor of…

A: The envelope theorem deals with the differentiability of specific variables and how they affect the…

Q: Production function is Q(K,E) =2KE where K is capital and E is employment in work hours. Use the…

A: In production, the isoquant curve shows the various possible and feasible combinations of inputs…

Q: If a firm's production function is Leontief and the wage rate goes up, the: Multiple Cholce firm…

A: Leontief production function use a fixed proportion of labor and capital. We can say that technology…

Q: Suppose that the production function is given by y = 2x0.5 The price of x is $3 and the price of y…

A: The production function shows the mathematical relation between the input used to produce given…

Q: 1.XYZ Co. operates in a competitive market. Its production function is q = LαKβ. The firm takes the…

A: (a) The firm’s production function is, q = f(L,K) = L^α*K^ꞵ The firm's cost function is, C = w*L +…

Q: The marginal product of labor (MPL) is defined as

A: The firm would result in profit maximisation by maximising the revenue which would be earned by the…

Q: Given the production function for labor and capital: Q = L^½(K^½), and q = 100. If the firm wants…

A: Production function:- Production function can be defined as an economic equation that represents the…

Q: Let L represent the number of workers hired by a firm, and let Q represent that firm's quantity of…

A: Marginal Product: Marginal product is an extra output produced by employing an extra unit of the…

Q: Find the optimal input combination that maximizes firm’s profits.

A: A firm always desires to maximize its profit from the sale of its output. The production function of…

Q: Question 1 The total cost function of a firm is given by: 2 C = q(W){cv) Where q is total output, W…

A: Note: Since a student has asked more than one question, we are going to ask the first question as…

Q: What is the difference between the factor demand derived from cost minimization and that obtained…

A: Cost minimization simply means that businesses maximize their productivity or use the least…

Q: the marginal product per dollar spent on capital

Q: A competitive, profit-maximizing firm uses two inputs labor (2) and capital (K). Its production…

Q: Consider the following production function: Q = 2K + 8L. Capital (K) is on the vertical axis and…

A: MRTS is the slope of isoquant. An isoquant shows all combination of L and K which yield the same…

Q: Given the production function: Where CES stands for Constant Elasticity of Substitution. K is…

A: We are going to find the profit function, Production function to answer this question.

Q: Consider the production function Q = 2(KL)0.5 What is the marginal rate of technical…

A: The rate at which one input is reduced when the other input increases keeping the output constant is…

Q: The Principle of Diminishing Marginal Returns states that adding one more unit of input, say,…

A: We are going to learn a concept known as Diminishing marginal returns.

Q: onsider the following production function TPL = 12L2 – 0.8L3 Determine the marginal…

A: Hello. Since your question has multiple sub-parts, we will solve the first three sub-parts for you.…

Q: Consider a firm that employs capital (K) and labour (L) and uses the production technology Q = 3K +…

A: We have given the cost minimization problem of a firm given the production function and the price of…

Q: Consider the table below that describes the production function for a good (Q) in terms of inputs…

A: Marginal product is the additional output produced by employing an additional unit of input.

Q: A significant property of the Cobb- Douglas production function is that the elasticity of…

A: To find : Elasticity of substitution.

Q: Consider a firm with production function: Q(L, K) = 400 + 12.3L – 0.8L² + 10.1K – 0.3K² + 0.2Lk,…

A: Production function of the firm; Where; L= units of labor K= units of capitals Q= Output Maximum…

Q: Answer the question on the basis of the following output data for a firm. Assume that the amounts of…

A: The formula:Marginal product = change in total output

Q: Find the supply function as well as the unconditional factor demand functions fo capital and labor…

A: We are going to use profit maximization method to find supply function and unconditional demand for…

Q: Consider the following production function: Q= 2K + 8L. Capital (K) is on the vertical axis and…

A: MRTS refers to the rate at which capital can be substituted with labor by the firm.

Q: For a competitive firm; production function, market price and unit costs for capital and labour are…

A: Given, Q(K,L) = K1/2L1/4 and p = 8, r =0.1 , w = 10 Input demand for Labor L = f (w,r,p) Input…

Q: Consider a firm with Total Output function (Production Function) given by Q = 6L2 – 0.4L3, where L…

A: Answer given in image below...

Q: Consider a Cobb-Douglas production function: f(l, k) = Alα k1−α , where A is the total factor of…

A: Since you have provided multiple parts and multiple subpart question, we will solve the first three…

Q: e the two factors are perfect complements and the production function is given by y=min { 13x1,2x2}…

A: Given Production function y = min 13x1 , 2x2Where X1 = 300, X2=50

Q: In each of the following four cases, MRPL and MRPC refer to the marginal revenue products of labor…

A: The Marginal Product of labor is marginal revenue generated by employing an additional unit of labor…

Q: In the specific factor model in a market equilibrium the mobile factor's productivity must be the…

A: Factors of production: - The inputs that are used to produce goods and services are known as the…

Q: production function of this nature; AX1aX2b determine the Marginal Rate of Technical Substitution.

A: Marginal rate of technical substitution means the rate at which one factor is substitute by other…

Q: Production Function and Input Demand Consider the production function Q = K + √L. Derive the input…

Q: Answer the question on the basis of the following output data for a firm. Assume that the amounts of…

A: Marginal product: A marginal product is defined as the change in output as a result of utilizing an…

Q: For each of the following cases, determine whether the firm should (A) Use more labor and less…

A: We will answer the first three questions only. Please resubmit the question mentioning any other…

Q: Suppose a firm has the following Production Function: f(x1, x2) = x1/3x21/3 Find out the profit…

A: Profit maximizing input where using

Q: ONLY ANSWER C & D Consider a firm with Total Output function (Production Function) given by Q =…

A: please find the answer below.

Q: Given the production function: Where CES stands for Constant Elasticity of Substitution. K is…

A: We are going to find the Profit function and First order conditions to answer the question.

Q: Consider Delta, a price-taking single-output, single input firm with the following production…

A: Non decreasing returns to scale implies that the rate of change of output w.r.t to the rate of…

Q: inction: Consider the 'Cobb-Douglas' production function: f(k;, n4) = ki'n}-a where a is an…

A: The marginal products are calculated by differentiating total output with respect to the inputs viz.…

Q: Jackson employs labor (L) and capital (K) to produce his output. The marginal product of labor MPL…

A: A firm minimizes the production cost at the following point. i.e., (MPL / PL) = (MPK / PK)…

Q: Suppose the Cobb-Douglas production function is given as: , where b0 = level of technology, b1 =…

A: “Since you have asked multiple subparts, we will solve the first three parts for you. If you want…

Q: Suppose a firm’s production function is ? = ?2?. a) Determine the labor and capital demand…

A: While delivering labour and products, organizations require labour and capital as inputs to their…

Question

Show that the quantity of labor(L) and capital(K) that a firm demand decreases with a factor’s

own factor price (w for labor and r for capital) and increases with the output price (P) when the

production function is a Cobb-Douglas of the form ? = ?????

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.

Similar questions

Consider a production function: Q = f (L), where Q represents the output and L is thefactor of production. Let w be the per unit price of factor L and p be the per unit price ofoutput Q. Using the Envelope theorem determine the supply function and the factor demand function.
A firm employs labor and capital by paying $40 per unit of labor employed and $200 per hour to rent a unit of capital. The production function is given by: Q=60L-2L^2+180K-3K^2, where Q is total output. Determine the firm's optimal combination of capital (K) and labor (L)?
Suppose the long-run production function for a competitive firm is f(L,K)= L 1/3 K 1/4 , where L is the amount of labor and K is the amount of capital. The cost per unit of labor is w and the cost of capital is r, which is the interest rate. Fixed costs are zero. .a. Find the cheapest input bundle, i.e. amount of labor and capital, that yields the given output level of y. .b. Draw the conditional input demand functions for labor and capital in the L-y and K-y spaces. .c. Write down the formula and draw the graph of the firm’s total cost function as a function of y, using the conditional input demand functions. What is the relationship between the returns to production scale and the behavior of the total costs? .d. Write down the formula and draw the graph of the average cost and marginal cost functions, as functions of y.
Suppose the long-run production function for a competitive firm is f(x1,x2)= min {x1,2x2}. The cost per unit of the first input is w1 and the cost of the second input is w2. .a. Find the cheapest input bundle, i.e. amount of labor and capital, that yields the given output level of y. .b. Draw the conditional input demand functions for labor and capital in the x1-y and x2- y spaces. .c. Write down the formula and draw the graph of the firm’s total cost function as a function of y, using the conditional input demand functions. What is the relationship between the returns to production scale and the behavior of the total costs? .d. Write down the formula and draw the graph of the average cost function, as a function of y. .e. Write down the formula and draw the graph of the marginal cost function, as a function of y.
Production function is Q(K,E) =2KE where K is capital and E is employment in work hours. Use the production function to fill the table below. Wage Rent Total Cost Optimal combination of inputs $15 $45 $15 000 $20 $40 $15 000 $25 $30 $15 000
Given the production function: Where CES stands for Constant Elasticity of Substitution. K is capital and L is labor. The price per unit produced is p, interest (unit price K) is r and wages (unit price L) are w. a) Find the profit function π(K,L) and simplify b) Find the first order conditions to maximize the profit c) Find the value function for L and K, i.e the functions L* = L*(p,r,w) and K* = K*(p,r,w) and simplify. What is the meaning of the value functions d) Find the best production quantity and the maximum profit, i.e Q*(P,r,w) and π*(P,r,w) simplify results
Let y = f(x1, x2)=x11/2 + x1x2 be a firm’s production function, where x1≥0, x2≥0. Write down the firm’s production possibility set, and its input requirement set. Is this production function concave, quasi-concave? Is this production function homogenous? Find its returns to scale when x1=1, and x2=1.
Suppose that Zamboni Enterprises is the only company that sells zambonis (ice resurfacing machines). To produce the machines, the company hires assembly workers. Since these workers can work in many different companies, Zamboni Enterprises must pay them the market wage, which is equal to $6. The number of zambonis that the company produces, which is denoted by y, is proportional to the number of assembly workers that it hires, which are denoted by N; in particular, the production function is given by y=0.76N. The economywide demand for zambonis is given by the following demand function: y=2191-219p, where y is the number of zambonis that consumers are willing to purchase at price p. Given this market structure, how many assembly workers will Zamboni Enterprises choose to hire? How many zambonis will Zamboni Enterprises produce and sell?
Suppose that Zamboni Enterprises is the only company that sells zambonis (ice resurfacing machines). To produce the machines, the company hires assembly workers. Since these workers can work in many different companies, Zamboni Enterprises must pay them the market wage, which is equal to $6. The number of zambonis that the company produces, which is denoted by y, is proportional to the number of assembly workers that it hires, which are denoted by N; in particular, the production function is given by y=0.76N. The economywide demand for zambonis is given by the following demand function: y=2191-219p, where y is the number of zambonis that consumers are willing to purchase at price p. Given this market structure, how many assembly workers will Zamboni Enterprises choose to hire? How many zambonis will Zamboni Enterprises produce and sell? What will be the price of a zamboni? If the market for zambonis were competitive, how many zambonis would be produced? If the market for…
Suppose that Zamboni Enterprises is the only company that sells zambonis (ice resurfacing machines). To produce the machines, the company hires assembly workers. Since these workers can work in many different companies, Zamboni Enterprises must pay them the market wage, which is equal to $6. The number of zambonis that the company produces, which is denoted by y, is proportional to the number of assembly workers that it hires, which are denoted by N; in particular, the production function is given by y=0.76N. The economywide demand for zambonis is given by the following demand function: y=2191-219p, where y is the number of zambonis that consumers are willing to purchase at price p. If the market for zambonis were competitive, how many zambonis would be produced? If the market for zambonis were competitive, how many assembly workers would be hired? If the market for zambonis were competitive, at what price would zambonis be sold?