1. Suppose the total-cost function for a firm is given by C = qw²/3v!/3. a. Use Shephard's lemma to compute the (constant output) demand functions for inputs I and k. b. Use your results from part (a) to calculate the underlying production function for q (q as a function of "k" and "I").

1. Suppose the total-cost function for a firm is given by C = qw²/3v!/3. a. Use Shephard's lemma to compute the (constant output) demand functions for inputs I and k. b. Use your results from part (a) to calculate the underlying production function for q (q as a function of "k" and "I").

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter10: Cost Functions

Section: Chapter Questions

Problem 10.6P

See similar textbooks

Related questions

Q: Consider a firm that produces cars with the following production function: q = min(aK, bL) a. Find…

A: In economics, a production function is a means of examining the relationship between input and…

Q: The total cost function of a firm is given by: C = q(wy{v)! Where q is total output, W and V are…

Q: For a firm to maximize profit, it must minimize the cost of producing whatever quantity it produces.…

A: An isoquant shows the different combinations of labor and capital that can produce a given level of…

Q: A firm called a produces output Q using labor and capital according to the production function Q =…

A: We have been given the following: production function :Q = f( k,l) = 3L + 6k W = 4 R = 6

Q: Assume that you have a production function f(x, y) = √ x + ln(y). The marginal product with respect…

A: The marginal product of input refers to a change in output due to a change in input, keeping other…

Q: f(x1, 12) = (x1 - 1)0.25x9-5.

A: We are going to use the relationship between upward sloping marginal cost curve and supply curve to…

Q: Define a production function F:R X X 12 F(x, x2 ) = { x₁ + x2 1 2 + if x +x >0 1 2 0 if x +x¸ = 0 1…

A: If these conditions are satisfied, then the solution is a local minimum. If λ>0, these conditions…

Q: Given the production function f(x,x2) = x,ax, calculate the profit maximizing demand and supply…

A: The optimal degree of utilisation of a firm's inputs might help it reach the point of profit…

Q: b Now suppose Q = 2L +3K. Let the market price of L be w = 5 and the price of K be r = 4. Let both L…

A: b) Suppose the production function is Q = 2L + 3K, where Q represents the output quantity, L is the…

Q: A firm faces a production function of twittle-twaps: Q(K,Lp,Ln) = 5*K(2/5)*LP (1/3)*LN(1/5) per…

A: The production function is the mathematical relationship between the output produced and the inputs…

Q: A firm has the production function y=4z₁+10z₂. Input prices are w₁=5 and w₂=6. a) What is the cost…

A: We need to find the ratio of marginal products to the ratio of input prices to determine the optimal…

Q: 2. Suppose a producer's production function is F(X,L) = 3KL The cost of K is 20 (r=20) and the cost…

A: The production function of the firm represents the relationship between the physical inputs used by…

Q: The total cost function of a firm is given by: C = q(W)¹³(V) Where q is total output, W and V are…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Suppose the production function is Cobb-Douglas and f(x1;x2)=x11/2x23/2 Write an…

A: The Cobb-Douglas production function is a mathematical equation that represents the relationship…

Q: Question-2 (Cost Minimization) A firm uses labor and machines to produce output according to the…

A: For the given output level of the firm and per unit cost of various inputs like capital (K) and…

Q: 1) A firm uses two inputs K and Lof capital and Labor respectively, to produce a single output Q…

Q: Suppose the long-run production function for a competitive firm is f(x1,x2)= min {x1,2x2}. The cost…

A: Given: Production function: f(x1,x2)= min {x1,2x2} Cost per unit of x1 = w1 Cost per unit of x2 =…

Q: A firm has the production function F(L, K) = L^(3/4)K^(1/4) The price of labor is $9 and the price…

A: “Since you have posted a question with multiple sub-parts, we will provide the solution only to the…

Q: Suppose that a firm has production function F(L, K) = L2/3 K1/3 for producing widgets, the wage rate…

A: The production function is a concept in economics that describes the relationship between inputs…

Q: Suppose the production function for a competitive firm is y=f(x1,x2)= x1 1/4 x2 1/4 . The cost per…

A: Cost minimization problem of producer: For the given output level the firm and per unit cost of…

Q: Given the prices of labour and capital inputs, the cost minimizing combination of inputs suggests…

A: Production function is a mathematical expression that shows different combinations of inputs that…

Q: In a few words, name the reason that production function q = f(L,K) might have diminishing marginal…

A: Answer in step 2.

Q: b) Suppose a business faces a production function which is of the Cobb-Douglas form: Q(L, K) = ALªKB…

A: We have cobb double production function with alpha and beta as parameters.

Q: For the total cost function TC (a) = - 30q² + 800q, find the minimum marginal and average cost. Show…

Q: Question 2. A firm has the production function q = L¹/2K¹/2. The firm can purchase labor, L at a…

A: Production function: This production function is in the form of Cobb Douglas production function so…

Q: An apple grower has discovered a process for producing oranges that requires two inputs. The…

A: In economics, perfect complements imply a type of product or input where the two items are consumed…

Q: c. Given the wage of production workers and the price of twittle-twaps, what is the optimal number…

A: The production function shows the connection between inputs such as land, labor capital, and…

Q: A firm has the following production function: Q=f (L/K). It must pay $20 per hour of labor and rents…

A: Figure -1 shows the AVC, AFC, ATC and MC curve as follows:

Q: A firm uses labor and machines to produce outputaccording to the production function f(L, M) =…

A: Cost minimization problem of producer: For the given output level the firm and per unit cost of…

Q: Miguel and Jake run a paper company. Each week they need to produce 1,000 reams of paper to ship to…

A: Cost is minimized at the point where ratio of marginal product of inputs is equal to price ratio of…

Q: 1. Suppose that a producer has the following production function: Q = K LU6 Where Q is output, and L…

A: Given Q = K1/3. L1/6 Cost minimization: q(K,L) = Lβ.KαSo that MPL=βLβ-1.Kαand, MPk = αLβ.Kα-1Let, α…

Q: d. In the short-run, Prunella cannot vary the amount of land she uses. Plot the output as a function…

A: Factors of production is used in production process and production function establishes the…

Q: 3. A firm’s production function is q = 8K.25L.75 MPL = 6 K.25L-.25 MPK = 2 K-.75L.75 a. Determine…

Q: A company can manufacture a product according to the production function Q=3K1/2L1/2, and capital is…

A: The cost of production is delineated in social science because the expenses spent to urge the…

Q: None

A: Cost-Minimizing Input BundleGiven:Production function: y = 4z1 + 10z2Input prices: w1 = 5 and w2 =…

Q: A firm has the production function X = LK (X = output, L = labour, K = capital); labour and capital…

A: Production is a critical component of economics as it adds value to the economy by putting labor to…

Q: The estimated production function is Q = 12K ½ L1/4 The firm pays workers (L) and rents boats (K) in…

A: Q = 12K1/2L1/4 -------> Production function. Where Q is the quantity of fish. K is boats rented…

Q: 1. Suppose that the production function for a firm is given by the CES function q = f(z1, z2) = (z +…

A: The firm’s production function is, q = f(z1, z2) = (z1^? + z2^?)^(1/?) The firm's cost function is,…

Q: Suppose that a firm’s production function is Q =10 K^(3/4)L^(1/4). The cost of a unit of labor is $1…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: b) Suppose a business faces a production function which is of the Cobb-Douglas form: Q(L,K) = AL“ K®…

A: Given output is a function of A, L and K. When we scale all factors of production in a given…

Q: Output is produced according to production function y = f (L, M) = L2 M2, where L is the number of…

A: Production function: y=fL,M=L2M2 .... (1) The cost of labor is w and the cost of the…

Q: 2. A firm produces a product with labor and capital. Its production function is described…

A: production function, in economics, equation that expresses the relationship between the quantities…

Q: Sugar Enterprises manufactures high speed personal computers as its main product line. Its short run…

A: Factors of production are used in the production process for goods and services. There are four…

Q: 2. A firm faces the production function 1 Q = f(K,L) = 80 [0, 4K-0,25 +0,4L-0,25] 0.25. It can buy…

A: Price of labor = 2 and price of capital =5 total cost C=150

Question

1. Suppose the total-cost function for a firm is given by C = qw²/3v!/3.
a. Use Shephard's lemma to compute the (constant output) demand functions
for inputs I and k.
b. Use your results from part (a) to calculate the underlying production
function for q (q as a function of "k" and "I").

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 1 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

Given the production function y 1/x05, if Price of output is P and price of input X is V and fixed cost is FC, what is the expression for marginal cost (MC) as a function of Y? O MC = Vy0.5 O MC = -2Vy-3 O MC = Vy-0.5 O MC = y/V
2) The general Cobb-Douglas production function for two inputs is given by: q = f (k, l) = AKªL® where 0 0, f¡ > 0, frk 0. b.) Show that = a and ɛg,i Eq,k B (Note that ɛ's are elasticities). || C.) Show that, for this Cobb-Douglas function, production is CRS if a + ß = 1.
The Acme Anvil Company's output is given by the Cobb-Douglas Production function P = 60L2/3 K1/3, where P is the number of anvils produced when Lis the amount spent on labor and K is the amount spent on capital. a. What is the production if L = 150 and K = 150? b. Find the marginal productivities. C. Evaluate the marginal productivities with L = 150 and K = 150. d. Interpret the meanings of the marginal productivities found in part c. e. If their budget is $300 then there is a constraint L+ K = 300. Use Lagrange multipliers (2) to find the values of L and K that will maximize production and find the maximum production f. Find 2. 12| is called the marginal productivity of money and will give the number additional units produced for each dollar increase in the budget. Interpret 2 for this problem. MacBook Pro urses/34419/files/5014304?wrap=1
The production function for a product is given by q= 10K^(1/2)L^(1/2) where K is capital, and L is labor and q is output d) Now suppose w =30 and r = 120. What is the minimum cost of producing q=1000. (You must show your work by clearly writing the equations that you use to derive the cost minimizing levels of L and K.) e) Now suppose that the firm is in the short run and cannot vary the amount of capital. That is, it must use the same amount of capital as in part d). However, the firm wants to produce 1200 units of output. How much labor should it use to minimize its cost and what is the minimum cost of producing q =1200?
A firm uses labor and machines to produce outputaccording to the production function f(L, M) = 4L1/2M1/2, where L is the number of units of laborused and M is the number of machines. The cost of labor is $40 per unit and the cost of using amachine is $10.1. Draw an isocost line for this firm, showing combinations of machines and labor that cost $400and another isocost line showing combinations that cost $200.2. Suppose that the firm wants to produce its output in the cheapest possible way. Find thenumber of machines it would use per worker. (Hint: The firm will produce at a point wherethe slope of the production isoquant equals the slope of the isocost line.)
Please no written by hand The estimated production function is Q = 12K ½ L1/4 The firm pays workers (L) and rents boats (K) in order to produce fish. Currently, the company has no fixed inputs and pays $12 per hour for labour (w) and $16 per hour for capital (r). The quantity of fish produced per day (Q) is 153. A. Derive the conditional input demand functions for labour (L) and capital (K) for IFC. B. What is cost-minimizing amount of labour and capital that IFC should hire and rent? C. Determine the minimum cost of producing 153 units of output? D. Use the isocost and isoquant to illustrate the optimal choice of this firm.
1. Suppose that the production function for a firm is given by the CES function q = f (z1, z2) = (z + z)/Y. Where z1 and z2 are the two inputs used by the firm. The inputs prices are respectively wi and w2 a. Set up the cost minimizing problem of the firm and derive the first order conditions for cost minimization b. Derive the conditional inputs demand functions for inputs 1 and 2 c. Derive the associated cost function for the firm
Suppose a firm producing wood burning stoves has the following production function Q(K, L) = 4K¹/2 [1/2 Where L, the labour, and K, the capital are the 2 inputs of production and Q the quantity of stoves. Assume the price of one unit of L is £1 and the price of one unit of K is £2. a) b) Assume that K=9 in the short run. Draw the production function and calculate the marginal products of L as L changes from L= 1 to L= 6. What does an isoquant curve show? Draw the graph of a production isoquant representing input combinations that will produce 8 units of output.
6 A production function is given by f(x1,x2)=(max{x1,x2})^0.5. Prices of inputs are p1=10 and p2=20. What is the lowest cost of producing 10 units of output?
1. Find the cost minimizing input demand functions (x¿(w,q)) and the cost function (c(w,q)) for the following production functions: 1/3 21382 a. f(x) = x₁
5. The production function is given by y=x₁ + 2x2. If w₁ = 10, w₂ = 8, will the firm use input factor 2 to minimize the cost? In what case will the firm use input factor 2?
A firm has the production function F(L, K) = L^1/2 + K^1/2The price of labor is $10 and the price of capital is $15. The firm has a production goal of Q = 100 units ofoutput.a) Neatly specify this firm’s cost minimization problem, using the particulars associated with this problem.b) Give two equations that an interior solution satisfies, tailoring your equations to the particulars of thisproblem.c) Solve the two equations for the firm’s optimal choice. Show your work.