A firm's cost function is given by C(x,y)=2x²+y²+2, where two outputs are produced, x and y. What are the outputs levels that minimize the costs to the firm? What is that minimal cost? Using hessian determinant show that cost is indeed minimized

A firm's cost function is given by C(x,y)=2x²+y²+2, where two outputs are produced, x and y. What are the outputs levels that minimize the costs to the firm? What is that minimal cost? Using hessian determinant show that cost is indeed minimized

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Related questions

Q: A factory that you are managing has an hourly production process that can be represented by the…

A: Cost is minimized when production takes place where marginal rate of technical substitution is equal…

Q: 1 1 2. Suppose a producer's production function is F(K, L) = 3KZL The cost of K is 20 (r = 20) and…

A: Microeconomic firm theory investigates how companies maximize profit through production, resource…

Q: Suppose a firm manufactures coffee makers and sells them for $75$75 each. The costs incurred for…

A: "Since you have asked multiple parts, we will answer only first three parts for you. If you have any…

Q: Draw an example of the Total Fixed Cost, Total Variable Cost, and Total Cost of a company whose…

A: Total Cost: The term total cost refers to the sum of all the costs that are used in the production…

Q: that the dollar cost of producing X appliances is c(x) = 1000+70x-0.1x². ■ Find the average cost per…

A: Total cost is the cost incurred by the firm on the production of final goods and services. The total…

Q: Skylar owns a firm that produces holiday ornaments. Her production function is given by: f (L, K)…

A: Given- y = (min{x1, 2x2})^1/2 let, We increase X1, X₂ by some constant 'C' y' = ( min { CX₁ + 2 CX ₂…

Q: For a certain production process, fixed costs are $60,000. Variable costs are $30 per unit of…

Q: Suppose a firm's production function can be specified as Q = 10KL.This firm's cost function…

A: This can be described as a concept that shows when an individual, firm, or any entity uses an…

Q: Question 5 Show that if a production function exhibit constant returns to scale, then the cost…

A: Constant returns to scale means when inputs increases by some percentage then output increases by…

Q: Given the following costs functions C1=5q C2=5q+5 C3=5q-5 1. Calculate the marginal costs functions.

A: Marginal cost is the change in the total cost of a firm that arises when the firm produces one more…

Q: a) Does the product function provide constant, increasing, or decreasing scale benefits? b) Kjell…

A: x = 100N0.8K0.2 When both inputs are doubled, new production function is x* = 100 x (2N)0.8(2K)0.2 =…

Q: As a production process requires labor L and capital K, q = F (L, K). The wage for a labor is $500,…

A: The optimal level of labor and capital is given by the point where the marginal rate of technical…

Q: Define the production function, f(x), and the average product associated with it. How do you…

A: Production is the process of transformation of inputs into output by using factors of production .…

Q: Give the formulas for and plot average fixed cost, AFC, marginal cost, MC, average variable cost,…

A: Given Cost function: C=3+q2 .....(1) Fixed cost: The cost of production which remains…

Q: aryan plans to offer the services for $45 per lesson, as (A) Write down the total cost as a…

A: Total cost(TC): refers to the total cost incurred by the industries in the production process. Costs…

Q: If C(x) is the total cost function of producing x items, then the marginal cost at x = a, given by…

A: Fixed costs don't change based on the volume of sales or output. The number of products or services…

Q: Find the marginal cost function. C(x) = 174 + 1.7x The marginal cost function is C'(x) = ||.

A: The cost function is: C(x) = 174+1.7x

Q: A computer company produces hardware and software using the same plant and labor. The total cost of…

A: Economies of scope occur when producing multiple products together reduces the total cost, as shared…

Q: If the production function is given by f(x1, x2) = min{x1, x2} + min{x3, x4}, what is the minimum…

A: A production function in economics describes the technological relationship between the quantities…

Q: The cost curve for producing widgets passes through the following points and is piecewise linear in…

A: Given Information: Units produced Costs 0 $600 200 $1200 400 $1600 600 $1800 The fixed…

Q: The number of units that minimizes the average cost is

A: The average cost is the cost computed by diving the total cost of production by the total quantity.

Q: Does this production function exhibit constant returns to scale? Using the marginal products you…

A: To evaluate if the production function displays consistent returns to scale, we must first see if…

Q: Introduction to Calculus in Economics: Calculus is a powerful tool used in economics. One of the…

A: The Average Cost is the per unit cost of production acquired by separating the total cost (TC) by…

Q: A firm has a cost function given by C(y)=100+12y-8y^2+2y^3. At what output level is marginal cost…

A: "In economics, cost refers to the value of money that is spent in order to produce a good." "A cost…

Q: For the cost function c = √q, show that marginal and average costs are always decreasing.

A: The firm produces goods and services which would result in the firm to incur cost. The production of…

Q: Given the cost function , TC = 4q2 + 9 - calculte marginal cost ?

A: Marginal cost is the cost incurred when producing one additional output.

Q: If the marginal cost for ski gloves is C'(x) = 3.5x + 12.5 and C(0) = 462, find the cost function.…

A: Marginal cost is the addition to the total cost for producing an additional unit of output.

Q: The total cost function is : C= 2x3+4x2+2 Find the marginal cost of C?

A: Given: C= 2x3+4x2+2 Where, x is the number of units that has been produced.

Q: dollars. C'(x)=15+ 500 X + 1 If the fixed costs are $4,000 per week, find the cost function. What is…

Q: Suppose a firm has the following production function Q = f(K,L) = (1/2)L(2/3)K(1/3) and a total…

A: Production and cost function: The production function determines all the input bundles that produce…

Q: The cost, in dollars, of producing z units of a certain item is given by C (z) = 5z – 8V 3. %3D Find…

A: Cost function C(x) = 5x-8x-3 .......... (1) We have to find a production level that minimizes…

Q: Emma sells hot chocolate outside of Yankees baseball games. They have two inputs in the production…

A: Given Production function f(x1,x2)=x11/3x21/3

Q: A firm estimates its production function as Q = -2.4 + 20*L -.5*L2 + 30*K -1.00*K2 + 15*F -.3*F2.…

A: Given, The production function, Q = -2.4+ 20 L - 0.5L2+30K - 1.00K2+15F- 0.3F2 The total cost…

Q: The marginal cost of producing the xth box of DVDs is 7 + 80,000 C(x) = and the fixed cost is…

A: The marginal cost is the extra cost incurred by the firm upon producing more units of a good or…

Q: Consider the following cost function: 3 When output is 19 units, average cost is $ C=0.2q³-69²…

A: Average cost is the cost incurred from the production of a single unit of good. The producer wants…

Q: Consider the following short run cost function: TC = 4Q3 - 24Q² + 16Q + 100 Derive the expressions…

A: Total cost or expenses is the cost incurred by the producer in producing a certain level of output.…

Question

A firm's cost function is given by C(x,y)=2x²+y²+2, where
two outputs are produced, x and y. What are the outputs
levels that minimize the costs to the firm? What is that
minimal cost?
Using hessian determinant show that cost is indeed
minimized

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1: Hessian matrix

VIEW

Step 2: Working

VIEW

Solution

VIEW

Step by step

Solved in 3 steps

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

The manager of a T-shirt stand found that the cost to produce 10 T-shirts is $105.68, while the cost to produce 40 T-shirts is $402.98. Assume the cost C(x) is a linear function of x, the number of T-shirts produced. Calculate the marginal cost of a T-shirt, that is, the change in cost of producing one additional T-shirt. (Round to 2 decimal places)
A firm's total cost function is C=24x2−xy+8y2C=24x2−xy+8y2 and they are required to produce a combination of products totalling 128. In order words, the firm is subject to the constraint x+y=128x+y=128. What is the Lagrangian function?
The marginal cost of producing the xth box of DVDS is 15 + and the fixed cost is $100,000. Find the cost function C(x). 130,000 C(x) =
Firm D has production function F(K,L) = aK+2L. Very briefly, what is the interpretation of a in this function?
Calculate a cost function from a production function and explain how economic costs differ from accounting costs.
The production function for a product is given by q = 100KL. If the price of capital is $120 per day and the price of labor $30 per day, what is the minimum cost of producing 1000 units of output?
Consider the following cost function. a. Find the average cost and marginal cost functions. C(x) = 1700 + 0.4x, 1700 +0.4. a. The average cost function is C(x) = The marginal cost function is C'(x) = 0.4|.
Consider a company that has fixed costs of $6,700 and a marginal cost of $26 per item. What is the company's average cost function? How many items must the company produce to have an average cost of $36.31 per item?
Assume quantities need not be integers. Marginal cost is MC(q) = 6 + (9/10) * q. Total cost is TC = 456 at q=5. What is the fixed cost of production?
A firm has the following production function:q = ƒ (z1, z2) = z1αz2βc. Derive the firm's cost function (simplify)
No hand written solution and no image
Assume that cost curves have the standard U-shape. Suppose average total cost (ATC) is at its minimum when the output is 10 units. Also, we know that marginal cost of the 9th unit is $5. What is the ATC when 10 units are produced? 1) $5. 2) Greater than $5. 3) Less than $5. 4) There isn't sufficient information to answer the question.