A firm's average cost function is given by the quadratic y = x2 - 20x + 100 where y is average cost in dollars per unit of output. the output price is $10 per unit, and is the same at all levels of output. Find the output levels at which the firm just breaks even (i.e., price=average cost).

A firm's average cost function is given by the quadratic y = x2 - 20x + 100 where y is average cost in dollars per unit of output. the output price is $10 per unit, and is the same at all levels of output. Find the output levels at which the firm just breaks even (i.e., price=average cost).

Microeconomics

13th Edition

ISBN:9781337617406

Author:Roger A. Arnold

Publisher:Roger A. Arnold

Chapter8: Production And Costs

Section: Chapter Questions

Problem 6QP

See similar textbooks

Related questions

Q: Suppose the total cost function of a firm is given as: TC = 720 - 45Q + 20². Determine the average…

A: Total cost of production is the summation of fixed cost and variable cost . It is the monetary value…

Q: company manufacturing laundry sinks has fixed costs of $100 per day but has total costs of $2,500…

A: (a) Total cost is the sum of fixed cost and variable cost. Fixed cost for manufacturing the sink is…

Q: A fast-food company in Hermanus has the following cost function: TC = 10 + 3K + 2L, where Lis the…

A: Given total cost: TC=10+3K+2L ......... (1) and production function Q=2KL ........…

Q: Consider the following statements when answering this question: I. A firm's marginal cost curve does…

A: Marginal cost is the additional cost that occurs from the production of one additional unit of the…

Q: A firm's short-run cost function is given by: C (q) = 50 + 10q – 6q² + q³ |3D What is the lowest the…

A: Cost function: The production function model is used by management to run numerous production…

Q: The short-run cost function of a company is given by the equation TC = 200 + 55q, where TC s the…

A: Since you have asked for the solution of B and C only. So, I am answering only B and C.

Q: When a firm produces 50,000 units of output, its total cost equals $6.5 million. When it increases…

A: Economics is a branch of social science that describes and analyzes the behaviors and decisions…

Q: Suppose that a firm’s production technology is described by the production function f(x1, x2) =…

A: The production function is given as follows: Q = x12 x2 The cost of the firm is minimized at a point…

Q: Suppose a wind turbine producer faces this production function: Q=0.25KL with MP = 0.25K; MPk =…

A: Given wage = 12 and rental cost = 22

Q: Fixed costs differ from sunk costs in that a firm can avoid fixed costs by not producing anything

A: Avoidable costs are costs that do not occur if the activity is not performed. For example, supply…

Q: Randall Cars repair Factory has the total Cost Function TC (Q) = 4₁1 Q¹+ 26/Qx+30 where Q stands for…

Q: The marginal cost curve of a firm is MC = 6y + y2 .

A: Answer: Given that: The marginal cost curve of a firm is MC = 6y + y^2 . Total variable costs to…

Q: Suppose a firm with a production function given by Q = 30K0.5L0.5 produces 1,800 units of output.…

A: Firm minimizes cost by employing inputs at a point where ratio of marginal product of inputs is…

Q: Suppose each firm of the industry has a short-run total cost curve of TC = 5+4q+q², where q is…

A: Total cost of production refers to the total monetary value incurred on fixed as well as variable…

Q: A firm's unit capital and labor costs are $1 and $2 respectively. If the production function is…

A: The maximum output of the production function can be determined by finding the marginal product of…

Q: a firm has the production function Q=min{2L,K}, find the cost function in the long run if wage is $2…

A: The provided production function is: Q=min{2L,K}

Q: Given prices for the two inputs as w1 = 1, w2 = 2, find the cost function of the (attached)…

A: Answer to the question is as follows:

Q: A firm has the following Cobb-Douglas production function: q = LªK!-a, where 0 < a <1 is a…

A: Rental cost of capital = r = $10 Wage of labor =w = $20 Capital quantity, K = 1 The production…

Q: The cost function for Managerial Enterprises is given by C(Q) = 20 + 3Q2. Determine the marginal…

Q: The cost function for the manufacture of x number of goods by a company is C(x) = x3-9x2+24x. Find…

A: Given the cost function, the marginal cost (MC) equation is; C(x) = x3-9x2+24xMC=∂C(x)∂x=3x2-18x+24

Q: The cost function for Managerial Enterprises is given by C(Q) = 20 + 30. Determine the marginal…

A: The cost of the production of the goods and services would result in the firms costs. The costs of…

Q: Consider the total cost function, TC = 25 + 6Q - 5Q^2 + 6Q^3 Find the marginal cost if firm want to…

A: Marginal cost is nothing but the cost incurred to the firm when they want to produce additional unit…

Q: The profit, P(x), generated after producing and selling x units of a product is given by the…

A: Given, The quantity of roast beef sandwich = x The total cost per week represent by = C(x) The fixed…

Q: An economist estimated that the cost function of a single-product firm is C(Q) = 100 + 20Q + 15 Q^2…

A: Total Cost is the cost that includes the fixed cost and variable cost of production. Cost function;…

Q: Suppose a firm’s cost function is given by C(q) = 20 + 10q − 4q^2 + q^3 (a) What is fixed cost? (b)…

A: Given information: We have given the cost function. i.e., C=20 + 10q - 4q2 + q3 The cost function…

Q: Consider that a company has a total cost function TC = 3Q3+2Q2+6. a.What is the average and…

A: Part a: Average Cost = Total Cost/ Quantity Marginal Cost = dTC/dQ TC = 3Q3+2Q2+6 Average Cost =…

Q: 25) If a firm has the cost function C(q) = 5q² + 20q + 180 and the marginal cost function MC(q) =…

A: average cost or unit cost is equal to total cost divided by the number of units of a good produced…

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

A: Answer -

Q: An economist estimated that the cost function of a single-product firm is C(Q) = 100 + 20Q + 15Q^2+…

A: The cost function of a single-product firm is: C(Q)=100+20Q+15Q2+10Q3

Q: Assume a firm's short-run cost function is given by the following expression: C(q) = 2+q+q2 If the…

A: The producer is in equilibrium at the point when MC=MR, at this point the value of producing an…

Q: A firm has the following production function where q represents the output level per week, L…

Q: Suppose a firm’s production function is q= 2L+ 5K, the wage is w= 4, and the rental rate of capital…

A: Cost function is the total cost incurred to produce a good. It is the total sum of cost incurred on…

Q: A competitive firm uses two variable factors to produce its output, with a production function q =…

A: The production function exhibits the relationship between the factors of production and the output.…

Q: The short-run cost function of a company is given by the equation TC = 200 + 55q, where TC is the…

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

Q: Suppose that a firm has a short-run cost function C(q) = q2 +1. Part a Find the short-run supply…

A: In a market, a firm’s cost function can provide information about different types of costs such as…

Q: c) If the total cost of a product is TC = 45 + 5Q − 2Q 2 + 2Q 3 , Find i) Marginal cost function at…

A: Total cost is the cost that includes fixed cost as well as the variable cost of the production…

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

A: Cobb Douglas production function; Q=K0.25L0.25 Price of one unit of capital per hour; r= $10 Price…

Q: The four statements below describe properties of a firm's short run cost curves. Complete the…

A: Average cost is the per unit cost of production. Marginal cost is the additional cost incurred to…

Q: The average fixed cost curve a. always rises with increased levels of output b. declines as long as…

A: The average fixed cost is the per unit fixed cost incurred in the production process as it is…

Q: A firm has the following production function, Q = Q(K,L) = K²+L², where Q is output, and K (capital)…

A: Firm gets maximum profit with use of optimal level of input where the condition Of MRTS = factor…

Q: An economist estimated that the cost function of a single-product firm is C(Q) = 100 + 20Q + 15 Q^2…

A: Given Data:Cost function, C(Q)=100+20Q+15Q2+10Q3

Q: Consider the following table illustrating the production function of gadgets. Furthermore, suppose…

A: Answer to the question is as follows :

Q: A firm has the following Cobb-Douglas production function: q=(L^α)(K^1-α) 0<α < 1 is a…

A: Production Function: q = LαK1-α In the short run, K = 1. Therefore: q = Lα⇒L = q1α Total Cost: TC =…

Concept explainers

Isocost and Isoprofit Curve Analysis

An isocost curve in the production theory that is a crucial part of economics depicts different combinations of factor inputs at a given market cost. In other words, this shows all the combinations of production factors that cost the same for the firm to employ. Usually, this can be depicted as a downward sloping straight line when the firms act as the price-takers in the factor markets. The slope of this mainly depicts the relative prices of different production factors.

Question

A firm's average cost function is given by the quadratic

y = x² - 20x + 100

where y is average cost in dollars per unit of output. the output price is $10 per unit, and is the same at all levels of output. Find the output levels at which the firm just breaks even (i.e., price=average cost).

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

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

For a firm with a Total Cost function TC C(Q), recall that the definitions of Marginal Cost (MC) and AverageTotal Cost (ATC) are given as follows:Marginal Cost (MC) = C'(0)Average Total Cost (ATC) = C(Q)/QProve that the marginal cost is equal to the average total cost (MC = ATC) when the average total cost is at itsminimum value.(Hint: By using the definition of average cost function, find the quantity that minimizes it by applying unconstraint optimization.Show that the FOC of the minimization problem implies that MC=ATC has to be satisfied at the minimum level of average cost.)
The cost function of a UC Irvine donut shop is: C(q)=10+ 10q + q?, so the marginal cost function is: MC= 10+ 2q. In these equations, q is the output in terms of boxes of donuts. (a) What is the firm's average cost curve? (Note: just write the equation, no graph necessary) What is the firm's average variable cost curve? (Note: just write the equation, no graph (b) necessary) (c) If the price of a box of donuts is $20, what is the optimal output for this firm?
Given a firm's cost function C = F(x) = ax² +bx + d: Find the firm's Average cost funetion (A(x) and Marginal cost function M(x). O Is C(x) more appropriatc as a long-run or short-run cost function? Explain. Determine whether the Marginal cost function is strictly monotonic for a> 0, b>0, and d> 0. Does this finction have an inverse for economically meaningful values of x? If yes, find dx/dM. If not, show/explain what restriction would be necessary for inverse to exist. a. b. c. d.
K A cereal factory has weekly fixed costs of $22,000. It costs $1.26 to produce each box of cereal. A box of cereal sells for $4.06. Find the rule of the cost function c(x) that gives the total weekly cost of producing x boxes of cereal. OA. c(x)=1.26x OB. c(x)=22,000+ 1.26x OC. c(x)=22,000 +4.06x OD. c(x)=22,000+ 2.8x
The cost function of a firm is c(y) = 3y^2 + 6y + 5.1. Find the Average variable and Marginal Cost curves of the firm.2. What is the quantity level where the average variable cost is minimized?
Suppose the total cost function of a firm is given as: TC = 720 - 45Q + 2Q². Determine the average variable cost, average cost and marginal cost function. At what rate of output, average cost is minimized? How much is the minimum average cost for this firm? Draw a diagram to show the minimum point of average cost functions. a. b. d.
Suppose Honda's total cost of producing 4cars is $225000and its total cost of producing 5cars is $250000 .what is the average total cost of producing 5cars? What is the marginal cost of the fifth car? Draw the marginal cost curve and the average cost curve for a typical firm and explain why these curves cross where they do.
We expect the marginal cost to increase as this firm produces more computers. But when the firm shifts from producing 1 to 2 computers, marginal cost falls. What might explain this?
A Chinese high technology manufacturing firm has a production function of 9=12L0.20K0.80 (based on Zhang, et al., 2012). It faces prices of w = $2 and r= $8. What are its short-run average variable and marginal cost curves? Let K be fixed in the short run. The firm's short-run average variable cost curve, AVC, as a function of K and q is AVC = $ (Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a superscript can be created with the ^ character.) The firm's marginal cost curve, MC, as a function of K and q is MC = $. (Properly format your expression using the tools in the palette.)
Each graph illustrates three short-run cost curves for firms, where ATC is average total cost (also referred to as average cost), MC is marginal cost, and AVC is average variable cost. Please classify each of the graphs as valid or invalid based on what you know about the relationships between these curves.