Given TC = 120 + 50Q – 10Q2 + Q3 Find a. The equations of the TVC, AVC, and MC functions. b. The level of output at which AVC and MC are minimum, and prove that the AVC and MC curves are U-shaped. c. Find the AVC and MC for the level of output at which the AVC curve is minimum.

Given TC = 120 + 50Q – 10Q2 + Q3 Find a. The equations of the TVC, AVC, and MC functions. b. The level of output at which AVC and MC are minimum, and prove that the AVC and MC curves are U-shaped. c. Find the AVC and MC for the level of output at which the AVC curve is minimum.

Microeconomics

13th Edition

ISBN:9781337617406

Author:Roger A. Arnold

Publisher:Roger A. Arnold

Chapter8: Production And Costs

Section: Chapter Questions

Problem 7WNG

See similar textbooks

Related questions

Q: On the following graph, plot the three SRATC curves for Ike's Bikes from the previous table.…

A: If Q=100 bikes are produced at a single plant, the short-run ATC is $440. In the long run, the…

Q: A cob Douglas production function for a firm is given as Q=4L ½K½. The firm has also established…

A: Cobb Douglas Production Function-It represents connection between its inputs( physical capital and…

Q: On the following graph, plot the three SRATC curves for Ike's Bikes from the previous table.…

A: If it is producing Q=100 bikes in one factory, then its short-run ATC = $440. In the long run, the…

Q: Production Function with Two Inputs Assume that a firm choose K and L inputs. At the start of a…

A: Given information Y=ALαKβ Price is paid to Labor=W Price Paid to capital=r Total cost=LW+Kr

Q: Suppose the utility function of a person consuming two commodities X and Y with income Birr 600 is…

A: Answer to the question is a follows:

Q: What is meant by an expansion path? Illustrate expansion paths for a normal input and an inferior…

A: The expansion path may be defined as the locus of the points of tangency between the Isoquant curve…

Q: A firm’s production function is - y = f(X1, X2)= X11/2 + X1X2 , Where X1≥0, X2≥0 1. Write down the…

A: Since the question you have posted consists of multiple parts, we will answer the first three parts…

Q: total revenue (TR) and total variable cost (VC) if the price is equal to the AVC

A: Relationship between TR and TVC 1. TR represents sum of MR and TVC represents Sum of MC Gross…

Q: Suppose the Sunglasses Hut Company has a profit function given by P(q) = – 0.02q + 5q - 38 where q…

A: As given total profit function is P(q) = -0.02q2 +5q-38

Q: Consider a firm with the production function ƒ(x1, x2) = x₁/²x2. The price of the two inputs is w₁ =…

A: Given information Production function q=X10.5X2 W1=2--- price of factor X1 W2=1---- price of factor…

Q: You are the manager of a firm and you are required to optimize the Cobb-Douglas function given the…

A: Lagrangian method is used to find optimal equilibrium by maximizing or minimizing function subject…

Q: > The production function for gadgets is: Q = Q(L, G) = L½ + G½ ne price of L is w = $2. The price…

A: A production function has Diminishing returns to scale when change the inputs changes the output by…

Q: Given that TC=2000+100Q-10Q2+Q3 where Q is level of output and maximum level of MP is 15 units,…

A: TC=2000+100Q-10Q2+Q3 The maximum level of MP = 15 units

Q: 6. 3.4 from Microeconomic Analysis Given the production function f(r1, 22) = r, calculate the…

A: Production function : f(x1 , x2 ) = x1a1x2a2 Let the output price be (p) , cost of (x1) be (w) and…

Q: KINDLY ANSWER B. Solve for the marginal rate of transformation (MRT) for combinations A - B; B - C;…

A: The production possibility curve shows the combination of two goods that can be produced with the…

Q: You are the manager of a firm and you are required to optimize the Cobb- Douglas function given the…

A: Lagrangian is : q + λ ( M - PK*K - PL*L) where, q is the output function M is the income PK is the…

Q: Maximize and minimize functions 3.The owner of a soda factory knows that his profit in thousands of…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: the wage rate of labour is GH¢2 per hour and capital is rented at GH¢5 per hour. Also, the unit…

A: Production function : Q = 14K0.5 L0.5 + 10 Profit maximizing utilization of any input is the till…

Q: If the ATC curve is continually declining, what does this imply about MC curve? Explain your answer

A: Average Total Cost: The average total cost is the cost per unit of output. It can be determined by…

Q: Question 1: Based on this information, what can you expect to happen to the price you pay for random…

A: *ANSWER :- * ( 1)

Q: Suppose we have one consumer with a Cobb Douglas utility function for consumption, x, and leisure,…

A: Cobb Douglas utility function is the functional form of the production function which is used to…

Q: Suppose that the market for dress shirts is a competitive market. The following graph shows the…

A: Here, the given graph shows the marginal cost, average variable cost and average total cost curves…

Q: The AVC and the AC curve can intersects each other at any point True/False

A: # The average per unit variable cost isris to be as Average variable cost and the average per unit…

Q: Given TC = 100 + 60Q – 12Q2 + Q3, find: (a) The equations of the TVC, AVC, and MC functions. (b)…

A: (a) TC=100+60Q-12Q2+Q3Now,TVC=Variable factor depends on…

Q: Problem 3: Long-Run Cost minimization Consider two cost-minimizing firms producing drones as their…

A: Cost minimisation is the optimisation problem of firm in which cost of production includes wages and…

Q: A firm faces the production function Q = 6K0 L0.5. If it can buy input K at £32 a unit and input L…

A: Cost is minimized when marginal rate of technical substitution equals price ratio of inputs.…

Q: Output Refer to the above graph. Curves 1, 2, 3, and 4 represent the: MC, ATC, AVC, and AFC curves,…

A: ATC or the average total cost is indicated to be as the given amount of the sum total of the…

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: A firm has the following production function: y = f(x) where y is the output and x is the input. If…

A: ANS AP is the amount of output (o/p) per unit of labor. It is given by the following formula: AP =…

Q: Catalina Films produces video shorts using digital editing equipment (K) and editors (L). The firm…

A: Disclaimer:- as you posted multipart questions we are supposed to solve only the first 3 questions.…

Q: Functions of several variables and partial differentiation, Unconstrained Optimization with two…

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

Q: Stretch the MC, ATC and AVC curves in a diagram. Explain the reason why MC and ATC curve is shaped…

A: The marginal cost (MC) shows the incremental cost incurred when one additional unit is produced. It…

Q: Suppose that a technological innovation decreases BYOB's costs so that it now faces the marginal…

A: A monopoly is a market structure where there is only one seller and they are the price makers and…

Q: Consider the units of output, TFC, and TVC given in the following table. Units of output Total…

A: Units of output Total fixed cost (TFC) Total variable cost (TVC) Total cost Average fixed…

Q: QUESTION Given TC = 100 + 60Q – 12Q2 + Q3 find: (a) The equations of the TVC, AVC, and MC…

A: Marginal cost is the additional cost incurred by producing one extra unit of output. Variable cost…

Q: An is a collection of input bundles that yield the same output level

A: An Isoquant is a collection of the input bindles that yield the same output level

Q: For function Y= 10+0.3x-0.006x2 suppose that price of the output is $5 and the price of input is $3…

A: Y= 10+0.3x-0.006x2 given prices py =5 and px = 3

Q: For the typical Cobb-douglas function, q=AKaLb whereas APL / APK = 1 , find out the marginal rate…

A: Marginal rate of technical substitution refers to the rate at which the use of 1 factor should be…

Q: equations of the TVC, AVC, and MC functions. b. The level of output at which AVC and MC are minimum,…

A: Average variable cost (AVC) is a firm's variable costs (labour, electricity, etc.) divided by the…

Q: Which of the following does not have a U-shaped curve? a) The AC curve b) The AVC curve c) The AFC…

A: The average cost curve, average variable cost curve, and marginal cost all are U-shaped due to law…

Q: Joe's coffee shop faces an isocost curve given by C=10L+5K where L is the number of employees and K…

A: Answer: Given, Isocost curve: C=1OL+5KWhere,L=number of employeesK=number of coffee machinesC=total…

Q: What economic principle explains why average variable costs and marginal costs initialy decrease as…

A: A U-shaped curve represents the average variable cost function. Initially, as output increases, the…

Q: Suppose that the Travnikar Corporation manufactures widgets. Analysts that work for the company have…

A: A firm maximizes profit by producing at level of output where MR = MC. When MR > MC, firm should…

Concept explainers

Short-Run Costs and Long-Run Costs

Cost of short-run and the long-run is an economic term that describes the cost involved in the production of goods in a firm in the short as well as long period.

Question

Given TC = 120 + 50Q – 10Q² + Q³
Find
a. The equations of the TVC, AVC, and MC functions.
b. The level of output at which AVC and MC are minimum, and prove that the AVC and
MC curves are U-shaped.
c. Find the AVC and MC for the level of output at which the AVC curve is minimum.

Defintion Defintion Curve that represents the graphical relationship between the total supply of goods and services and the price level in the economy. When the price level increases, producers tend to supply more of a product in the market to earn a higher revenue or vice versa.

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 6 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

QUESTION Given TC = 100 + 60Q – 12Q2 + Q3 find: (a) The equations of the TVC, AVC, and MC functions. (b) The level of output at which AVC and MC are minimum, and prove that the AVC and MC curves are U-shaped. (c) Find the AVC and MC for the level of output at which the AVC curve is minimum
The AVC and the AC curve can intersects each other at any point True/False
Suppose that the Travnikar Corporation manufactures widgets. Analysts that work for the company have found a function C(x) which reports the cost to produce x widgets and a function R(x) which reports the total revenue from selling x widgets. Currently, the company is producing 500 widgets, but the analysts find that R'(500)=85 and C'(500)=79. In order to maximize profits, should the analysts recommend increasing or decreasing production?
Given that TC=2000+100Q-10Q2+Q3 where Q is level of output and maximum level of MP is 15 units, answer the following question based on the given information. A. Determine the TFC ,TVC,AVC,AFC,AC and MC functions b. Calculate the level of output at which AVC and AC reaches its minimum c Draw the relationship between production and cost curve and What relationship do you observe between production and cost curves? Why is this so? G At 5 units AVC,APL is 10,what is the maximum APL?
In 50 words, answer the following question: In the class, we know the reason why the MC curve intersects the ATC curve at the minimum level of ATC. Actually, MC curve also intersects the AVC curve at the minimum level of AVC. Is it a coincidence? What make the similarity? (Hint: How MC affect the change in ATC? Does it the same for AVC?)
Joe's coffee shop faces an isocost curve given by C=10L+5K where L is the number of employees and K is the number of coffee machines. If Joe's total budget is 100 and he has 5 employees, he can afford ___ machines. The slope of the isocost curve (with K on the y-axis) is ___. For each additional employee, to keep his costs the same, Joe has to give up ___ machines.
Consider the following total cost function: TC = 2/3Q3 – 10Q2 + 200Q + 50 A) Identify the FC and VC function? B) Calculate AVC, AFC, ATC, and MC functions C) Determine the level of output at which AVC reaches minimum point and the minimum AVC at that level of output?
Assume that Donnell Corp. is currently producing 500 units of output per period, using 25 units of labor and 20 units of capital. Values for the marginal product of each input and the prices of the inputs are as follows: MPK = 100, MPL = 200, w = 2, and r = 3. Given the information above, which of the following is true? a. The firm is currently using the optimal levels of capital and labor. b. The firm should increase labor and reduce capital usage. c. The firm is not using the optimal levels of capital and labor, and it is impossible to determine the optimal levels from the given information.
A firm’s production function is - y = f(X1, X2)= X11/2 + X1X2 , Where X1≥0, X2≥0 1. Write down the firm’s production possibility set, and its input requirement set. 2. Is this production function concave, quasi-concave? 3. Is this production function homogenous? 4. Find its returns to scale when X1=1, and X2=1
Functions of several variables and partial differentiation, Unconstrained Optimization with two independent variables, Stationary points, Sufficient conditions for optimisation and saddle point Question 2: A firm has the production function Q=f(L,K)=100L0.5K0.5, where L is labour and K is capital. The wage rate is $5 per hour and the rental price of capital is $4 per hour and the price of the good is $1. 1. Find the marginal product (MP) of labour and capital (that is, fL,fK ) 2. Show that there are diminishing marginal productivities, that is, fLL<0,fKK<0 3. Find the cost function. 4. Find the amount of labour and capital the firm should hire to maximize profits. [Hint: write the profit function in terms of L and K and then take partial derivatives. Use the concepts involved in Question 1 above to determine the profit is maximised.] (Question 1: Let f(x,y)=2x2+x2y+y3+12y2. Find the stationary points and for each stationary point determine whether it is a maximum, minimum,…
Why does the ATC curve reach its minimum point further along the Quantity Axis than the AVC curve and a higher point along the MC curve?
You are the manager of a midsized company that assembles personal computers. You purchase most components – such as random access memory (RAM) – in a competitive market. Based on your marketing research, consumers earning over RM80,000 purchase 1.5 times more RAM than consumers with lower incomes. One morning, you pick up a copy of The Wall Street Journal and read an article indicating that input components for RAM are expected to rise in price, forcing manufacturers to produce RAM at a higher unit cost. Based on curve, discuss the following scenarios. Question 1: Based on this information, what can you expect to happen to the price you pay for random access memory (RAM)? Question 2: In addition to this change in RAM input prices, the article indicated that consumer incomes are expected to fall over the next two years as the economy dips into recession?