Given the total cost equation: TC = 144 + 2Q + Q², what is the average cost when the firm produces at the level of Q that yields the minimum average cost?To find the minimum average cost, follow these steps:1. **Understand the Formulas:** - Total Cost (TC) is given by the equation TC = 144 + 2Q + Q². - Average Cost (AC) is the Total Cost divided by the quantity (Q), or AC = TC/Q.2. **Calculate Average Cost:** - Substitute the TC expression into AC: \[ AC = \frac{144 + 2Q + Q^2}{Q} = \frac{144}{Q} + 2 + Q \]3. **Find Minimum Average Cost:** - To find the quantity (Q) that minimizes the average cost, take the first derivative of AC with respect to Q and set it to zero: \[ \frac{d(AC)}{dQ} = -\frac{144}{Q^2} + 1 = 0 \] - Solve for Q: \[ -\frac{144}{Q^2} + 1 = 0 \implies \frac{144}{Q^2} = 1 \implies Q^2 = 144 \implies Q = 12 \] - Check the second derivative to ensure it is a minimum: \[ \frac{d^2(AC)}{dQ^2} = \frac{288}{Q^3} \] This is positive for Q = 12, confirming a minimum.4. **Substitute Q into the AC Formula:** - AC = $\frac{144}{12} + 2 + 12 = 12 + 2 + 12 = 26$Thus, the minimum average cost occurs when the firm produces 12 units, yielding an average cost of 26.

Total cost is sum total of the fixed cost and variable cost. The average cost is calculated by the…

Answered: Given the total cost equation: TC = 144…

Given the total cost equation: TC = 144 +2Q+ Q² what is the average cost when the firm produces at the level of Q that yields the minimum average cost?

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: For the cost function C(Q) = 200+3Q2+4Q3, what is the average fixed cost of producing 10 units of…

A: We have total cost function: C(Q)=200+3Q2+4Q3 ... (1) We have to calculate average fixed…

Q: The average cost for a firm is given as a function as follows:- AC 3Q²-6Q + 20 = Calculate the Total…

A: WE Know that the average cost simply defined as the total cost per unit of output. That is :- AC =…

Q: Ing fong TC = 8Q³ - 96Q² + 32Q Derive the expressions for marginal cost and average cost. What is…

A: Average cost: ‘average cost’ is the ‘total cost’ divided by the number of units of the good. It…

Q: A multiproduct firm’s cost function is C(Q1 ,Q2 ) = 50 -0.2Q1Q2 + 0.1Q22 Are there economies of…

A: Cost function:Economies of scope occur when the total cost of producing a combination of goods or…

Q: The average cost function for skateboards is given by: AC = (15)^2 - 30(15) + 350 = 225 - 450 + 350…

A: The relationship between average cost (AC) and marginal cost (MC) is crucial for understanding…

Q: The total cost function of a firm is:- 23Q² - 13Q + 40 Find the average cost function

A: The total cost (TC) is divided by the entire output to get the average cost of production (Q). All…

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: The average cost function for skateboards. AC = (q^3 - 30q^2 + 350q) / q AC = q^2 - 30q + 350 Draw…

A: The graph of the average cost function AC=q2−30q+350, along with labeled critical points and the…

Q: For the cost function C(Q) = 100 + 4Q + 19Q2 + 2Q3, what is the marginal cost of producing the…

A: Answer to the question is as follows:

Q: Given the following production cost function: TC=5+29 R1 R² +0.5 R³ TC: total cost in '00 (hundreds)…

A: Production costs are the costs a company incurs while creating a something or providing a service…

Q: Diseconomies of scale exists over the range of output for which the long run average cost curve is?

A: Diseconomies of scale exists over the range of output for which the long run average cost curve is…

Q: A watch manufacturer finds that at 1,000 units of output, its marginal costs are below average total…

A: In business, the average total cost, or ATC, is the sum of all product costs divided by the volume…

Q: A firm's short-run cost function is C(a) = 240q – 69° + 0.6q° + 600. Determine fixed cost, F;…

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

Q: In the following problem, c represents the average cost per unit, which is a function of the number…

A: Marginal cost refers to the addition to the total cost when one more unit of the variable factor is…

Q: Suppose a firm has an average total cost function given by: ATC = 11094/q +6 + 6q. Calculate the…

A: Total cost is the sum of fixed cost and variable cost.Fixed cost is the cost that doesn't changes…

Q: The hourly operating cost of a plane which seats up to 405 passengers is estimated to be $5,328. If…

Q: Consider the following cost function: C(Q) = 1000+0.1Q I| Calculate total costs when Q=100 O 1,001…

A: Total cost function shows the relationship between cost and output produced. To determine cost at a…

Q: For the cost function C(Q) = 500+12Q+4Q2+Q3, what is the marginal cost of producing the eighth unit…

A: Cost is a function of the quantity produced. It measures the cost incurred in the production of…

Q: The total cost function of a firm is:- 23Q? - 13Q + 40 Find the average cost function

Q: From the following cost function find the Average Cost, Variable Cost and Marginal Cost Function.…

A: Total cost is the cost of producing all the units of good. Average cost is the cost of production…

Q: For the cost function 125x + 375 C(x) = x+7 where C is in dollars and x is the number produced in…

A: Here we are given the cost function. A cost function is the function of output, and it gives the…

Q: Compute the average variable cost, average cost, and marginal cost for each function.

A: Total cost is the cost that is incurred in production of a hiven level of output.Variable cost is…

Question

100%

Given the total cost equation: TC = 144 + 2Q + Q², what is the average cost when the firm produces at the level of Q that yields the minimum average cost?

To find the minimum average cost, follow these steps:

1. **Understand the Formulas:**
- Total Cost (TC) is given by the equation TC = 144 + 2Q + Q².
- Average Cost (AC) is the Total Cost divided by the quantity (Q), or AC = TC/Q.

2. **Calculate Average Cost:**
- Substitute the TC expression into AC:
\[
AC = \frac{144 + 2Q + Q^2}{Q} = \frac{144}{Q} + 2 + Q
\]

3. **Find Minimum Average Cost:**
- To find the quantity (Q) that minimizes the average cost, take the first derivative of AC with respect to Q and set it to zero:
\[
\frac{d(AC)}{dQ} = -\frac{144}{Q^2} + 1 = 0
\]
- Solve for Q:
\[
-\frac{144}{Q^2} + 1 = 0 \implies \frac{144}{Q^2} = 1 \implies Q^2 = 144 \implies Q = 12
\]
- Check the second derivative to ensure it is a minimum:
\[
\frac{d^2(AC)}{dQ^2} = \frac{288}{Q^3}
\]
This is positive for Q = 12, confirming a minimum.

4. **Substitute Q into the AC Formula:**
- AC = $\frac{144}{12} + 2 + 12 = 12 + 2 + 12 = 26$

Thus, the minimum average cost occurs when the firm produces 12 units, yielding an average cost of 26.

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

The weekly marginal cost of producing x pairs of tennis shoes is given by the following function, where C(x) is cost in dollars. C′(x)=15+500x+1 If the fixed costs are $4,000 per week, find the cost function. What is the average cost per pair of shoes if 1,000 pairs of shoes are produced each week?
Using the figure above, what is the total cost for the firm?
The cost function of a firm is given as C1 = 400 + 20Q + 4Q using this cost function what is the efficient scale of the firm?.
Consider the following cost function (C): C= 0.25q3 - 4q? + 75q + F. The equation for average cost (AC) is: AC = |. (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 equation for variable cost (VC) is: Vc=. (Properly format your expression using the tools in the palette.) The equation for marginal cost (MC) is: MC =. (Properly format your expression using the tools in the palette.)
Average total cost decreases when marginal cost is average total cost. less than greater than equal to
Consider the following cost function: 3 C=0.2q³-6q² + 80q + 150. (Enter a numeric response using a real number rounded to two decimal places.) When output is 19 units, average cost is $ When output is 19 units, marginal cost is $ The output level where average variable cost equals marginal cost is units.
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?
Can you please solve question # 14
The following equation represents the cost structure of a firm: C= 10 + 3q. The average cost of production is
The long-run cost function for a firm in the personal computer business is: C(q) = 8q² + 7200, for q> 0. What is the average cost function AC (g)? AC (q) = 16q AC (q) = 8q+ 7200 9 AC (q) = 16q+ AC (g) 16q+7200 AC(q) = 8q+7200 = 7200 9 The long-run cost function for a firm in the personal computer business is: C(q) = 8q² + 7200. for q> 0. What is the marginal cost function MC (q)? MC(q) = 8q+7200 MC(q) = 8q MC (g) MC (q) = 16q MC (q) = 16q+ 16q+72000 7200 The long-run cost function for a firm in the personal computer business is: C(q) = 8q²+7200, for q> 0. At what level of output does average cost equal marginal cost? The level of output at which average cost and marginal cost are equal is type your answer... -01