A firm has the short-run total cost function C(q)=100+10q-2q^2+q^3. a) Derive the equations for...
Question:
A firm has the short-run total cost function {eq}C(q)=100+10q-2q^{2}+q^{3} {/eq}.
a) Derive the equations for average total cost, average fixed cost, average variable cost, and marginal cost.
b) Derive the short-run supply equation.
Total cost function
A firm's total cost function is a sum of its fixed and variable costs. Fixed costs are any costs that does not change with output while the variable cost are costs that change with output.
Answer and Explanation: 1
Become a Study.com member to unlock this answer! Create your account
View this answera) {eq}ATC = \frac{TC}{Q} = \frac{100+10Q-2Q^{2}+q^{3}}{Q} = \frac{100}{Q} + 10 - 2Q + Q^2 \\AFC = \frac{FC}{Q} = \frac{100}{Q} \\AVC =...
See full answer below.
Ask a question
Our experts can answer your tough homework and study questions.
Ask a question Ask a questionSearch Answers
Learn more about this topic:
Get access to this video and our entire Q&A library
Average Cost Vs. Total Cost: Making Production Decisions in the Short-Run
from
Chapter 4 / Lesson 8
13K
Learn what the average cost of a firm is and how it differs from total cost. Understand the distinction between short run and long run average total cost.
Related to this Question
- a. A competitive firm has a short run total cost curve represented by the following equation: C(q) = 50 + .05q2 Derive the marginal cost. Derive the expressions for average total cost and average vari
- 1. a.) A competitive firm has a short run total cost curve represented by the following equation:C(q) = 50 + .05q^2 Derive the marginal cost. Derive the expressions for average total cost, average va
- A firm's long-run total cost function is TC = q3 - 40q2 + 100q. 1) Calculate the average cost function. 2) At what level of output does average cost reach a minimum? 3) Calculate the marginal cost function. 4) Prove this marginal cost curve intersects
- Over the short run, total cost is equal to: a) average total cost plus marginal cost. b) total fixed cost plus total variable cost. c) total variable cost multiplied by average total cost. d) average fixed cost multiplied by average variable cost.
- A firm has the following total cost function: STC=900+50Q-2.7Q^2+0.045Q^3 a. Write equations for average fixed cost and average variable cost, and marginal cost. b. At what level of output will averag
- Graph the marginal cost, average variable cost, average total cost, and average fixed cost of a firm.
- 1. Given the total cost function TC = 100 + 40Q - 15Q2 + 5Q3, calculate the: a. average fixed cost function (AFC). b. average variable cost function (AVC). c. marginal cost function (MC).
- When the average total cost curve is at its minimum, we know that the: a. marginal cost curve is above the average total cost curve. b. marginal cost curve intersects the average total cost curve. c. average fixed cost curve is above the marginal cost
- Determine the marginal cost, short-run average cost curve, and the long-run average total cost curve.
- The total cost is given by A) TC(y) = 2y^3 - 13y^2 + 50y + 10, B) TC(y) = 2e^{3y+4} . Compute: fixed cost, variable cost, average cost, and marginal cost.
- Average fixed cost plus average variable cost equals A. marginal cost. B. total cost. C. average total cost. D. total variable cost. E. marginal fixed cost.
- Consider the equation/function: TC = 20 + 4Q - 0.1Q^2. Calculate the following: Total cost, Total fixed cost, Total variable cost, Average total cost, Average fixed cost, Average variable cost, Marginal cost.
- Consider the equation/function: TC = 20 + 2Q + 0.5Q^2. Calculate the following: Total cost, Total fixed cost, Total variable cost, Average total cost, Average fixed cost, Average variable cost, Marginal cost.
- Consider the equation/function: TC = 20 + 4Q. Calculate the following: Total cost, Total fixed cost, Total variable cost, Average total cost, Average fixed cost, Average variable cost, Marginal cost.
- Based on the assumptions below, find the firm's long-run total, average total and average variable, and marginal cost functions. Calculate the same cost functions for the short run, supposing K=K_o.
- The sum of fixed and variable costs is: A. total cost B. marginal cost C. variable cost D. average cost
- A competitive firm has a short-run cost function c(y) = y^3 - 2y^2 + 5y + 6. a. Write down equations for the firm's average variable cost function and the firm's marginal cost function. b. At what le
- When a firm is experiencing diseconomies of scale, long-run: a. average total cost is minimized, b. average total cost is greater than the long-run marginal cost, c. average total cost is less than the long-run marginal cost, d. marginal cost is minimi
- Calculate this firm's marginal cost and, for all output levels except zero, the firm's average variable cost and average total cost.
- A firm's short-run cost function is C(Y) = Y^3 - 8(Y^2) + 30Y + 5. a) What is the firm's marginal cost function? b) What is the firm's average variable cost function? c) Marginal cost equals ave
- Given the total cost function TC(q) = 100 + 5q + 1/2q2, find an expression for (a) fixed cost (b) average cost (c) average fixed cost (d) average variable cost (e) marginal cost (f) Scale Econom
- If marginal cost is between average variable cost and average total cost, then: a. both average variable cost and average total cost are increasing. b. both average variable cost and average total cost are decreasing. c. average variable cost is increasin
- Marginal cost is equal to both average variable cost and average total cost when: a. average total cost and average variable cost are decreasing. b. average variable cost and average total cost are their minimums. c. the marginal product of labor is incre
- A competitive firm has the short-run cost function c(y) = y^3 - 2y^2 + 5y + 6. (a) Write down equations for the firm's average variable cost function and the firm's marginal cost function. (b) At what
- A perfectly competitive firm has the following short-run total cost function: SR-TC = 18 + 5q + 2q^2. a. Find the firm's short-run marginal cost (SR-MC), short-run average total cost (SR-ATC), and sh
- The sum of fixed cost and variable cost at any rate of output is equal to: a. Average total cost. b. Total profit. c. Total cost. d. Marginal cost.
- Total cost divided by the quantity of output is a. average variable cost. b. average total cost. c. average fixed cost. d. marginal cost. e. total variable cost.
- Total cost is a. the sum of variable cost and fixed cost. b. average variable cost times quantity. c. the sum of average fixed cost and marginal cost. d. the sum of fixed cost and average variable cost.
- Calculate the Total Cost, Average Cost, and Marginal Cost using the given Quantity, Total Fixed Cost, and Total Variable Cost
- A firm's total cost function is given by the equation TC = 4000 + 5Q + 10Q^2 and marginal cost is given by the equation MC=5+20Q . (A) Write an expression for each of the following cost concepts:
- Define marginal cost, average total cost, average variable cost, and average fixed cost.
- Suppose that the cost function of X is given by: C = 500 - 10 X + 5 X^2. a) Find the variable cost and the fixed cost. b) Find the average cost and the marginal cost. c) Find the point where marginal cost equals average cost. d) Find the point where the a
- In the short run, the marginal cost curve crosses the average total cost curve at: A. a point just below the average fixed cost curve. B. the minimum point of the average total cost curve. C. the maxi
- Given the total cost function C = 100 + 20Q + Q^2: A) Find the average cost function. B) Find the marginal cost function. C) Find the derivative of the average cost function with respect to output. D)
- When average total cost is at its minimum point: a. Marginal cost is also at its minimum point, b. Marginal cost is equal to zero, c. Marginal cost is constant, d. Average total cost is equal to marginal cost, e. The firm is maximizing profit.
- A competitive firm has the short-run cost function c(y) = y^3 - 2y^2 + 5y + 6. Write down the equations for A. the firm's average variable cost function B. the firm's marginal cost function C. At what level of output is the average variable cost minimized
- Suppose a firm has the (short run) cost function c(y) = y2 + 2y + 9. (a) Suppose the firm is in a perfectly competitive market. i. Derive the firm?s average variable cost curve, average total cost cur
- Find and graph the short-run (a) total cost, (b) fixed cost, (c) variable cost, (d) average total cost, (e) average fixed cost, (f) average variable cost, and (g) marginal cost curves for the producti
- A competitive firm's short-run supply curve is its cost curve above its cost curve. a. average total cost, marginal b. average variable, marginal c. marginal, average total d. marginal, average variable
- Suppose the cost function is TC(q) = 3ln(q) - 1.5q^2 + 0.25q^3 - 235. Find Variable cost, Average Variable Cost, Fixed Cost, Average Fixed Cost, Marginal Cost when q=10.
- The short-run supply curve for a perfectly competitive firm is given by: a. the entire marginal cost curve. b. the marginal cost curve at and above average variable cost. c. the marginal cost curve at and above average total cost. d. the average variable
- If average variable costs are increasing while average total costs are decreasing, then A) marginal cost must lie between average variable and average total costs. B) marginal cost must equal averag
- If the short-run total cost function for a firm is TC = 3,000+100Q, show step by step calculation: a. the average total cost (ATC) when the output Q=10. b. the marginal cost (MC) for the 10th unit of output. c. the fixed cost in the short-run.
- The long-run average total cost equation for a perfectly competitive firm is LRAT C=620-5Q+0.025Q^2 a. What is the firm's long-run total (LRTC) cost equation? b. What is the quantity of output when the long-run average cost is minimized?
- If a firm's marginal cost is below its average total cost, what must be true? a) Average total cost is rising. b) Average total cost is falling. c) Average total cost is at its lowest point. d) The average total cost must be negative.
- A firm is productively efficient if it produces at the minimum point of its: a. average variable cost curve. b. marginal cost curve. c. average total cost curve. d. total cost curve.
- Marginal cost is average variable cost when. a. equal to; average total cost is minimized b. less than; total cost is maximized c. greater than; average fixed cost is minimized d. equal to; average variable cost is minimized
- 2. A competitive firm has the following short-run cost function: c(y) = y3 - 8y2 + 30y + 5. What is the firm's marginal cost function? What is the firm's average cost function? Average variable cost i
- Marginal cost is the slope of the: a. variable cost curve. b. total product curve. c. marginal curve. d. average cost curve.
- A firm shuts down if the price is? A) below average total cost. B) above minimum average fixed cost. C) below minimum average variable cost. D) above minimum average variable cost. E) less than marginal cost.
- A firm shuts down if price is: A) below average total cost. B) above minimum average fixed cost. C) below minimum average variable cost. D) above minimum average variable cost. E) less than marginal cost.
- If average variable costs are increasing while average total costs are decreasing, then A) marginal cost must lie between average variable and average total costs. B) marginal cost must equal average variable cost. C) marginal cost must equal average tota
- If average variable costs are increasing while average total costs are decreasing, then A) marginal cost must lie between average variable and average total costs. B) marginal cost must equal average variable cost. C) marginal cost must equal the avera
- A firm's total cost function is given by the equation: TC = 4000 + 5Q + 10Q^2. a) Write an expression for each of the following cost concepts: i) Total Fixed Cost ii) Average Fixed Cost iii) Total Variable Cost iv) Average Variable Cost v) Average Total C
- A firm's cost curve is TC(q) = 250 + 10q + 2q^2, q is the quantity produced. What is the firm's marginal cost (MC), average variable cost (AVC), and average total cost (ATC)?
- In the short run, a perfectly competitive firm will shut down if the price is less than: a. average total cost b. average variable cost c. marginal cost d. total cost e. average fixed cost
- A competitive firm's short-run supply curve is its ...................... cost curve above its ...................... cost curve. a. average variable, marginal b. average total, marginal c. marginal, average total d. marginal, average variable
- A firm shuts down if price is: A) above minimum average variable cost. B) below minimum average variable cost. C) above minimum average fixed cost. D) less than marginal cost below average total cost.
- A competitive firm has a short-run cost function: a. Sketch a diagram showing the shapes of the marginal cost function, the average total cost function and the average variable cost function. Be sure
- A competitive firm's short-run supply curve is its cost curve above its cost curve. a. average total, marginal b. average variable, marginal c. marginal, average total d. marginal, average variable
- The marginal cost curve intersects the average variable cost curve at the value of the average variable cost curve. a. maximum b. minimum c. zero d. average
- A firm has a fixed production cost of $10,000 and a constant marginal cost of $1000 per unit. A. Calculate the firm's average variable cost, average fixed cost and average total cost curves. B. If the firm wishes to minimize the average total cost of prod
- Marginal cost is the slope of the: a. variable cost. b. total product curve. c. marginal product curve. d. average cost curve.
- The marginal cost curve intersects the average variable cost curve at the {Blank} value of the average variable cost curve. A. maximum B. minimum C. zero D. average 2. Marginal cost is {Blank} average variable cost when {Blank} A. equal to; average total
- A firm shuts down if price: a. is above minimum average variable cost. b. is above minimum average fixed cost. c. is below average total cost. d. is below minimum average variable cost. e. is less than marginal cost.
- A firm's short-run supply curve is equal to the firm's: a. marginal cost curve above minimum average total cost (ATC). b. demand curve. c. marginal revenue curve. d. marginal cost curve below minimum average variable cost (AVC). e. marginal cost curv
- The marginal cost curve passes through the _ points of the _ cost curve and the _ cost curve. a. maximum; total cost; total variable b. minimum; average total; average variable c. minimum; average var
- Given marginal cost is 3 + (3/2)q and the average variable cost is (30/q) + (3q/4), show that the marginal cost is always above the average variable cost.
- For the total variable cost (TVC), draw a positive total fixed cost (TFC) and total cost (TC) curves. Then derive the associated marginal cost (MC), average total cost (ATC), average variable (AVC) an
- A firm's short-run supply curve is part of which of the following curves: a. Marginal revenue, b. Average variable cost, c. Average total cost, d. Marginal cost.
- When a firm is experiencing economies of scale, long-run: a. average total cost is minimized, b. average total cost is greater than long-run marginal cost, c. average total cost is less than long-run marginal cost, d. marginal cost is minimized.
- Marginal cost is the slope of the: a. variable cost curve. b. total product curve. c. marginal product curve. d. average cost curve.
- When marginal cost is below average variable cost, average variable cost must be: A. above average total cost. B. rising. C. below average total cost. D. falling.
- If marginal cost is below average variable cost: A. both the average total cost and average variable cost are decreasing. B. average total cost is increasing but the average variable cost is decreasing. C. both the average total cost and average variab
- The long term total cost function is: TC = 100 q^3 - 1,000 q^2 +10,000 q a) What is the general shape of TC function? b) Derive or calculate the average cost function. what is the general shape of AC function? c) Derive marginal cost function? d) Do AC an
- A perfectly competitive firm has the following short-run total cost. Calculate the firm's marginal cost and, for all output levels except zero, the firm's average variable cost and average total cost.
- If marginal cost is less than average total cost: a. average total cost is at its minimum b. average total cost is falling c. average total cost = 0 d. average total cost is rising
- A firm short-run supply curve is equal to the firm's a) marginal revenue curve. b) demand curve. c) marginal cost curve above the minimum average total cost (ATC). d) marginal cost curve below the minimum average variable cost (AVC). e) marginal cost curv
- A firm has a total cost function TC = 10y^2 + 6y + 60 for producing pizza. The marginal cost is MC = 20y + 6. a) Write down the expressions for the firm's average cost and average variable cost. b) Ca
- Where long run average cost equals short run average cost, a) short run average cost is minimized. b) long run average variable cost equals short run average variable cost. c) long run average cost equals long run marginal cost. d) long run average cost i
- Suppose that a firm's total cost equation is TC=10000+100Q+0.25Q^2 where TC is total cost and Q is the level of output. a. What output level will minimize the firm's average total cost? b. Calculate the average total cost and marginal cost at the average
- Consider a general cost function C(q), with Average Cost = C(q)/q. Prove using calculus that the quantity which minimizes the Average Cost function is also at the point where the Marginal Cost equals the Average Cost. Find when AC is a minimum.
- A profit-maximizing firm in the short run has total fixed costs of $100. Its variable costs are as below. (A) Calculate average total cost when output is five units. (B) What is the marginal cost of the 7th unit?
- It would not pay a firm to produce anything in the short run if the price were: a. above average total costs. b. equal to marginal cost and above the average variable cost. c. equal to total revenue divided by output. d. below average variable cost. e. be
- A firm's output is 80 units, its marginal cost is $42, its average variable cost is also $42, and its average fixed cost is $10. The slope of its average fixed cost curve is A. positive but the precise slope cannot be calculated. B. positive and the slope
- A firm's supply curve corresponds to: a. the average total cost curve. b. the marginal cost curve above the minimum variable cost curve. c. the average variable cost curve. d. the marginal cost curve.
- A firm will go out of business if the price is below: A. marginal cost B. marginal revenue C. average total cost D. average fixed cost
- In the short-run, under what conditions should the firm shut down? a) average total cost at the minimum point. b) price greater than average variable costs. c) price less than average variable costs. d) marginal revenue greater than marginal costs. e) ma
- In the short-run, under what conditions should the firm shut down (a) average total cost at the minimum point (b) price greater than average variable costs (c) price less than average variable costs (d) marginal revenue greater than marginal costs (e) mar
- Your firm has a cost function C=6+4Q+Q^2. (The correYour firm has a cost function C=6+4Q+Q^2. (The corresponding average cost function is AC=(6/Q)+4+2Q and the corresponding marginal cost function is
- Define the following variables: average fixed cost, average variable cost, average total cost, and marginal cost.
- Each potential short-run average total cost curve is tangent to the long-run average cost curve at a. the level of output that minimizes short-run average total cost. b. the minimum point of the average total cost curve. c. the minimum point of the long-r
- A firm short-run supply curve is equal to the firm's (a) marginal revenue curve (b) demand curve (c) marginal cost curve above minimum average total cost (ATC) (d) marginal cost curve below minimum average variable cost (AVC) (e) marginal cost curve above
- Assume both the marginal cost and the average variable cost curves are U-shaped. At the minimum point on the AVC curve, marginal cost must be a. greater than the average variable cost. b. less than the average variable cost. c. equal to the average variab
- Each potential short-run average total cost curve is tangent to the long-run average cost curve at: a. the level of output that minimizes short-run average total cost. b. the minimum point of the average total cost curve. c. the minimum point of the long-
- 1. A firm has the following long-run total cost function: LTC = 3500Q - 450Q2 + 15Q3. Write the equation for the long-run average cost. 2. Determine the minimum value of LAC. 3. c. If the firm is a
- A firm's short-run cost function is C(q)= 240q-6q^2 +0.6q^3 + 400. Determine fixed cost, F; average variable cost, AVC; average cost, AC, marginal cost, MC; and average fixed-cost, AFC. The fixed co
- Determine the marginal cost and average cost functions for each of the following total cost functions. Graph the marginal cost and average cost curves in each case. Be sure to show all work. Your 3 gr
Explore our homework questions and answers library
Browse
by subject