1) (Cost functions) a) Consider total cost function: C(q) = 48 + 3q2 + 2q, derive...
1) (Cost functions) a) Consider total cost function: C(q) = 48 + 3q2 + 2q, derive the average cost function, the marginal cost function, and the minimum efficient scale, and carefully graph the average cost and marginal cost curves.
b) Consider total cost function: C(q) = 20 + 5q, derive the average cost function, the marginal cost function. How does the marginal cost compare to the average cost? Graph these two functions. Does the average cost obtain a minimum at a finite quantity, q?
Homework Answers
1. MC is increasing and
rising. It touches ATC at its minimum at q = 4.
2. MC is constant at 5. ATC does not reach its minimum at finite q. It does not intersect with MC as well. First order derivate is negative.
Add Answer to:
1) (Cost functions) a) Consider total cost function: C(q) = 48 +
3q2 + 2q, derive...
Firm B’s short-run cost function is: C = 12 - 2q + 3q2 + F Find...
Firm B’s short-run cost function is:
C = 12 - 2q + 3q2 + F Find the following: A. AFC B. AVC C. ATC D. MC E. At what output quantity is average total cost (ATC) minimized? Assume F = 63. F. At what output quantity does the MC curve cross the ATC and AVC curves? Assume F = 63 G. Graph the AFC, AVC, ATC and MC curves. Assume F = 63.
1 Economies of Scale Consider the total cost function (TC): TC(q) = 100+ 40 + 492...
1 Economies of Scale Consider the total cost function (TC): TC(q) = 100+ 40 + 492 where q is output. 1.1 (10 points) Obtain the index of the extent of scale economies S = MCQ, where AC is average cost and MC is marginal cost. What is the value of this index when q = 2? Provide an intuitive interpretation for this number. 1.2 (10 points) Is there any range of production characterized by scale economies? At what production level...
Consider the following cost function: TC(Q)=(2Q^3)-(4Q^2)+6Q+3. What is the total variable cost function? What are the...
Consider the following cost function: TC(Q)=(2Q^3)-(4Q^2)+6Q+3. What is the total variable cost function? What are the total fixed costs? What is the average variable cost function? What is the average fixed cost function? What is the average total cost function? What is the marginal cost function? For what level of output is average variable cost a minimum? What is the relationship between average and marginal cost?
Consider the cost function C(Q) = 60Q – 12Q2 + Q3. a. Sketch the total cost,...
Consider the cost function C(Q) = 60Q – 12Q2 + Q3. a. Sketch the total cost, the total variable cost, and the fixed cost for 0-12 units of output. b. Find expressions for the ATC, AVC, AFC, and MC curves, and sketch the curves on a single graph, making sure the curves are correctly related to each other. At what output level does ATC reaches its minimum? c. What can you say about the shape of the marginal product of...
Suppose that every firm in an industry has identical cost curves given by C(q) = 3q2...
Suppose that every firm in an industry has identical cost curves given by C(q) = 3q2 + 2700 MC(q) = 6q What is the value of the efficient scale, qE ? Remember, the efficient scale occurs where MC(q) = ATC(q)
You are given the following cost functions: TC=100+60Q-3Q2 +0.1Q3 TC = 100 + 60Q + 3Q2...
You are given the following cost functions: TC=100+60Q-3Q2 +0.1Q3 TC = 100 + 60Q + 3Q2 TC = 100 + 60Q 1. Compute the average variable cost, average cost, and marginal cost for each function. Plot them on a graph. 2. In each case, indicate the point at which diminishing returns occur. Also indicate the point of maximum cost efficiency (i.e., the point of minimum average cost). 3. For each function, discuss the relationship between marginal cost and average variable...
Derive the cost function associated with the production function in questions 2 is C(q) = 4...
Derive the cost function associated with the production function
in questions 2 is C(q) = 4 + 2q and in questions 3 is
C=wL+rK=1*8+2*4=16. The cost function is of the general form C(Q) =
xQ. What is the value of x?
2. The inverse market demand function is given by P()-20 q. Would consumers prefer to face a monopolist in this market with a cost function given by C(g)4+ 2q, or a perfectly competitive firm with a cost function given...
Question 01. Consider the cost function C = 5,000 + 50. Q, where C denotes the total cost, and Q denotes the quanti...
Question 01. Consider the cost function C = 5,000 + 50. Q, where C denotes the total cost, and Q denotes the quantity produced. A. Complete the following table: (Hint: MC = AC/AQ) Quantity | Cost Fixed Cost Total Cost Average | Marginal Total Cost Cost 10 20 50 100 1000 B. Using the above table, plot average total cost and marginal cost. Cost Quantity C. Explain how you know that this firm has increasing returns to scale.
2. Propose and sketch a demand function for a product that currently sells for $500 with...
2. Propose and sketch a demand function for a product that currently sells for $500 with quantity sold at 25. Write both regular and inverse demand functions. 3. Representative firm in an industry has total cost function TC(a) -1849+and marginal cost function MC-2q a) What is the fixed cost function for the firm? What is the variable cost function? b) Derive average total, average fixed and average variable cost functions. c) Find the minimum efficient scale (-output that corresponds to...
Consider a market that faces the following market supply and demand functions Q^S = −2 +...
Consider a market that faces the following market supply and demand functions Q^S = −2 + 2p Q^D = 16 − p where identical firms face the total cost function of T C = 8 + 3q + 1/2q^2 a) What is the market price? b) Derive the average variable cost, average total cost, and marginal cost functions. c) In the short run, how much does each firm produce? d) In the short run, how much economic profit or loss...
Firm B’s short-run cost function is:
C = 12 - 2q + 3q2 + F Find the following: A. AFC B. AVC C. ATC D. MC E. At what output quantity is average total cost (ATC) minimized? Assume F = 63. F. At what output quantity does the MC curve cross the ATC and AVC curves? Assume F = 63 G. Graph the AFC, AVC, ATC and MC curves. Assume F = 63.
1 Economies of Scale Consider the total cost function (TC): TC(q) = 100+ 40 + 492 where q is output. 1.1 (10 points) Obtain the index of the extent of scale economies S = MCQ, where AC is average cost and MC is marginal cost. What is the value of this index when q = 2? Provide an intuitive interpretation for this number. 1.2 (10 points) Is there any range of production characterized by scale economies? At what production level...
Derive the cost function associated with the production function
in questions 2 is C(q) = 4 + 2q and in questions 3 is
C=wL+rK=1*8+2*4=16. The cost function is of the general form C(Q) =
xQ. What is the value of x?
2. The inverse market demand function is given by P()-20 q. Would consumers prefer to face a monopolist in this market with a cost function given by C(g)4+ 2q, or a perfectly competitive firm with a cost function given...
Question 01. Consider the cost function C = 5,000 + 50. Q, where C denotes the total cost, and Q denotes the quantity produced. A. Complete the following table: (Hint: MC = AC/AQ) Quantity | Cost Fixed Cost Total Cost Average | Marginal Total Cost Cost 10 20 50 100 1000 B. Using the above table, plot average total cost and marginal cost. Cost Quantity C. Explain how you know that this firm has increasing returns to scale.
2. Propose and sketch a demand function for a product that currently sells for $500 with quantity sold at 25. Write both regular and inverse demand functions. 3. Representative firm in an industry has total cost function TC(a) -1849+and marginal cost function MC-2q a) What is the fixed cost function for the firm? What is the variable cost function? b) Derive average total, average fixed and average variable cost functions. c) Find the minimum efficient scale (-output that corresponds to...
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