3. Suppose that the cost function of q is given by: C (q) = 16 +...
3. Suppose that the cost function of q is given by: C (q) = 16 + 4q + q^2
(a) Find the fixed and variable cost.
(b) Find the average cost and marginal cost. 1
(c) Draw the relationship between MC and AC. Prove that they always intersect at the minimum. (Hint: compute the derivative of AC with respect to q and set it equal to zero. Then use this equation to show that MC=AC)
Homework Answers
need help with 5 and 6 Suppose a perfectly competitive firm's cost function is C(q)-4q*+16. Marginal cost for the firm...
need help with 5 and 6
Suppose a perfectly competitive firm's cost function is C(q)-4q*+16. Marginal cost for the firm is given by MC=8q. 1) Find equations for variable cost, fixed cost, average total cost, average variable cost and average fixed cost for this firm. Illustrate on a graph the firm's average variable cost curve, average total cost curve, and marginal cost curve. 2) Find the outputs that minimize average total cost, average variable cost and average fixed cost. 3)...
Suppose the total benefit derived from a continuous decisions, Q, is B(Q)=20Q-2Q^2 and the total cost...
Suppose the total benefit derived from a continuous decisions, Q, is B(Q)=20Q-2Q^2 and the total cost from deciding Q is C(Q)=4+2Q^2. The marginal benefit (MB) and marginal cost (MC) is the first order derivative of these functions. MB(Q)=20-4Q and MC(Q)=4+4Q. What level of Q minimizes total cost?
A firm’s short run cost function is C(q)=150q-4q^2+0.4q^3+275 . Determine the fixed cost, F; the average...
A firm’s short run cost function is C(q)=150q-4q^2+0.4q^3+275 . Determine the fixed cost, F; the average variable cost, AVC; Average Fixed Cost, AFC; Average Cost, AC; and the Marginal Cost, MC.
3) Suppose the cost curve for a firm producing sneakers is TC 1010 q - 4q-...
3) Suppose the cost curve for a firm producing sneakers is TC 1010 q - 4q- + 3.1 (10 points) What are the firm's fixed costs, variable costs, average costs, average fixed cost, average variable costs, and marginal costs? 3.2 (10 points) Graph all 7 cost functions (TC, VC, FC, AC, AVC, AFC, MC) for quantities q 0 to q 10. You can use the Excel program to generate these graphs, plot C, VC, and FC in one graph and...
Suppose the total benefit derived from a continuous decisions, Q, is B(Q) = 20Q − 2Q...
Suppose the total benefit derived from a continuous decisions, Q, is B(Q) = 20Q − 2Q and the 2 total cost from deciding Q is C(Q) = 4Q + 2Q . The marginal benefit (MB) and marginal cost (MC) 2 is the first order derivative of these functions. MB(Q) = 20 − 4Q and MC(Q) = 4 + 4Q . (6) (4 points) What level of Q minimizes total cost?
5. Consider the following cost function: c(q; F) = F + 10q + q2 , where2...
5. Consider the following cost function: c(q; F) = F + 10q + q2 , where2 F > 0 represents the fixed cost: F = c(0; F). (a) Compute the marginal cost function, MC(q) = c0(q; F). (b) Show that the marginal cost function MC(q) is increasing. (c) Recall the average cost function, AC(q; F) = c(q;F) . Find qˉ(F),q the value of q (given F) at which AC(q; F) = MC(q).
Suppose a firm's cost function is C (q) = 2q2 + 8. The output q that...
Suppose a firm's cost function is C (q) = 2q2 + 8. The output q that minimizes average total cost is: (Hint: At the minimum of the ATC, ATC is equal to MC) a)4 b) 2 c) 0 d) 8
Suppose that the cost function of a firm is C(Q) = 490 + 10Q^2 . (a)...
Suppose that the cost function of a firm is C(Q) = 490 + 10Q^2 . (a) Provide the mathematical expressions for AFC, AVC, AC and MC. (b) Graph all the costs above as a function of Q. (c) What is true about the relation between the marginal cost and the average costs when the latter are at their minimum? And when the average cost are increasing (decreasing)? Explain.
4. The average cost of producing q units of a good is the total cost of production C(q), divided by the total produ...
4. The average cost of producing q units of a good is the total cost of production C(q), divided by the total production q: AC(q) calculus by MC(g) = C"(a) = . Ca for q> 0 The marginal cost MC is given in terms of G dThe fired cost of production is C(0). Why is C(0) called the fized cost? What does it represent? a. b. If C(g) is continuous for q 2 0 and C(0)> 0, what is lim...
2. Find an expression for the MC function given the following average cost functions (a) AC...
2. Find an expression for the MC function given the following average cost functions (a) AC 20 5+30/Q (b) AC 302-4Q+6+100/Q In each case 1) state the value of fixed cost and variable cost, and 2) calculate the value of marginal cost when Q 50
need help with 5 and 6
Suppose a perfectly competitive firm's cost function is C(q)-4q*+16. Marginal cost for the firm is given by MC=8q. 1) Find equations for variable cost, fixed cost, average total cost, average variable cost and average fixed cost for this firm. Illustrate on a graph the firm's average variable cost curve, average total cost curve, and marginal cost curve. 2) Find the outputs that minimize average total cost, average variable cost and average fixed cost. 3)...
3) Suppose the cost curve for a firm producing sneakers is TC 1010 q - 4q- + 3.1 (10 points) What are the firm's fixed costs, variable costs, average costs, average fixed cost, average variable costs, and marginal costs? 3.2 (10 points) Graph all 7 cost functions (TC, VC, FC, AC, AVC, AFC, MC) for quantities q 0 to q 10. You can use the Excel program to generate these graphs, plot C, VC, and FC in one graph and...
4. The average cost of producing q units of a good is the total cost of production C(q), divided by the total production q: AC(q) calculus by MC(g) = C"(a) = . Ca for q> 0 The marginal cost MC is given in terms of G dThe fired cost of production is C(0). Why is C(0) called the fized cost? What does it represent? a. b. If C(g) is continuous for q 2 0 and C(0)> 0, what is lim...
2. Find an expression for the MC function given the following average cost functions (a) AC 20 5+30/Q (b) AC 302-4Q+6+100/Q In each case 1) state the value of fixed cost and variable cost, and 2) calculate the value of marginal cost when Q 50
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