Suppose the cost function of a firm is given by c(y) = y 3 + 16...
Suppose the cost function of a firm is given by c(y) = y 3 + 16 for y > 0 and c(0) = 0.
(a) Derive the Marginal Cost and Average Total Cost functions.
(b) Find is the lowest price at which the firm will produce a positive quantity.
(c) Derive the firm’s supply function y(p).
(d) Draw the firm’s Average Total Cost and Marginal Cost curves. On your graph, determine the firm’s supply curve. Your graph should have output on the horizontal axis and price/costs on the vertical axis.
(e) Suppose the market price is p = 27. How many units of output will the firm produce? How much profit will the firm make from producing this quantity?
Homework Answers
**Only [Harder] Question** Problem 2. Consider a firm that has a cost function of c(y) =...
**Only [Harder] Question** Problem 2. Consider a firm that has a cost function of c(y) = 5y 2 + 50, 000. In other words, this is a firm with a fixed cost of $50,000 (which might be something like the cost of rent on the firm’s building, which they have to pay whether they produce any output or not) and a variable cost of $5Y 2 , (which we’ll think of as the cost of the labor and machinery necessary...
Suppose a firm’s production function is given by Q = L1/2*K1/2. The Marginal Product of Labor...
Suppose a firm’s production function is given by Q = L1/2*K1/2. The Marginal Product of Labor and the Marginal Product of Capital are given by: MPL = ½ L-1/2K1/2and MPK = ½ L1/2K-1/2 a) Suppose the price of labor is w = 18, and the price of capital is r = 2. Derive the firm’s total cost function. b) What is the firm’s marginal cost? c) For this problem, you will sketch the graph of the firm’s isoquant for Q...
2. A firm has the production function y = 4LK. The marginal products are given by...
2. A firm has the production function y = 4LK. The marginal products are given by MPL = 4K and MPK = 4L. (a) Provide an expression for the long run total cost function. (b) Now suppose that wi = WK = 25. Write out the expression for the long run total cost curve, and plot it on a graph. (C) With wi = wK = 25, derive the long run average cost curve, and plot it on a graph....
2. A firm has the production function y = 4LK. The marginal products are given by...
2. A firm has the production function y = 4LK. The marginal products are given by MP = 4K and MPx = 4L. (a) Provide an expression for the long run total cost function. (b) Now suppose that wu = WK = 25. Write out the expression for the long run total cost curve, and plot it on a graph. (c) With WL = WK = 25, derive the long run average cost curve, and plot it on a graph....
competitive firm is the . 4. the vert Mive is atroduction. The short-run supply curve of...
competitive firm is the . 4. the vert Mive is atroduction. The short-run supply curve of ortion of its short-tun marginal cost curve that is competitive firm in the above its average variable cost curve, The o ward sloping an u petitive firm is the portion of its short-run marginal cost curve that supply curve of a Leuward-sloping and lies above its long-run average cost curve. Example: A firm has the long-run cost function cy) = 2y + 200 for...
Problem 4: A firm has total cost function: c(y) = 50y2 + 40y + 30 A)...
Problem 4: A firm has total cost function: c(y) = 50y2 + 40y + 30 A) What is the total fixed cost? B) What is the average fixed cost? C) What is the total variable cost? D) What is the average variable cost? E) What is the marginal cost? F) What is the average total cost? G) In a competitive market, what is the lowest price at which the firm will supply a positive quantity in long-run equilibrium? H) What...
In a perfectly competitive market, a firm has the following short-run total cost function: C(q)=16+4q+q2 The...
In a perfectly competitive market, a firm has the following short-run total cost function: C(q)=16+4q+q2 The market demand is Q(p)=220-p a. Show that marginal cost curve passes through the minimum point of average cost curve. Draw a figure to show it. b. Find the firm’s individual short-run supply function. Draw it on the above figure. For the following questions, suppose that there are currently 10 identical firms in this market. c. What is the market supply curve? What are the...
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)...
Keep c(y) = 200−10y+ 0.5y^2 as the cost function of the firm. a) What is the...
Keep c(y) = 200−10y+ 0.5y^2 as the cost function of the firm. a) What is the average cost of producing y units of output? b) What, therefore, will be the optimum output in the long run (y*LR)? c) What is the average cost at the optimum output? d) What is the long run market price, p*LR? e) What is the firm’s total revenue in the long run? f) What is the firm’s total cost in the long run?
. Suppose the production function of a firm is given by q = L1/4K2/4. The prices of labor and cap...
. Suppose the production function of a firm is given by q = L1/4K2/4. The prices of labor and capital are given by and w = $9 and r = $18, respectively. Derive the long run cost function. Show your work. What happens to the firm’s average cost as it increases production and why? Derive the firm’s long run supply function. What will be the quantity of output that maximizes the firm’s profit when the price of output is $1?...
2. A firm has the production function y = 4LK. The marginal products are given by MPL = 4K and MPK = 4L. (a) Provide an expression for the long run total cost function. (b) Now suppose that wi = WK = 25. Write out the expression for the long run total cost curve, and plot it on a graph. (C) With wi = wK = 25, derive the long run average cost curve, and plot it on a graph....
2. A firm has the production function y = 4LK. The marginal products are given by MP = 4K and MPx = 4L. (a) Provide an expression for the long run total cost function. (b) Now suppose that wu = WK = 25. Write out the expression for the long run total cost curve, and plot it on a graph. (c) With WL = WK = 25, derive the long run average cost curve, and plot it on a graph....
competitive firm is the . 4. the vert Mive is atroduction. The short-run supply curve of ortion of its short-tun marginal cost curve that is competitive firm in the above its average variable cost curve, The o ward sloping an u petitive firm is the portion of its short-run marginal cost curve that supply curve of a Leuward-sloping and lies above its long-run average cost curve. Example: A firm has the long-run cost function cy) = 2y + 200 for...
Problem 4: A firm has total cost function: c(y) = 50y2 + 40y + 30 A) What is the total fixed cost? B) What is the average fixed cost? C) What is the total variable cost? D) What is the average variable cost? E) What is the marginal cost? F) What is the average total cost? G) In a competitive market, what is the lowest price at which the firm will supply a positive quantity in long-run equilibrium? H) What...
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)...
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