Question three An enterprising entrepreneur produces widgets and has a production function given by q=sq root...
Question three An enterprising entrepreneur produces widgets and has a production function given by q=sq root lk In particular, factory has k =25, where. Rental rates for k and l are given by w =v = $1. a. If the entrepreneur wishes to minimize short-run total costs of widget production, how much output be produced? b. Given that output is optimally allocated, calculate the short-run total, average, and marginal cost curves. What is the marginal cost of the 100th widget? The 125th widget? The 200th widget? c. Calculate the long-run total, average, and marginal cost curves for widget production. d. what returns to scale does it exhibit?
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Question three An enterprising entrepreneur produces widgets and
has a production function given by q=sq root...
5. (20 points) An entrepreneur purchases two factories to produce frisbees. Each factory produces...
5. (20 points) An entrepreneur purchases two factories to produce frisbees. Each factory produces identical products, and each has a production function given by: he factories differ, however, in the amount of capital equipment each has. Factory 1 has K1-25 and factory 2 has K2 -100. The wage rate and the rental rate for capital are givern If the entrepreneur wishes to minimize short-run total costs of frisbee production, how should output be allocated between the two factories? Please explain...
5. A firm produces widgets with production function: q-2vKL. In the short run, the firm's amount...
5. A firm produces widgets with production function: q-2vKL. In the short run, the firm's amount of capital is fixed at K = 100. The rental rate is v = 1 and the wage for L is w= 4. (a) Find the firm's short-run total cost curve (SRTC), short-run average cost curve (SRAC), and the short-run marginal cost (SMC) function. (b) Graph the firm's SAC and SMC using the following levels of production: q 25 and q= 100. (c) Find...
2. Suppose the production function for widgets is given by where q represents the annual quantity...
2. Suppose the production function for widgets is given by where q represents the annual quantity of widgets produced, K represents the annual capital input, and L represents the annual labor input. a. Suppose K 10, write down the expressions for the total product and the average product of labor. At what level of labor input does average productivity reach a maximum? How many widgets are produced at that point? b. Again, assuming that K-10, graph the average product of...
Suppose the production function is given as Q = VLK. Suppose also that the price of...
Suppose the production function is given as Q = VLK. Suppose also that the price of labor w = 10 and the price of capital r = 40 1) Derive the equation of the isoquant corresponding to this production function? 2) What type of return to scale does this production exhibit? 3) Does this production function exhibit a diminishing MRTS? Why? 4) Based on this production function, is the law of diminishing marginal returns satisfied? 5) Derive the demand curves...
5) A firm producing hockey sticks has a production function given by F(L,K) = 2 LK...
5) A firm producing hockey sticks has a production function given by F(L,K) = 2 LK . In the short-run, the firm's amount of capital equipment is fixed at K = 100. The rental rate of capital is r=$1, and the wage rate of labor is w=$4. a. Derive the firm's short-run total cost curve. What is the short-run average total cost? What is the short-run average variable cost? b. Find the short-run marginal cost function. What are the total...
A company A can produce widgets according to Q=5K3/4L1/4 where Q is the output of widgets,...
A company A can produce widgets according to Q=5K3/4L1/4 where Q is the output of widgets, and K, L are quantities of capital and labor used. Are there constant, increasing or decreasing returns to scale in widget production? Explain. Are there, constant, increasing or decreasing marginal products of factors? Explain In the short run, the amount of capital used by company A. is fixed. Derive the short-run cost function. (Note that the short-run cost function will show C as a...
Suppose the production function is given as ? = √??. Suppose also that the price of...
Suppose the production function is given as ? = √??. Suppose also that the price of labor ? = 10 and the price of capital ? = 40 1) Derive the equation of the isoquant corresponding to this production function? 2) What type of return to scale does this production exhibit? 3) Does this production function exhibit a diminishing MRTS? Why? 4) Based on this production function, is the law of diminishing marginal returns satisfied? 5) Derive the demand curves...
Suppose that a firm has a production function given by: ? = ?^?.???^?.? . The wage...
Suppose that a firm has a production function given by: ? = ?^?.???^?.? . The wage rate is $18 and the rental rate is $9. 12. Suppose that the firm has 4 units of capital in the short run. Find the short run total cost function. ________________________________ 13. Find the marginal product of labor (MPL) function. ________________________________ 14. Solve the optimization condition for K and write that equation. ________________________________ 15. Suppose the firm wants to minimize the cost of producing...
A firm produces a product with labor and capital as inputs. The production function is described...
A firm produces a product with labor and capital as inputs. The production function is described by Q = LK. The marginal products associated with this production function are MPL= K and MPK= L. Let w = 1 and r = 1 be the prices of labor and capital, respectively. a) Find the equation for the firm’s long-run total cost curve as a function of quantity Q. b) Solve the firm’s short-run cost-minimization problem when capital is fixed at a...
Consider a production function of three inputs, labor, capital, and materials, given by Q= LKM
Consider a production function of three inputs, labor, capital, and materials, given by Q= LKM. The marginal products associated with this production function are as follows: MPL = KM, MPk = LM, and MPM = LK. Let w = 5, r = 1, and m = 2, where m is the price per unit of materials. (a) Suppose that the firm is required to produce Q units of output. Show how the cost-minimizing quantity of labor depends on the quantity Q....
5. (20 points) An entrepreneur purchases two factories to produce frisbees. Each factory produces identical products, and each has a production function given by: he factories differ, however, in the amount of capital equipment each has. Factory 1 has K1-25 and factory 2 has K2 -100. The wage rate and the rental rate for capital are givern If the entrepreneur wishes to minimize short-run total costs of frisbee production, how should output be allocated between the two factories? Please explain...
5. A firm produces widgets with production function: q-2vKL. In the short run, the firm's amount of capital is fixed at K = 100. The rental rate is v = 1 and the wage for L is w= 4. (a) Find the firm's short-run total cost curve (SRTC), short-run average cost curve (SRAC), and the short-run marginal cost (SMC) function. (b) Graph the firm's SAC and SMC using the following levels of production: q 25 and q= 100. (c) Find...
2. Suppose the production function for widgets is given by where q represents the annual quantity of widgets produced, K represents the annual capital input, and L represents the annual labor input. a. Suppose K 10, write down the expressions for the total product and the average product of labor. At what level of labor input does average productivity reach a maximum? How many widgets are produced at that point? b. Again, assuming that K-10, graph the average product of...
Suppose the production function is given as Q = VLK. Suppose also that the price of labor w = 10 and the price of capital r = 40 1) Derive the equation of the isoquant corresponding to this production function? 2) What type of return to scale does this production exhibit? 3) Does this production function exhibit a diminishing MRTS? Why? 4) Based on this production function, is the law of diminishing marginal returns satisfied? 5) Derive the demand curves...
5) A firm producing hockey sticks has a production function given by F(L,K) = 2 LK . In the short-run, the firm's amount of capital equipment is fixed at K = 100. The rental rate of capital is r=$1, and the wage rate of labor is w=$4. a. Derive the firm's short-run total cost curve. What is the short-run average total cost? What is the short-run average variable cost? b. Find the short-run marginal cost function. What are the total...
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