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age 2 pages 5. .Given the production function Q1OLK12,...
For a production function F(KL) = K-L2 and factor prices wK-2 and WL-3 Assume that K equals 27 un...
For a production function F(KL) = K-L2 and factor prices wK-2 and WL-3 Assume that K equals 27 units in the short run a. Derive the long run optimum bundle of inputs if the quantity of output is q-25-32. b. Derive the long run cost function of a firm with this technology. c. Derive the short run cost function of a firm with this technology.
For a production function F(KL) = K-L2 and factor prices wK-2 and WL-3 Assume that...
Part I: Long-Run Production and Cost Functions (12 points) Suppose the production function of a firm...
Part I: Long-Run Production and Cost Functions (12 points) Suppose the production function of a firm is given by q Lo.5 K0,5. The prices of labor and capital are given by w 2 and r 5, respectively. a) Write the firm's cost minimization problem formally. b) What returns to scale does the production function exhibit? Why? c) What is the optimal capital to labor ratio? Show your work. d) What is the slope of the expansion path and what is...
A firm has the production function ?= ?1/3?2/3.Does this production function have upper and lower ridge...
A firm has the production function ?= ?1/3?2/3.Does this production function have upper and lower ridge lines? If no, explain why. If yes, derive the equations of upper and lower ridge lines. Now suppose that a different production function is given as: ?= 12−(27−?)1/3(8−?)2/3 where L and K is nonnegative. Does this production function have upper and lower ridge lines? If no, explain why. If yes, derive the equations of upper and lower ridge lines. Suppose that the wage rate...
a. A firm has the production function X =L^1/3K^2/3. Does this production function have upper and...
a. A firm has the production function X =L^1/3K^2/3. Does this production function have upper and lower ridge lines? If no, explain why. If yes, derive the equations of upper and lower ridge lines. b. Now suppose that a different production function is given as: X=12−(27−L)^1/3(8−K)^2/3 where L and K is nonnegative. Does this production function have upper and lower ridge lines? If no, explain why. If yes, derive the equations of upper and lower ridge lines. c. Suppose that...
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. Let the firm's production function be given by y 1+2. Note that the inputs r1...
5. Let the firm's production function be given by y 1+2. Note that the inputs r1 and 2 are perfect substitutes in this production process. Suppose wi 2 and w2 1 (a) Derive the conditional factor/input demands and use them to find the long-run cost function for this firm. (b) For these factor prices, derive the firm's long-run supply curve. (c) For these factor prices graph the firm's long-run supply curve. (d) Suppose the price of the second input, w2,...
Suppose labor (L) and capital (K) are fixed proportion inputs, and that each unit of output...
Suppose labor (L) and capital (K) are fixed proportion inputs, and that each unit of output must be produced with exactly 5 units of labor and 2 unit of capital. The price of a unit of labor is w, and the price of a unit of capital is r. a. Write down the production function. b. Derive the equation for the expansion path. c. Derive the equation for the long-run total cost function. d. Graphically depict the labor demand curve....
5. Let the firm's production function be given by y = + x2. Note that the...
5. Let the firm's production function be given by y = + x2. Note that the inputs 2 and 2 are perfect substitutes in this production process. Suppose w = 2 and we = 1. (a) Derive the conditional factor/input demands and use them to find the long-run cost function for this firm. (b) For these factor prices, derive the firm's long-run supply curve. (c) For these factor prices graph the firm's long-run supply curve. (d) Suppose the price of...
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....
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...
For a production function F(KL) = K-L2 and factor prices wK-2 and WL-3 Assume that K equals 27 units in the short run a. Derive the long run optimum bundle of inputs if the quantity of output is q-25-32. b. Derive the long run cost function of a firm with this technology. c. Derive the short run cost function of a firm with this technology.
For a production function F(KL) = K-L2 and factor prices wK-2 and WL-3 Assume that...
Part I: Long-Run Production and Cost Functions (12 points) Suppose the production function of a firm is given by q Lo.5 K0,5. The prices of labor and capital are given by w 2 and r 5, respectively. a) Write the firm's cost minimization problem formally. b) What returns to scale does the production function exhibit? Why? c) What is the optimal capital to labor ratio? Show your work. d) What is the slope of the expansion path and what is...
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. Let the firm's production function be given by y 1+2. Note that the inputs r1 and 2 are perfect substitutes in this production process. Suppose wi 2 and w2 1 (a) Derive the conditional factor/input demands and use them to find the long-run cost function for this firm. (b) For these factor prices, derive the firm's long-run supply curve. (c) For these factor prices graph the firm's long-run supply curve. (d) Suppose the price of the second input, w2,...
5. Let the firm's production function be given by y = + x2. Note that the inputs 2 and 2 are perfect substitutes in this production process. Suppose w = 2 and we = 1. (a) Derive the conditional factor/input demands and use them to find the long-run cost function for this firm. (b) For these factor prices, derive the firm's long-run supply curve. (c) For these factor prices graph the firm's long-run supply curve. (d) Suppose the price of...
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....
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