The graph below shows the production function for a certain firm that uses labor and capital as inputs. The function is drawn for a given level of capital.
In the space underneath the graph with the function, sketch a
graph of this firm’smarginal product of labor and average product
of labor curves. Label them clearly. It may help you to know that
marginal product equals Q0/15 when labor is 15 (or when labor is
raised from 14.9 to 15.1). Note: You just need to sketch these
curves; do show all important points and intersections.
Homework Answers
The marginal product curve of labor denotes the slope of the total product curve and increases upto the point where Total Product curve is increasing with an increasing rate. The curve starts falling when Total product curve is increasing at a decreasing rate and is equal to zero when Total product curve is maximum and enters the negative zone when Total product curve is falling. The Average Product curve of labor is equal to total product curve / Quantity of labor.
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The graph below shows the production function for a certain firm
that uses labor and capital...
4. The graph below shows the production function for a certain firm that uses labor and...
4. The graph below shows the production function for a certain firm that uses labor and capital as inputs. The function is drawn for a given level of capital. In the space underneath the graph with the function, sketch a graph of this firm's marginal product of labor and average product of labor curves. Label them clearly. It may help you to know that marginal product equals Qw/15 when labor is 15 (or when labor is raised from 14.9 to...
7. For the production function q min(K,4L ): (a) Assume that capital K is fixed at...
7. For the production function q min(K,4L ): (a) Assume that capital K is fixed at 100 units. Derive and plot: i, The total product function q(L) ii. The marginal product function MPL(L). iii. The average product function APL(L). (b) Suppose the price of labour w is $1 and the rental rate r is also $1. Derive and plot all cost functions; that is: i. Short run total cost. ii. Variable cost. iii. Fixed cost. iv. Short run average cost....
8.13. A firm produces a product with labor and capital. Its production function is described by...
8.13. A firm produces a product with labor and capital. Its production function is described by Q = L + K. The marginal products associated with this production function are MPL = 1 and MPK = 1. 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 when the prices labor and capital are w = 1 and...
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...
3) Consider the production function ? = 6? 0.3? 0.6 . The marginal products are ???...
3) Consider the production function ? = 6? 0.3? 0.6 . The marginal products are ??? = 1.8? −0.7? 0.6 and ??? = 3.6? 0.3? −0.4 . a. In the short run assume that capital is fixed at ? = 10. Derive formulas for the short-run Total Product (TP), Average Product (APL), and Marginal Product (MPL). Graph these three functions. b. In the long run, capital is not fixed. Graph the isoquant for ? = 6. Identify and label three...
Equation Description: A firm is attempting to minimize total cost subject to sufficiently employing units of labor and u...
Equation Description: A firm is attempting to minimize total
cost subject to sufficiently employing units of labor and units of
capital to produce an output level at least as large as a specified
output quota. Total cost equals the cost to employing units of
labor plus the cost to employing units of capital. A firm's
production function is the product of two terms: the
first term is units of capital raised to the .25 power; and, the
second term is units...
can you pls do these two 7 and 8, thank you 7. Consider a firm whose...
can you pls do these two 7 and 8, thank you
7. Consider a firm whose total cost equals $18 when output is zero. The following table shows average variable cost for this firm at several output levels AVC $20 $22 $25 a. Find the marginal cost of producing the first second, and third unit of output. Show your work clearly b. Assuming that this firm starts experiencing diminishing returns to labor as soon as the second unit of output...
7. For the production function q= min(K, 4L) (a) Assume that capital K is fixed at...
7. For the production function q= min(K, 4L) (a) Assume that capital K is fixed at 100 units. Derive and plot Page 2 of . The total product function q(L) ii. The marginal product function MPL(L) ii. The average product function AP(L) (b) Suppose the price of labour w is $1 and the rental rate r is also $1. Derive and plot all cost functions; that is: i. Short run total cost. ii. Variable cost. iii. Fixed cost. iv. Short...
A firm uses capital and labor to produce output according to the production q = 4VLK...
A firm uses capital and labor to produce output according to the production q = 4VLK (a) Find the marginal product of labor (MPL) and marginal product of capital (MPK). (b) If the wage w=$1/labor-hr. and the rental rate of capital r-$4/machine-hr., what is the least expensive way to produce 16 units of output? (c) What is the minimum cost of producing 16 units? (d) Show that for any level of output, q, the minimum cost of producing q is...
Hello below is the question , Many thanks for your help :) A competitive firm uses...
Hello below is the question , Many thanks for your help :) A competitive firm uses two inputs, capital (?) and labour (?), to produce one output, (?). The price of capital, ??, is $1 per unit and the price of labor, ??, is $1 per unit. The firm operates in competitive markets for outputs and inputs, so takes the prices as given. The production function is ?(?,?)=3?0.25?0.25. The maximum amount of output produced for a given amount of inputs...
4. The graph below shows the production function for a certain firm that uses labor and capital as inputs. The function is drawn for a given level of capital. In the space underneath the graph with the function, sketch a graph of this firm's marginal product of labor and average product of labor curves. Label them clearly. It may help you to know that marginal product equals Qw/15 when labor is 15 (or when labor is raised from 14.9 to...
7. For the production function q min(K,4L ): (a) Assume that capital K is fixed at 100 units. Derive and plot: i, The total product function q(L) ii. The marginal product function MPL(L). iii. The average product function APL(L). (b) Suppose the price of labour w is $1 and the rental rate r is also $1. Derive and plot all cost functions; that is: i. Short run total cost. ii. Variable cost. iii. Fixed cost. iv. Short run average cost....
8.13. A firm produces a product with labor and capital. Its production function is described by Q = L + K. The marginal products associated with this production function are MPL = 1 and MPK = 1. 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 when the prices labor and capital are w = 1 and...
Equation Description: A firm is attempting to minimize total
cost subject to sufficiently employing units of labor and units of
capital to produce an output level at least as large as a specified
output quota. Total cost equals the cost to employing units of
labor plus the cost to employing units of capital. A firm's
production function is the product of two terms: the
first term is units of capital raised to the .25 power; and, the
second term is units...
can you pls do these two 7 and 8, thank you
7. Consider a firm whose total cost equals $18 when output is zero. The following table shows average variable cost for this firm at several output levels AVC $20 $22 $25 a. Find the marginal cost of producing the first second, and third unit of output. Show your work clearly b. Assuming that this firm starts experiencing diminishing returns to labor as soon as the second unit of output...
7. For the production function q= min(K, 4L) (a) Assume that capital K is fixed at 100 units. Derive and plot Page 2 of . The total product function q(L) ii. The marginal product function MPL(L) ii. The average product function AP(L) (b) Suppose the price of labour w is $1 and the rental rate r is also $1. Derive and plot all cost functions; that is: i. Short run total cost. ii. Variable cost. iii. Fixed cost. iv. Short...
A firm uses capital and labor to produce output according to the production q = 4VLK (a) Find the marginal product of labor (MPL) and marginal product of capital (MPK). (b) If the wage w=$1/labor-hr. and the rental rate of capital r-$4/machine-hr., what is the least expensive way to produce 16 units of output? (c) What is the minimum cost of producing 16 units? (d) Show that for any level of output, q, the minimum cost of producing q is...
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