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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...
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...
Please solve and show full work for a rating. Thank you. Plastic bags are great 2) The production of plastic bags is gi...
Please solve and show full work for a rating. Thank you.
Plastic bags are great 2) The production of plastic bags is given by the production function q K is capital and L is labor. f(LK) s, where Short Run Production a. ) Find the expressions for the Marginal Product of Labor (MP) and Average Product of Labor (APL) in the Short Run, when K is fixed at 400. i) Derive L() in the Short Run, again with K fixed...
In the short-run, we assume that capital is a fixed input and labor is a variable...
In the short-run, we assume that capital is a fixed input and labor is a variable input, so the firm can increase output only by increasing the amount of labor it uses. In the short-run, the firm's production function is q =f(L,K), qs8LK + 3L2-1.3 where q is output, L is workers, and K is the fixed number of units of capital. What is the marginal product of labor as a function of L and K? MPL=/ -(Properly format your...
Question 7 Consider the following production function: Q=AL' K• Assume A > 0. Further assume 0...
Question 7 Consider the following production function: Q=AL' K• Assume A > 0. Further assume 0 <a <1, and 0 <b<1. 1. What is the Marginal Product of Labor (MPL)? Is it diminishing as L increases? What is the Marginal Product of Capital (MPK)? Is it diminishing as K increases? 2. What is the Average Product of Labor (APL)? What is the Average Product of Capital (AP)? 3. What is the TRSL,K? Is the absolute value of TRSL K diminishing...
Suppose the firm's production function is Q = 2KL where Q is units of output, K...
Suppose the firm's production function is Q = 2KL where Q is units of output, K is units of capital (which are fixed at 2), and L is units of labor. a. What is the firm’s short-run production function? b. Over the labor input usage range of 0 to 5, that is L ranging from 0 to 5, graph the firm’s Total Product curve. c. Derive and graph the firm’s Average Product curve and the Marginal Product curve. Graph/plot them...
A firm produces toasters using capital (K) and labor (L). The price of capital is r...
A firm produces toasters using capital (K) and labor (L). The price of capital is r > 0 and the price of labor is w > 0. The quantity Q of toasters produced is given by the function: Q = f(L, K) = L^(1/2) K^(1/3) (a) What type of returns to scale does the firm have? (b) Assume that the firm minimizes costs and that all factors are variable . i. Explain the conditions that hold when the plant produces...
Please answer the two sub-parts Question 4 (20 points) A firm has the following short-run production...
Please answer the two sub-parts
Question 4 (20 points) A firm has the following short-run production function as follows: Q = 15L +18L2-0.5L, where Q = total products per period and L = number of workers employed per period. 4.1) (3 points) Derive the marginal product of labor (MPL). At what number of workers (L) does the law of diminishing returns begin? MPL = f(L) = Law of diminishing return begins when L = workers. . 4.2) (3 points) Derive...
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...
The production function for widgets takes the following form: q = 4L + 6K a. What...
The production function for widgets takes the following form: q = 4L + 6K a. What is the least cost combination of L and K that the firm should employ to produce 48 widgets when w = 2 and r = 4. b. Suppose the price of labor increases to w = 4 but the rental rate of capital is unchanged. If the firm still wants to produce 48 widgets at the lowest cost possible, should it alter its input...
1. Imagine a firm has the following short-run production function: q=f(L,K) = K L – L?...
1. Imagine a firm has the following short-run production function: q=f(L,K) = K L – L? Assume K = 25. a. Fill in the following table. (First, find the total output from the production function, then find the marginal product by dividing the change in total output by change in labor.) Capital MPL Labor 7 Total Output 126 APL 18 25 12 25 25 25 25 25 10 11 12 13 14 15 25 25 25 b. How many units...
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...
Please solve and show full work for a rating. Thank you.
Plastic bags are great 2) The production of plastic bags is given by the production function q K is capital and L is labor. f(LK) s, where Short Run Production a. ) Find the expressions for the Marginal Product of Labor (MP) and Average Product of Labor (APL) in the Short Run, when K is fixed at 400. i) Derive L() in the Short Run, again with K fixed...
In the short-run, we assume that capital is a fixed input and labor is a variable input, so the firm can increase output only by increasing the amount of labor it uses. In the short-run, the firm's production function is q =f(L,K), qs8LK + 3L2-1.3 where q is output, L is workers, and K is the fixed number of units of capital. What is the marginal product of labor as a function of L and K? MPL=/ -(Properly format your...
Question 7 Consider the following production function: Q=AL' K• Assume A > 0. Further assume 0 <a <1, and 0 <b<1. 1. What is the Marginal Product of Labor (MPL)? Is it diminishing as L increases? What is the Marginal Product of Capital (MPK)? Is it diminishing as K increases? 2. What is the Average Product of Labor (APL)? What is the Average Product of Capital (AP)? 3. What is the TRSL,K? Is the absolute value of TRSL K diminishing...
Please answer the two sub-parts
Question 4 (20 points) A firm has the following short-run production function as follows: Q = 15L +18L2-0.5L, where Q = total products per period and L = number of workers employed per period. 4.1) (3 points) Derive the marginal product of labor (MPL). At what number of workers (L) does the law of diminishing returns begin? MPL = f(L) = Law of diminishing return begins when L = workers. . 4.2) (3 points) Derive...
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...
1. Imagine a firm has the following short-run production function: q=f(L,K) = K L – L? Assume K = 25. a. Fill in the following table. (First, find the total output from the production function, then find the marginal product by dividing the change in total output by change in labor.) Capital MPL Labor 7 Total Output 126 APL 18 25 12 25 25 25 25 25 10 11 12 13 14 15 25 25 25 b. How many units...
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