A firm can manufacture a product according to the production
function:
Q = F(K, L) =
K3/4L1/4.
Instruction: Enter your responses rounded to
three decimal places.
a. Calculate the average product of labor, APL, when the level of capital is fixed at 81 units and the firm uses 16 units of labor.
____
What is the average product of labor when the firm uses 256 units
of labor?
____
Instruction: The second response is the
exponent on L in the expression. Enter your responses
rounded to two decimal places.
b. Find an expression for the marginal product of labor, MPL, when the amount of capital is fixed at 81 units.
____
MPL = ____ × L ^ ____
Instruction: Enter your responses rounded to three decimal places.
Then, illustrate that the marginal product of labor depends on
the amount of labor hired by calculating the marginal product of
labor for 16 and 81 units of labor.
MPL when L = 16: _____
MPLwhen L = 81: _____
c. Suppose capital is fixed at 81 units. If the firm can sell its
output at a price of $200 per unit of output and can hire labor at
$50 per unit of labor, how many units of labor should the firm hire
in order to maximize profits?
Instruction: Enter your response as a whole
number.
_____
A firm can manufacture a product according to the production function: Q = F(K, L) =...
Problem 05-01 A firm can manufacture a product according to the production function: Q=F(K.L) = 3/4 1/4 a. Calculate the average product of labor, AP, when the level of capital is fixed at 81 units and the firm uses 16 units of labor. Instruction: Round your responses to 3 decimal places. What is the average product of labor when the firm uses 256 units of labor? b. Find an expression for the marginal product of labor, MP4, when the amount...
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...
Please help explain how to do part b using the non calculus method. thank you. CONCEPTUAL AND COMPUTATIONAL QUESTIONS L. A firm can manufacture a product according to the production function (LOI, LO2. LOS, LO6) 0 F(K, L) K34L 14 a. Calculate the average product of labor, AP, when the level of capital is fixed at 81 units and the firm uses 16 units of labor. How does the average product of labor change when the firm uses 256 units...
Suppose the production function for a firm is given by: q=5L0.5K0.25. In the short run, the firm has 16 units of capital. Find the Marginal Product of Labor (MPL). Fill in the appropriate numbers in the function below. MPL = Answer ___ L-0.5 (Round to the nearest 2 decimal places if necessary.)
Consider a firm that faces the following production function: q = f(L, K) = L1/2 K1/2 where q is output, L is labor, and K is capital. Use this production function to answer the following questions. (a) What is the marginal product of labor (MPL)? (b) Does the MPL follow the law of diminishing returns? How do you know? (c) What is the marginal product of capital (MPK)? (d) Does the MPK follow the law of diminishing returns? How do...
The production function of the Auto parts firm is given by Q-5L-L, where Q is the units of output and L is the number of labor hours. Each output sells for 100 dollars per unit. The human resources manager estimates that the marginal cost of hiring an extra worker is 50 dollars. How many labor hours should this firm hire? Hint: MPL=5-2 L 1) 2) A frim's production function is given by Q(L)-6L, where Q measures output and L is...
You are an efficiency expert hired by a manufacturing firm that uses K and L as inputs. The firm produces and sells a given output. If w (price of labor) = $40, r (price of capital) = $100, MPL = 20, and MPK = 40 is the firm minimizing cost? Please explain and show any calculations. (b) The production function for a competitive firm is Q = K0.5L0.5. The firm sells its output at a price of $10 and can...
Suppose a firm has the following production function: Q = 2K L. The marginal product of capital is 2L, and the marginal product of labor is 2K. Assume that capital rents for $100 per unit per day, that labor can be hired for $200 per unit per day, and that the firm is minimizing costs. a. The firm will hire units of labor and - units of capital. b. What is the total cost of producing 60 units of output?...
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....
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...