Q5. Given the following short-run production function (x = variable input, Q = output):...
Q5. Given the following short-run production function (x = variable input, Q = output): Q = 3x2 - 0.1x3
(a) Determine the marginal product function (MPx) and the average product function (APx ).
(b) Find the value of x that maximizes Q.
(c) Find the value of x for which MPx is maximum.
(d) Find the value of x for which APx is maximum.
(e) Determine the boundaries of the three stages of
production.
Homework Answers
Add Answer to:
Q5. Given the following
short-run production function (x = variable input, Q = output):...
Consider the following short-run production function (where L = variable input, Q = output): Q=6L−0.4L2 Suppose...
Consider the following short-run production function (where L = variable input, Q = output): Q=6L−0.4L2 Suppose that output can be sold for $10 per unit. Also assume that the firm can obtain as much of the variable input (L) as it needs at $20 per unit. What is the marginal revenue product function (MRPL)? $20 $60−$8L $10 $6−$0.40L What is the marginal factor cost function (MFCLMFCL)? $6−$0.40L $60−$8L $10 $20 What is the optimal value of L, given that the...
5) A firm's short-run production function is given by Q=50 L-.02 L^{2}
5) A firm's short-run production function is given by Q=50 L-.02 L^{2}Where L denotes the number of workers.1. Find the size of the workforce that maximizes output.2. Find marginal product of labor (M PL)3. Find the average product of labor (APL)4. Find the size of the workforce which maximizes the average product of labor. Calculate M PL and A PL at this value. What do you observe.6) Find and classify the critical (stationary) points of the following function and state...
You are given the following short-run production function for Superfast Hairdryers, Inc., where X is material...
You are given the following short-run production function for Superfast Hairdryers, Inc., where X is material inputs, and Q is output. Q = 10X - 0.25X2 Suppose the hair dryers are sold for $10 per unit to K-Mart. Also assume that the firm can obtain as much of the variable materials, input (X), as it needs at $20 per unit. i) Determine the Marginal Revenue Product (MRP) of materials. ii) Determine the Marginal Cost (MC) function. iii) Determine the optimal...
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), where q is output, L is workers, and K is the fixed number of units of capital. Production Output or Marginal Product Product Labor Average Product Given a specific equation for production: 0 249 9 =...
A firm applies a production technology to produce units of output (q) according to the production...
A firm applies a production technology to produce units of output (q) according to the production function q = 20 x L^.5 x K^.5 , where L is a variable input and K is a fixed input. Assume K = 100 in the short run. solve for the short-run average product of labor (AP L) and the marginal product of labor (MP L) functions. If L = 100, what are the numerical values of AP L and MP L?
In the short run, we assume that capital is a fixed input and labor is a variable input, so the f...
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 fixed number of units of capital. fL, K), where q is output, L is workers, and K is the A specific equation for the production function is given by: Or , when K=29, q - (Bx29xL) 512- The...
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...
Suppose the production function for a firm is given by: q=5L0.5K0.25. In the short run, the...
Suppose the production function for a firm is given by: q=5L0.5K0.25. In the short run, the firm has 256 units of capital. Find the Marginal Product of Labor (MPL). Fill in the appropriate numbers in the function below. MPL = ( ) L-0.5
2. For each of the following production functions: Q = 3L2 +6K4 Q= V25KL Q =...
2. For each of the following production functions: Q = 3L2 +6K4 Q= V25KL Q = 5V1 + 101K a. Find the marginal product of each input, i.e. MP, and MPx: b. Determine whether the production function exhibits diminishing marginal returns to each input. c. Find the marginal rate of technical substitution, MRTSLK and discuss how it changes as the firm uses more L and less K, holding output constant. d. Determine whether the production function exhibits constant, increasing or...
Task 2: Short-Run Production: One Variable and One Fixed Input II.... Consider the following production function:...
Task 2: Short-Run Production: One Variable and One Fixed Input II.... Consider the following production function: q=8LK + 5L2 - L. Assume capital is fixed at K = 25. (a) At what level of employment does the marginal product of labor equal zero? (Hint: To answer this question mathematically, you will have to use the quadratic formula.) (b) Illustrate the above production function for values of L € [1,30] (Note: Your graph does not necessarily have to be precise at...
5) A firm's short-run production function is given by Q=50 L-.02 L^{2}Where L denotes the number of workers.1. Find the size of the workforce that maximizes output.2. Find marginal product of labor (M PL)3. Find the average product of labor (APL)4. Find the size of the workforce which maximizes the average product of labor. Calculate M PL and A PL at this value. What do you observe.6) Find and classify the critical (stationary) points of the following function and state...
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), where q is output, L is workers, and K is the fixed number of units of capital. Production Output or Marginal Product Product Labor Average Product Given a specific equation for production: 0 249 9 =...
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 fixed number of units of capital. fL, K), where q is output, L is workers, and K is the A specific equation for the production function is given by: Or , when K=29, q - (Bx29xL) 512- The...
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...
2. For each of the following production functions: Q = 3L2 +6K4 Q= V25KL Q = 5V1 + 101K a. Find the marginal product of each input, i.e. MP, and MPx: b. Determine whether the production function exhibits diminishing marginal returns to each input. c. Find the marginal rate of technical substitution, MRTSLK and discuss how it changes as the firm uses more L and less K, holding output constant. d. Determine whether the production function exhibits constant, increasing or...
Task 2: Short-Run Production: One Variable and One Fixed Input II.... Consider the following production function: q=8LK + 5L2 - L. Assume capital is fixed at K = 25. (a) At what level of employment does the marginal product of labor equal zero? (Hint: To answer this question mathematically, you will have to use the quadratic formula.) (b) Illustrate the above production function for values of L € [1,30] (Note: Your graph does not necessarily have to be precise at...
Most questions answered within 3 hours.
-
Assume Kw = 1.01 ✕ 10−14
For pure water, we can calculate [H3O+ ] = [OH...
asked 39 minutes ago -
Suppose that on a temperature scale X, water boils at 203.0°X
and freezes at -105.7°X. What...
asked 1 hour ago -
BaS crystallizes in a cubic unit cell with S2- ions on each
corner and each face....
asked 1 hour ago -
A. 0≤P(Oi)≤10≤P(Oi)≤1 for each i
B. P(Oi)≤0P(Oi)≤0
C. P(Oi)=1+P(OCi)P(Oi)=1+P(OiC)
D. P(Oi)≥1P(Oi)≥1
If an experiment consists of...
asked 3 hours ago -
A battery has an emf of 9.20V and an internal resistance of 1.20
ohm. a)What resistance...
asked 3 hours ago -
The area of an elastic circular loop decreases at a constant
rate, dA/dt = −6.60×10−3 m2/s...
asked 4 hours ago -
The denaturation of proteins can be described by the
equilibrium
F⇌U
where F and U represent...
asked 6 hours ago -
Please answer what the maximum and minimum force is, and the
angle on the ion is...
asked 6 hours ago -
implement a program that reads a number of rows and a symbol.
The program will draw...
asked 6 hours ago -
Assume that when adults with smartphones are randomly selected,
45% use them in meetings or classes....
asked 6 hours ago -
Determine the number of formula units of
Na2SO4 and moles of oxygen contained in 8.11
moles...
asked 6 hours ago -
Explain in steps on the following code
What would be the output when executed
using System;...
asked 6 hours ago