Question

Determine which of the following statement below are correct. Multiple statements may be correct.

If you are asked to evaluate an approximate variable, you should consider a 10% tolerance for the variable (plus or minus 10%).

A firm's production function is equal to Q = K^(1/2) L^(1/2) and the Marginal Product of Labor is equal to: MP(L) = 1/2 * K^(1/2) * L^(-1/2) You know that capital (K) is currently fixed at 100 units. When labor increases from 49 to 81 units, the Marginal Product of Labor declines from 0.71 to 0.55. |
A firm's production function is equal to Q = K^(1/2) L^(1/2) and the Marginal Product of Labor is equal to: MP(L) = 1/2 * K^(1/2) * L^(-1/2) You know that capital (K) is currently fixed at 100 units. When labor increases from 49 to 81 units, the Marginal Product of Labor declines from 0.71 to 0.55. As a result, the Average Product of Labor will increase when labor increases from 49 to 81 units. |
A firm's production function is equal to Q = K^(1/2) L^(1/2) and the Marginal Product of Labor is equal to: MP(L) = 1/2 * K^(1/2) * L^(-1/2) Capital is currently fixed at 81 units. The firm currently employs 256 units of labor. Given that the firm can sell its production at $50 a unit, it should offer to pay its workers approximately $14 an hour. |
A firm's production function is equal to Q = K^(1/2) L^(1/2) and the Marginal Product of Labor is equal to: MP(L) = 1/2 * K^(1/2) * L^(-1/2) Capital is currently fixed at 256 units. The firm currently employs 100 units of labor. Given that the firm can sell its production at $50 a unit, it should offer to pay its workers approximately $28 an hour. |

Answer #1

Two statements are correct

1) **A firm's production function is equal to Q = K^(1/2)
L^(1/2) and the Marginal Product of Labor is equal to: MP(L) = 1/2
* K^(1/2) * L^(-1/2) You know that capital (K) is currently fixed
at 100 units. When labor increases from 49 to 81 units, the
Marginal Product of Labor declines from 0.71 to 0.55.**

**3)** **A firm's production function is
equal to Q = K^(1/2) L^(1/2) and the Marginal Product of Labor is
equal to: MP(L) = 1/2 * K^(1/2) * L^(-1/2) Capital is currently
fixed at 81 units. The firm currently employs 256 units of labor.
Given that the firm can sell its production at $50 a unit, it
should offer to pay its workers approximately $14 an
hour.**

A firm can manufacture a product according to the following
production function, Q = 6K1/2 L1/2 and the
Marginal Product of Labor is MP(L) = 3 K1/2
L-1/2. Recall that VMP(L) = w.
Suppose that capital is fixed at 25 units. If the firm can sell
its output at $100 per unit and employs 49 units of labor, how much
should it pay its labor to maximize profits?
Using the information in (a), assume that you pay $5/unit for
capital....

1. A firm can manufacture a product according to the following
production function, Q = 4K1/2 L1/2 and the Marginal Product of
Labor is MP(L) = 2K1/2 L-1/2. Recall that VMP(L) = w. a. Suppose
that capital is fixed at 25 units. If the firm can sell its output
at $200 per unit and employs 64 units of labor, how much should it
pay its labor to maximize profits? b. Using the information in (a),
assume that you pay $5/unit...

A firm uses two inputs, capital K and labor L, to produce output
Q that can be sold at a price of $10. The production function is
given by Q = F(K, L) = K1/2L1/2 In the short run, capital is fixed
at 4 units and the wage rate is $5, 1. What type of production
function is F(K, L) = K1/2L1/2 ? 2. Determine the marginal product
of labor MPL as a function of labor L. 3. Determine the...

1. If some production function Q(L,K) exhibits and increasing
return to scale, then the marginal cost of production decreases as
output level increases. (a) True (b) False
2. If for some production function Q(L,K) the marginal product
of labor and the marginal product of capital both decreases as
output level increases, then the marginal cost of production
increases as output level increases. (a) True (b) False
3. A firms production function is represented by Q(M,R) = M^3R,
MPM = 3M^2R,...

The production function for a firm is Q = −0.6L 3 + 18L 2K + 10L
where Q is the amount of output, L is the number of labor hours per
week, and K is the amount of capital.
(a)Use Excel to calculate the total short run output Q(L) for L
= 0, 1, 2...20, given that capital is fixed in the short run at K =
1.
(b) Use Excel to calculate the total long run output Q(L) for...

A firm has the production function:
Q = L 1 2 K 1 2
Find the marginal product of labor (MPL), marginal
product of capital (MPK), and marginal rate of technical
substitution (MRTS).
Note: Finding the MRTS is analogous to finding the
MRS from a utility function:
MRTS=-MPL/MPK. Be sure to simplify your
answer as we did with MRS.
A firm has the production function:
Q = L 1 2 K 3 4
Find the marginal product of labor (MPL),...

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 = (K^1/2)/2L^1/2 & MPK = (L^1/2)/2K^1/2)
a) (12 points) If the price of labor is w = 48, and the price of
capital is r = 12, how much labor and capital should the firm hire
in order to minimize the cost of production if the firm wants to
produce output Q = 10?...

The table below presents estimates of the maximum levels of
output possible with various combinations of two inputs.
Capital (K)
5
13
27
39
49
53
4
12
25
35
43
46
3
10
20
27
33
36
2
7
13
18
22
24
1
3
7
10
12
13
1
2
3
4
5
Labor (L)
Assume that a unit of output sells for $5 and that the firm
currently employs 3 units of capital (K = 3)....

the demand function for a good x is given as:
qx=11-2p
Choose the correct statement:
a) if the quantity is 1 the elasticity is -10
b) none of the other answers
c) the demand represents a Giffen good
d) this D curve crosses the p axes at p=11
2.Consider the following function: Q(K-L) =5L+Kg =5L +7
Which statement about this particular production function is
FALSE?
a) With every additional unit of L added, Q increases at a
decreasing rate
b)...

The manger of a manufacturing company recently hired an
economist to estimate the firm’s production function.
based on the economist report. The manager now knows that the
firm production function is given by Q=K^3/4^L^1/^4 and that
capital is fixed at 81 unit.
a) calculate the average product of labor when 16 units of labor
are utilized
b) calculate the marginal product of labor when 16 units of
labor are utilized
c)suppose the firm can hire labor at a wage of...

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