Question

A firm can manufacture a product according to the following
production function, Q = 6K^{1/2} L^{1/2} and the
Marginal Product of Labor is MP(L) = 3 K^{1/2}
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. Can you, given the information at hand, determine total profits?

Answer #1

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...

firm can manufacture a product according to the production
function
Q = F (K, L) = K0.75 L 0.25 a. What is this type of function
called? Are the inputs perfect substitutes or should they be used
in a fixed proportion instead? © (3pts) b. Suppose capital is fixed
at 81 units. If the firm can sell its output at a price of $200 per
unit and wage is $50, how many units of labor should the firm hire
in...

A firm can manufacture a product according to the production
function Q = F (K, L) = K0.75 L0.25 a. What is this type of
function called? Are the inputs perfect substitutes or should they
be used in a fixed proportion instead? © (3pts) b. Suppose capital
is fixed at 81 units. If the firm can sell its output at a price of
$200 per unit and wage is $50, how many units of labor should the
firm hire in...

A firm can manufacture a product according to the production
function Q = F (K, L) = K0.75 L0.25 a. What is this type of
function called? Are the inputs perfect substitutes or should they
be used in a fixed proportion instead? © (3pts) b. Suppose capital
is fixed at 81 units. If the firm can sell its output at a price of
$200 per unit and wage is $50, how many units of labor should the
firm hire in...

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?...

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. Suppose a firm can manufacture a product using the following
production function:
Q = f (K,L) = K^0.60 L^ 0.40)
(a) What is the APL when the firm uses 10 units of fixed capital
and 30units of labor?
(b) How does the APL change when the firm uses 100 units of
labor?
(c) Write out an expression for the MPL when capital is
fixed
(d) Show that the MPL depends on the amount of labor that is
employed by...

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...

Suppose a firm can manufacture a product using the following
production function:
Q = f (K,L) =
"K0.60
"L0.40
(a) What is the APL when the firm uses 10 units of fixed capital
and 30units of labor?
(b) How does the APL change when the firm uses 100 units of
labor?
(c) Write out an expression for the MPL when capital is fixed
(d) Show that the MPL depends on the amount of labor that is
employed by calculating the...

1. A monopsonist has the production function
Q=4⋅L
and faces the following labor supply and product demand
equations respectively.
W=2+0.05⋅L
P=10−0.025⋅Q
How much labor should the firm hire in order to maximize profits
if they mark their price 300% above marginal cost? Answer is not
10
2.
A monopsonist has the production function
Q=4⋅L
and faces the following labor supply and product demand
equations respectively.
W=2+0.05⋅L
P=10−0.025⋅Q
What wage rate should the firm pay in order to maximize profits
if...

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