Question

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 order to maximize profits? (10pts)

Answer #1

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...

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...

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 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....

A firm produces X using the following production function: Q =
F(K,L) = 32K0.76L0.24. K=6 units. If the firm
can sell each unit X at $22.20 and can hire labor at $16.00 per
unit. Answer the below questions with the information provided.
The total profits when the firm uses optimal labor is?
How many workers the firm will hire in order to maximize
profits?
How many units of X the firm will produce in order to maximize
profits?

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...

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...

A firm’s production function is: Q = 6K1/3
L2/3. Suppose that capital is fixed at 125 units. If the
firm can sell its output at a price of $200 per unit, hire labor at
$20 a unit, and rent capital at $40 a unit, how many units of labor
should the firm hire to maximize profits?Given your answer, what is
the level of output that maximizes profits? Lastly, calculate the
level of profits at the profit-maximizing level of labor and...

Consider a firm which has the following production function
Q=f(L,K)=4?LK
(MPL=2?(K/L) and MPK=2?(L/K).
(a) If the wage w= $4 and the rent of capital r=$1, what is the
least expensive way to produce 16 units of output? (That is, what
is the cost-minimizing input bundle (combination) given that
Q=16?)
(b) What is the minimum cost of producing 16 units?
(c) Show that for any level of output Q, the minimum cost of
producing Q is $Q.

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