Question

A firm has modeled its production function, with 6 units of capital already deployed. The production function is:

*q=8**L**-2L*

The firm has also modeled its marginal profit function as:

*mp**q**=**q**3**-25**q**2**+206q-560*

The firm has three options as to how the quantity it can produce
that can potentially maximize its profits in the short run. The
firm can elect to supply 7 million units, 8 million units, or 10
million units. In other words, *q=7 or q=8 or q=10.*

How many widgets must the firm produce to maximize its profits and how many laborers will the firm need to employ to produce the optimal quantity?

Answer #1

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?

A firm has the production function: Q= 10K^.5L^.5 If the firm
has 36 units of capital (K), how much labor is needed to produce
240 units of output?

Firm B’s production function is q = min {8L,
10K} where L is the quantity of labor and
K is the quantity of capital used to produce output
q. Let PL and PK
denote price of labor and price of capital, respectively. Derive
Firm B’s long-run total cost function. Show your work.

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...

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’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...

1. Suppose a short-run production function is described as Q =
2L – (1/800)L^2 where L is the number of labors used each hour. The
firm’s cost of hiring (additional) labor is $20 per hour, which
includes all labor costs. The finished product is sold at a
constant price of $40 per unit of Q.
a. How many labor units (L) should the firm employ per hour
b. Given your answer in a, what is the output (Q) per hour...

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...

Suppose a firm has a production function q = f(L, K) =2L + 4K,
and the factor prices are w = $2 and r = $2. What is the minimum
cost at which the firm is able to produce 20 units of output?
a. $10 b. $30 c. $45 d. $100 e. $50
please explain why

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