Question

1. Suppose a short-run production function is described as Q = 2L – (1/800)L2 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:

c. Given your answer in b, what is the resulting profit per hour assuming only labor costs?

d. Suppose that labor costs remain unchanged but that the price received per unit of output increases to $50. How many labor units (L) will the firm now employ?

Answer #1

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...

Suppose a short-run production function is described as Q = L –
(1/400)L2where L is the number of labors used each hour.
The firm’s cost of hiring (additional) labor is $16 per hour, which
includes all labor costs. The finished product is sold for $40 per
unit of Q.
c. How many labor units(L)
should the firm employ per hour if they want to maximize profit?
L = 120
f. Suppose that the price of the product is unchanged...

1. Suppose a short-run production function is described as Q =
30L - 0.05L^2 where L is the number of labors used each hour.
a. Derive the equation for Marginal Product of Labor
b. Determine how much output will the 200th worker
contribute:
c. Determine the amount of labor (L) where output (Q) is
maximized (known as Lmax):
d. If each unit of output (Q) has a marginal revenue (price) of
$5 and the marginal cost of labor is $40...

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...

A firm produces an output with the production function Q=K*L2,
where Q is the number of units of output per hour when the firm
uses K machines and hires L workers each hour. The marginal product
for this production function are MPk =L2 and MPl = 2KL. The factor
price of K is $1 and the factor price of L is $2 per hour.
a. Draw an isoquant curve for Q= 64, identify at least three
points on this curve....

Suppose a firm’s long-run production function is given by
Q=K^0.25 L^0.25 ,where K is measured in machine-hours per year and
L is measured in hours of labor per year. The cost of capital
(rental rate denoted by r) is $1200 per machine-hour and the cost
of labor (wage rate denoted by w) is $12 per hour.
Hint: if you don’t calculate the
exponential terms (or keep all the decimals when you do), you will
end up with nice numbers on...

Consider a firm with the production function
f(K,L)=(K1/4)(L2/4).
In the short run, the firm has rented 25 units of capital. The
firm is a price taker in both the output market and labor market,
facing an output price of 11 and a market wage of 5 per hour.
Rounded to the nearest tenth, how many hours of labor will the firm
hire? (Make sure your answer only has 1 decimal before
submitting!)

A firm’s production function is Q = min(K , 2L), where Q
is the number of units of output produced using K units of capital
and L units of labor. The factor prices are w = 4 (for labor) and r
= 1 (for capital). On an optimal choice diagram with L on the
horizontal axis and K on the vertical axis, draw the isoquant for Q
= 12, indicate the optimal choices of K and L on that isoquant,...

A firm produces good X and has a production function X =
2L^0.25K^0.25, where L and K are the inputs.
Assume that the price of L is $6 and the price of capital is $12.
Let the firm have a target output
of X1 units.
a. Find the firm’s conditional demand for labor and capital.
b. Find the firm’s total cost function.
c. What is the firm’s marginal cost?

Suppose a firm’s production function is given by Q = L 1/2 , K
1/2.
a) Suppose the firm has a fixed cost FC=6, the price
of labor is w = 64 and the price of capital is r = 4. Derive the
firm’s total cost function, TC(Q).
b) What is the firm’s marginal cost?
c) Graph the firm’s isoquant for Q = 20 units of
output. On the same graph, sketch the firm’s isocost line
associated with the total...

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