Question

Consider a firm with the production function
f(K,L)=(K^{1/4})(L^{2/4}).

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!)

Answer #1

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....

(2) Consider the production function f(L, K) = 2K √ L. The
marginal products of labor and capital for this function are given
by MPL = K √ L , MPK = 2√ L. Prices of inputs are w = 1 per hour of
labor and r = 4 per machine hour. For the following questions
suppose that the firm currently uses K = 2 machine hours, and that
this can’t be changed in the short–run.
(e) What is the...

Consider a firm with the production function
f(L,K)=L1/2K2 Suppose the firm is in the
short run and has a level of capital K = 1. If the cost of labor is
w=2 and the cost of capital is r=2, derive the a) TVC, b) TFC, c)
TC, d) MC, e) ATC, f) AVC, ) AFC. Draw these curves in a relevant
set of well-labelled diagrams. Repeat the exercise if the firm was
in the short run with a capital level...

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:...

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 using the production technology given by q =
f(K, L) = ln(L^K)
If capital is fixed at K = 2 units in the short run, then what
is the profit maximizing allocation of output if the price of
output and respective input prices of labor and capital are given
by (p, w, r) = (2, 1, 5)?

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...

FACTOR PRICES QUESTION
Imagine firm Oracle is producing computers following
production function q(L,K) =L^0.5 K^2. In the short run, capital is
ﬁxed at K¯ = 5. Oracle faces price p = 50 and can hire as many
workers as it would like at a constant wage w = 25.
A. Find equilibrium labor (L∗) and wages.
B. What are Oracle’s proﬁts at this
equilibrium?
C. Prove that this proﬁt level is a global
maximum.

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...

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