Question

Firm A’s production function and cost line are given by:

Q=Q(L,K)=2 L^(1/2) K^(1/2) (The production function)

*?*L+*?*=30000 (The cost line of firm A):

*?*L is the amount of labor hired.

*?*K is the amount of capital hired.

*?**?*p_L or the price of labor is 1 dollar per
unit.

*?**?*p_K or the price of capital is 1 dollars per
unit.

C or cost (think of it as the firm’s budget) is 30000 dollars.

How much labor and capital should this firm optimally hire?

Answer #1

Ans. Production function, Q = 2*L^(0.5) * K^(0.5)

Marginal product of labour, MPL = dQ/dL = (K/L)^0.5

Margial product of capital, MPK = dQ/dK = (L/K)^0.5

=> Marginal rate of technical substitution, MRTS = dK/dL = MPL/MPK = K/L

At optimal level,

MRTS = pL/pK

=> K/L = 1/1

=> K = L ---> Eq1

Substituting Eq1 in the cost line, L+ K = 30000, we get,

K + K = 30000

=> K = L = 15000 units

Thus, optimal level of labour hired 15000 units and capital hired is 15000 units.

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...

A firm’s production function is Q(L,K) = K^1/2 + L. The firm
faces a price of labor, w, and a price of capital services, r.
a. Derive the long-run input demand functions for L and K,
assuming an interior solution. If the firm must produce 100 units
of output, what must be true of the relative price of labor in
terms of capital (i.e. w/r) in order for the firm to use a positive
amount of labor? Graphically depict this...

The production of sunglasses is characterized by the production
function Q(L,K)= 4L1/2K 1/2 . Suppose that the price of labor is
$10 per unit and the price of capital is $90 per unit. In the
short-run, capital is fixed at 2,500. The firm must produce 36,000
sunglasses. How much money is it sacrificing by not having the
ability to choose its level of capital optimally? That is, how much
more does it cost to produce 36,000 sunglasses the short-run
compared...

The production of sunglasses is characterized by the production
function Q(L,K)= 4L^1/2K^1/2.
Suppose that the price of labor is $10 per unit and the price of
capital is $90 per unit. In the short-run, capital is fixed at
2,500. The firm must produce 36,000 sunglasses. How much money is
it sacrificing by not having the ability to choose its level of
capital optimally? That is, how much more does it cost to produce
36,000 sunglasses the short-run compared to the...

Suppose a firm has a production function given by q = 3L +
K.
The firm can purchase labor, L at a price w = 24, and capital, K
at a price of r = 5.
What is the firm’s total cost function?

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?...

Suppose a monopolist has a production function given by Q =
(L^1/2)/(K^1/2). Therefore, MPL =( k^1/2) / 2(L^1/2) , and MPK
=(L^1/2) / 2(k ^1/2)The monopolist can purchase labor, L at a price
w = 16, and capital, K at a price of r = 9. The demand curve facing
the monopolist is P = 360 – 2Q.
a) (8 points) What is the monopolist’s total cost function?
b) (4 points) How much output should the monopolist produce in
order...

A firm produces good Q using inputs L & K. The firm’s
production function is X = 20L^0.5 + 11K. The
price of K is $P_K a unit and the price of L is $P_L a unit, and in
the short‐run, the capital input is
fixed at 3 units.
a. If the firm needs an output of X_1 in the short‐run, what is the
firm’s total cost and marginal
cost of production?
b. What is the firm’s fixed cost and...

Suppose a firm’s production function is given by Q = 2K^1/2 *
L^1/2 , where K is capital used and L is labour used in the
production.
(a) Does this production function exhibit increasing returns to
scale, constant returns to scale or decreasing returns to
scale?
(b) Suppose the price of capital is r = 1 and the price of
labour is w = 4. If a firm wants to produce 16 chairs, what
combination of capital and labor will...

a. A cost minimizing firm’s production is given by
Q=L^(1/2)K^(1/2)
. Suppose the desired output is
Q=10. Let w=12 and r=4. What is this firm’s cost minimizing
combination of K & L? What it the
total cost of producing this output?
b. Suppose the firm wishes to increase its output to Q=12. In
the short run, the firm’s K is fixed
at the amount found in (a), but L is variable. How much labor
will the firm use? What will...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 24 minutes ago

asked 29 minutes ago

asked 39 minutes ago

asked 55 minutes ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago

asked 4 hours ago