Question

The production engineers at Impact Industries have derived the
optimal combinations of labor and capital. These are the only two
inputs used by Impact. The following chart shows the combinations
of labor and capital for three levels of output.

Q is the output level. L* is the optimal amount of labor. K*
is the optimal amount of capital. The price of labor is $90 per
unit. The price of capital is $15 per unit.

Q

L*

K*

120

5

20

180

7

7

240

12

24

a) If the manager of Impact Industries decides to produce 120
units, what will the long-run total cost and long-run average cost
of producing 120 units? Show all calculations.

b) If the manager of Impact Industries decides to produce 180
units, what will the long-run total cost and long-run average cost
of producing 180 units? Show all calculations.

c) If the manager of Impact Industries decides to produce 240
units, what will the long-run total cost and long-run average cost
of producing 240 units? Show all calculations.

d) Are there economies of scale over the output range 120 to
180? Explain.

e) Are there diseconomies of scale over the output range 180
to 240? Explain.

Answer #1

w = $90; r = $15

Long run total cost, LRTC = wL* + rK*

Aong run average cost, LRAC = LRTC/Q

a. LRTC = wL* + rK* = 90(5) + 15(20) = 450 + 300 = 750

So, LRTC = $750

LRAC = LRTC/Q = 750/120 = $6.25

b. LRTC = wL* + rK* = 90(7) + 15(7) = 630 + 105 = 735

So, LRTC = $735

LRAC = LRTC/Q = 735/180 = $4.08

c. LRTC = wL* + rK* = 90(12) + 15(24) = 1080 + 360 = 1,440

So, LRTC = $1,440

LRAC = LRTC/Q = 1440/240 = $6

d. Yes, there are economies of scale over the output range 120 to 180 as LRAC is decreasing over this range.

e. Yes, there are diseconomies of scale over the output range 180 to 240 as LRAC is increasing over this range.

A firm discovers that when it uses K units of capital and L
units of labor, it is able to produce X= L^1/4*K^3/4 units of
output 1. Continue to assume that capital and labor can each be
hired at $1 per unit. Show that in the long run, if the firm
produces 24 units of output, it will employ 16 units of capital and
81 units of labor. What is the long-run total cost to produce 12
units of output?...

The production function is Y=K0.5L0.5 where K is capital, L is
labor and Y is output. The price of L is 1 and the price of K is
2.
a) Find the optimal levels of K and L that should be employed to
produce 100 units of output. What is
the cost of producing this level of output?
b) Will the optimal capital-labor ratio change if the price of
labor goes up to 2 and the price of K goes...

20. Output for a simple production process is given by Q = K2L,
where K denotes capital, and L denotes labor. The price of capital
is $30 per unit and capital is fixed at 5 units in the short run.
The price of labor is $20 per unit.
a. The total cost of producing 100 units of output is _____.b.
The variable cost of producing 100 units of output is ____.
21.Determine whether the production function Q = K3/2L2 exhibits...

Consider a firm that used only two inputs, capital (K) and labor
(L), to produce output. The production function is given by: Q =
60L^(2/3)K^(1/3) .
a.Find the returns to scale of this production function.
b. Derive the Marginal Rate of Technical Substitutions (MRTS)
between capital and labor. Does the law of diminishing MRTS hold?
Why? Derive the equation for a sample isoquant (Q=120) and draw the
isoquant. Be sure to label as many points as you can.
c. Compute...

A firm discovers that when it uses K units of capital
and L units of labor it is able to
produce q=4K^1/4
L^3/4 units of output.
a) Calculate the MPL, MPK and MRTS
b) Does the production function (q=4K^1/4 L^3/4) exhibit
constant, increasing or decreasing returns to scale and
why?
c) Suppose that capital costs $10 per unit and labor can
each be hired at $40 per unit and the firm uses 225 units of
capital in the short run....

Use the following production and cost function to answer the
questions that follow:
a. Assume capital is fixed at 100 units in the
short-run, how much labor is required to produce
1000 units of output?
b. How much will this amount of labor plus the 100 units of
capital cost the firm in the short run?
c. What is the “cost minimizing” input requirements (of L and k)
to produce 1000 units of output in the
long-run?
i. Cost minimizing...

2. A firm combines labor (L) and capital (K) to produce output
(Q). The price of one unit
of labor is 50 and the price of one unit of capital is 20. This
firm is producing in the
short run (remember that in the short run there is one fixed
resource, in this case,
capital). Complete the following information for this firm
L K Q TVC TFC TC ATC AVC AFC MC
0 20 0 -
1 18
2 60...

a firm produces a product with labor and capital as inputs. The
production function is described by Q=LK. the marginal products
associated with this production function are MPL=K and MPK=L. let
w=1 and r=1 be the prices of labor and capital, respectively
a) find the equation for the firms long-run total cost curve
curve as a function of quantity Q
b) solve the firms short-run cost-minimization problem when
capital is fixed at a quantity of 5 units (ie.,K=5). derive the...

1?Basic factors of production available to a society are
* A. natural resources, labor and capital.
* B. natural resources, labor and money.
* C. labor, money and environment.
* D. natural resources, money and infrastructure.
2?Total cost is
* A. the sum of total fixed cost and total variable
cost.
* B. increasing with output.
* C. equal to total fixed cost when production level is
zero.
* D. all the above true.
3?Suppose a certain firm is able...

Suppose you own a firm that producing shoes using both capital
and labor. The production function is q=f(K, L)=0.5K2 L4 . In long
run both capital (K) and labor (L) are variable. Price for each
pair of shoes is $50 (p=50), the wage rate is 0.04 (w=0.04) and the
rental price for capital is 1 (r=1). Given those output and input
prices, what is the profit maximizing input level of K and L (K*
& L* )?

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 27 seconds ago

asked 2 minutes ago

asked 4 minutes ago

asked 7 minutes ago

asked 8 minutes ago

asked 8 minutes ago

asked 8 minutes ago

asked 10 minutes ago

asked 11 minutes ago

asked 14 minutes ago

asked 15 minutes ago

asked 15 minutes ago