Question
In: Economics
A firm discovers that when it uses K units of capital and L units of labor...
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. How much labor is used and what is the short-run total cost to produce 600 units of output?
d) Continue to assume that capital and labor can be hired at $40 per unit for labor and $10 for capital. In the long run if the firm produces 600 units of output, how much labor and capital will be used and what is the LR Total cost of production?
Solutions
Rahul Sunny answered 1 year agoRelated Solutions
A firm discovers that when it uses K units of capital and L units of labor...
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.
Continue to assume that capital and labor can be hired at $40
per unit for labor and $10 for capital. In the long run if the firm
produces 600 units of output, how much labor and capital will be
used and what is the LR Total cost of production?
There is a firm who manufacturers and uses capital (K) and labor (L) to product output...
There is a firm who manufacturers and uses capital (K) and labor
(L) to product output Q such that Q=10KL. The unit price for K and
L are w = $15 and r = $5, respectively.
1).Does the firm’s production exhibit decreasing, constant, or
increasing returns to scale?
2)What is the optimal input bundle (K*, L*) to produce 480 unit
of output?
3)Derive the long run cost function.
Imagine a firm that only uses capital (K) and labor (L). Use an isocost / isoquant...
Imagine a firm that only uses capital (K) and labor (L). Use an
isocost / isoquant diagram to illustrate the firm’s equilibrium
input mix for given prices of capital and labor and a given rate of
output. Now illustrate what happens if the price of labor falls,
and the firm wants to produce the same rate of output. What happens
to the cost of production? Compare the relative marginal products
of labor and capital (the MRTS) at the two equilibria.
A firm produces output using capital (K) and labor (L). Capital and labor are perfect complements...
A firm produces output using capital (K) and labor (L). Capital
and labor are perfect complements and 1 unit of capital is used
with 2 units of labor to produce 1 unit of output. Draw an example
of an isoquant. If wages and rent are $2 and $3, respectively, what
is the Average Total Cost?
A firm has a production function given by Q=4KL where K, L and Q
denote capital, labor, and output, respectively. The firm wants to
produce...
Suppose your firm uses 2 inputs to produce its output: K (capital) and L (labor). the...
Suppose your firm uses 2 inputs to produce its output: K
(capital) and L (labor). the production function is q =
50K^(1/2)L^(1/2). prices of capital and labor are given as r = 2
and w = 8
a) does the production function display increasing, constant, or
decreasing returns to scale? how do you know and what does this
mean?
b) draw the isoquants for your firms production function using L
for the x axis and K for y. how are...
1a. The production function for computers is q(K,L) = 7K1/3L2 where K=capital and L=labor. A firm...
1a. The production function for computers is q(K,L) = 7K1/3L2
where K=capital and L=labor. A firm has two units of capital (K=2)
which it cannot change. A manager wants to know the marginal
productivity of labor if the firm goes from 2 to 3 workers.
Calculate the marginal productivity of labor for the manager.
Explain your answer carefully to the manager who is not familiar
with what the marginal productivity of labor means.
1b. Last year the price of bread...
Consider this table containing long run production data: Units of Capital, K Units of Labor, L...
Consider this table containing long
run production data:
Units of Capital, K
Units of Labor, L
1
2
3
4
1
100.00
131.95
155.18
174.11
2
141.42
186.61
219.46
246.23
3
173.21
228.55
268.79
301.57
4
200.00
263.90
310.37
348.22
Does this production function exhibit a constant return to scale?
Explain your answer.
How many units of output are produced with 4 units of labor and 2
units of capital?
Suppose the firm is using 3 units...
Consider an economy that uses two factors of production, capital (K) and labor (L), to produce...
Consider an economy that uses two factors of production, capital
(K) and labor (L), to produce two goods, good X and good Y. In the
good X sector, the production function is X = 4KX0.5 + 6LX0.5, so
that in this sector the marginal productivity of capital is MPKX =
2KX-0.5 and the marginal productivity of labor is MPLX = 3LX-0.5.
In the good Y sector, the production function is Y = 2KY0.5 +
4LY0.5, so that in this sector...
Q1: A firm uses physical capital, which is fixed at 4 units, and labour (L) to...
Q1: A firm uses physical capital, which is fixed at 4 units, and
labour (L) to make its product. The price of physical capital is
$250 per unit and the price of labour is $100 per unit.
a) Complete the following table by filling in the columns for
marginal product of labour (MPL), average product of
labour (APL), total fixed cost (TFC), total variable
cost (TVC), total cost (TC), average fixed cost (AFC), average
variable cost (AVC), average total cost...
Q1: A firm uses physical capital, which is fixed at 4 units, and labour (L) to...
Q1: A firm uses physical capital, which is fixed at 4 units, and
labour (L) to make its product. The price of physical capital is
$250 per unit and the price of labour is $100 per unit.
a) Complete the following table by filling in the columns for
marginal product of labour (MPL), average product of
labour (APL), total fixed cost (TFC), total variable
cost (TVC), total cost (TC), average fixed cost (AFC), average
variable cost (AVC), average total cost...
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