In: Economics

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.

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 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...

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?

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....

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.

Suppose output, Q, is produced by labor, L, and capital, K,
according to the following function: Q = K ½ L½.. Suppose the firm
sells each unit of output in a competitive market for a price P =
$100. Suppose the firm hires each unit of labor in a competitive
market for a wage W = $25. Suppose the firm has to make do for now
with a stock of capital K = 49; moreover, suppose each unit of
capital...

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...

A firm produces output y using two factors of production
(inputs), labour L and capital K. The firm’s production function is
?(?,?)=√?+√?=?12+?12. The wage rate w = 6 and the rental price of
capital r = 2 are taken as parameters (fixed) by the firm. a. Show
whether this firm’s technology exhibits decreasing, constant, or
increasing returns to scale. b. Solve the firm’s long run cost
minimization problem (minimize long run costs subject to the output
constraint) to derive this...

The production function has two input, labor (L) and capital
(K). The price for L and K are respectively W and V.
q = L + K a linear production function
q = min{aK, bL} which is a Leontief production function
1.Calculate the marginal rate of substitution.
2.Calculate the elasticity of the marginal rate of
substitution.
3.Drive the long run cost function that is a function of input
prices and quantity produced.

Suppose you are in the photocopying business, and are using
labor (L) and capital (K), in the form of copy machines. You can
hire workers for $150 a week and lease copy machines for $300 a
week.
(a) Suppose your current total cost of production is $3,000. Use
the information above to depict the isocost you are currently
operating on, carefully labeling the relevant intercepts (put L on
the x-axis and K on the y-axis).
(b) You are producing 10,000...

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