Question
In: Economics
Joe owns a tree cutting company. His firm uses tree cutters (L) and equipment (K) in...
Joe owns a tree cutting company. His firm uses tree cutters (L) and equipment (K) in cutting trees. Suppose that the cost of hiring a tree cutter (w) is $10 an hour and the cost of using equipment (r) is $30 an hour. We will consider how much K and L Joe should use to cut 75 (i.e., Q = 75) trees. (Make sure that you specify intercepts, optimal amounts of K and L and isoquants clearly on graphs.)
a) Suppose that Joe’s production function is Q = 15K + (2.5)L. Marginal product of capital MPK = 15, and marginal product of labor MPL = 2.5. What are the values of the cost-minimization bundle of K and L? Draw his isoquant and isocost curves and identify the firm’s cost minimizing combination of K and L to represent the cost minimization solution on the graph.
b) Suppose that Joe’s production function is now Q = KL. Joe’s marginal product of capital and labor are MPK = L and MPL= K, respectively. What are the values of the cost-minimization bundle of K and L? Draw his isoquant and isocost curves and identify the firm’s cost minimizing combination of K and L to represent the cost minimization solution on the graph.
c) Suppose that the wage rate increases to $15 per hour. For each of the production functions identified in parts (a) and (b), identify what will happen generally to the optimal amounts of K and L. (Just identify whether K will increase, decrease or stay the same and whether L will increase, decrease or stay the same. You do not have to solve for the exact changes.) Justify your answers using graphs.
Solutions
Rahul Sunny answered 7 months agoRelated Solutions
Joe owns a tree cutting company. His firm uses tree cutters (L) and equipment (K) in...
Joe owns a tree cutting company. His firm uses tree cutters
(L) and equipment (K) in
cutting trees. Suppose that the cost of hiring a tree cutter
(w) is $10 an hour and the cost of using
equipment (r) is $30 an hour. We will consider how much K and
L Joe should use to cut 75 (i.e., Q
= 75) trees. (Make sure that you specify intercepts, optimal
amounts of K and L and isoquants
clearly on graphs.)
1.)...
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.
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?
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....
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.
Zachary Moran manages the cutting department of Greene Adams Company. He purchased a tree-cutting machine on...
Zachary Moran manages the cutting department of Greene Adams
Company. He purchased a tree-cutting machine on January 1, 2018,
for $500,000. The machine had an estimated useful life of 5 years
and zero salvage value, and the cost to operate it is $104,000 per
year. Technological developments resulted in the development of a
more advanced machine available for purchase on January 1, 2019,
that would allow a 20 percent reduction in operating costs. The new
machine would cost $290,000 and...
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...
Consider a firm whose production is given by Q(K, L) = K^1/3L^1/3, where K and L...
Consider a firm whose production is given by Q(K, L) =
K^1/3L^1/3, where K and L are, respectively, the quantities of
capital and labour production inputs. Prices of capital and labour
are both $1 per unit.
(a) Derive and interpret the firm’s demand functions for capital
and labour.
(b) Derive and interpret the firm’s Long-Run Cost Function.
(c) In the long-run, if the firm wished to produce 16 units of
output, what quantities of capital and labour would it optimally...
Edison is a utility company. Edison uses both labors, L and capital, K to produce electricity....
Edison is a utility company. Edison uses both labors, L and
capital, K to produce electricity. The production function of
Edison’s is given by Q = L0.25K0.75 where Q
is measured in millions of kilowatts per hour. The price of a unit
of Lis $27per hour and the price of a unit of Kis $1 per hour.
Edison’s has additional fixed costs of $544per hour. For parts
(a)-(b) assume that Edisonmay chooses any amount of L and K.
a) What...
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...
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