Question

Assume that a profit maximizer firm uses only two inputs, labor (L) and capital (K), and its production function is f(K,L) = K2 x L. Its MRTS of capital for labor (i.e., how many units of capital does he want to give up one unit of labor) is given by MRTS = MPL / MPK = K / (2L) a) Assume that this firm wants to spend $300 for the inputs (total cost of factors of production). The wage per each unit of labor is $10, and the price of each unit of capital is $5. What quantities of labor and capital will he use? How many units of outputs will be produced? Sketch the equilibrium point (on a Cartesian graph with units of capital on Y axis and units of labor on X axis) using the isocost and isoquant curves

Answer #1

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....

a. A firm uses only two inputs: capital (K) and labor
(L).Currently, the firm’s choice of capital (K) and labor (L) are
such that marginal product of capital is 80 and the marginal
product of labor is 10. If one put Labor on the x-axis, derive the
slope of the firm’s isoquant given the information above (include
the formula you use to do this).
b. The price of capital (Pk) is $40 and the price of labor (PL)
is $20....

A firm uses two inputs, capital K and labor L, to produce output
Q that can be sold at a price of $10. The production function is
given by Q = F(K, L) = K1/2L1/2 In the short run, capital is fixed
at 4 units and the wage rate is $5, 1. What type of production
function is F(K, L) = K1/2L1/2 ? 2. Determine the marginal product
of labor MPL as a function of labor L. 3. Determine the...

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 has the production function:
Q = L 1 2 K 1 2
Find the marginal product of labor (MPL), marginal
product of capital (MPK), and marginal rate of technical
substitution (MRTS).
Note: Finding the MRTS is analogous to finding the
MRS from a utility function:
MRTS=-MPL/MPK. Be sure to simplify your
answer as we did with MRS.
A firm has the production function:
Q = L 1 2 K 3 4
Find the marginal product of labor (MPL),...

Suppose Cool T-Shirts Co produces T-shirts and employs labor (L)
and capital (K) in production. Suppose production function for Cool
T-Shirts Co is Q=K*L, and Cool T-Shirts Co wants to produce Q=625.
Suppose marginal product of labor (MPL) and marginal product of
capital (MPK) are as follows: MPL=K and MPK=L. Suppose Cool
T-Shirts Co pays workers $10 per hour (w=$10) and interest rate on
capital is $250 (r=250). What is the cost-minimizing input
combination if Cool T-Shirts Co wants to...

When capital increases by ?K units and labor increases
by ?L units, output (?Y) increases by:
A.
MPL + MPK units.
B.
(MPL × ?K) + (MPK × ?K)
units.
C.
(MPK × ?K) + (MPL × ?L)
units.
D.
?K + ?L units.

a firm uses (K) and labor (L) and these are perfect
substitutes. one unit of output can be produced using 1 unit of
capital or 2 units of labor. What is the equation for the
production function? show the isoquant map

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?...

2. Consider the following production functions, to be used in
this week’s assignment:
(A) F(L, K) = 20L^2 + 20K^2
(B) F(L, K) = [L^1/2 + K^1/2]^2
a (i) Neatly draw the Q = 2,000 isoquant for a firm with
production function (A) given above, putting L on the horizontal
axis and K on the vertical axis. As part of your answer, calculate
three input bundles on this isoquant. (ii) Neatly draw the Q = 10
isoquant for a firm...

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