Question

A firm produces output according to the production function.
Q=sqrt(L*K) The

associated marginal products are MPL = .5*sqrt(K/L) and MPK =
.5*sqrt(L/K)

(a) Does this production function have increasing, decreasing, or
constant marginal

returns to labor?

(b) Does this production function have increasing, decreasing or
constant returns to

scale?

(c) Find the firm's short-run total cost function when K=16. The
price of labor is w and

the price of capital is r.

(d) Find the firm's long-run total cost function when r=9 and
w=1.

Answer #1

Consider the production function Q = f(L,K) = 10KL / K+L. The
marginal products of labor and capital for this function are given
by
MPL = 10K^2 / (K +L)^2, MPK = 10L^2 / (K +L)^2.
(a) In the short run, assume that capital is fixed at K = 4.
What is the production function for the firm (quantity as a
function of labor only)? What are the average and marginal products
of labor? Draw APL and MPL on one...

3. Consider the production function, Q = [L0.5 +
K0.5] 2 . The marginal products are given as
follows: MPL = [L0.5 + K0.5] L-0.5
and MPK = [L0.5 + K0.5] K-0.5 and
w = 2, r = 1.
A). what is the value of lambda
B). Does this production function exhibit increasing, decreasing
or constant returns to scale?
C).Determine the cost minimizing value of L
D).Determine the cost minimizing value of K
E).Determine the total cost function
F).Determine the...

(2) Consider the production function f(L, K) = 2K √ L. The
marginal products of labor and capital for this function are given
by MPL = K √ L , MPK = 2√ L. Prices of inputs are w = 1 per hour of
labor and r = 4 per machine hour. For the following questions
suppose that the firm currently uses K = 2 machine hours, and that
this can’t be changed in the short–run.
(e) What is the...

(a) Show that the following Cobb-Douglas production function,
f(K,L) = KαL1−α, has constant returns to scale.
(b) Derive the marginal products of labor and capital. Show
that you the MPL is decreasing on L and that the MPK is decreasing
in K.

An electronics plant’s production function is Q = L 2K, where Q
is its output rate, L is the amount of labour it uses per period,
and K is the amount of capital it uses per period.
(a) Calculate the marginal product of labour (MPL) and the
marginal product of capital (MPK) for this production function.
Hint: MPK = dQ/dK. When taking the derivative with respect to K,
treat L as constant. For example when Q = L 3K2 ,...

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...

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...

Wheat is produced according to the production function Q = 100
K^0.8 L^0.2
a. Beginning with a capital input of 4 and a labor input of 49,
show that the marginal product of labor and the marginal product of
capital are both decreasing.
b. Does this production function exhibit increasing, decreasing,
or constant returns to scale?
please explain in 4 sentences thank you!

Answer the following questions about the producer’s production
function: Q = 2K1/2L2
Does the production function display increasing, constant, or
decreasing returns to scale? [Prove your answer by increasing all
inputs by a factor of c in your analysis.]
Find MPL if capital is fixed at K0=9 and
determine whether the production process follows the law of
diminishing returns (LDR) to labor.
If input prices are r=5 and w=4 for capital and labor,
respectively, and suppose MPK=40 and the firm...

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),...

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