Question

for a firm with Cobb-Douglas production function

q = f (k, L) = k ^ (1/2) L ^ (1/2)

calculate the total, average and marginal cost.

Answer #1

q = k^{1/2}L^{1/2}

Total cost (C) = wL + rK

Total cost is minimized when MPL/MPk = w/r

MPL =
q/L
= (1/2) x (k/L)^{1/2}

MPk =
q/k
= (1/2) x (L/k)^{1/2}

MPL/MPk = k/L = w/r

wL = rK

Therefore,

L = rK/w

k = wL/r

Substituting in production function,

q = L^{1/2}(wL/r)^{1/2} =
L^{1/2}L^{1/2}(wL/r)^{1/2} = L x
(w/r)^{1/2}

L = q x (r/w)^{1/2}

k = wL/r = (w/r) x q x (r/w)^{1/2} = q x
(w/r)^{1/2}

Substituting in total cost function,

C = wL + rK = w x q x (r/w)^{1/2} + r x q x
(w/r)^{1/2} = q x (wr)^{1/2} + q x
(wr)^{1/2} = **2q x (wr) ^{1/2} [Total
cost]**

**Average cost = C/q = 2 x (wr) ^{1/2}**

**Marginal cost =** dC/dq = **2 x
(wr) ^{1/2}**

Consider the Cobb-Douglas production function F (L, K) =
(A)(L^α)(K^1/2) , where α > 0 and A > 0.
1. The Cobb-Douglas function can be either increasing, decreasing
or constant returns to scale depending on the values of the
exponents on L and K. Prove your answers to the following three
cases.
(a) For what value(s) of α is F(L,K) decreasing returns to
scale?
(b) For what value(s) of α is F(L,K) increasing returns to
scale?
(c) For what value(s)...

1. In previous problem, the given Cobb-Douglas
production function was Q = 6 L½
K½ and the cost function was given as:
C = 3L + 12K. For $384
of total cost, the optimum labor usage was determined to be 64, and
capital of 16.
a. If the cost
function now changes to C = 3L + 18K, it implies that the total
cost will become $480. Compute the new level of total cost for Q =
192. Can...

2. Consider a Cobb-Douglas production function Q = A . L^a . K^b
. Answer the following in terms of L, K, a, b
(a) What is the marginal product of labour ?
(b) What is the marginal product of capital ?
(c) What is the rate of technical substitution (RTS L for
K)?
(d) From the above what is the relation between K L and RT
SL,K?
(e) What is the relation between ∆ K L ∆RT SL,K (f)...

para uma firma com função de produção Cobb-Douglas
q = f(k,L) = k^(1/2) L^(1/2)
calcule o custo total , medio e marginal.

1. Using the Cobb-Douglas production function:
Yt =
AtKt1/3Lt2/3
If K = 27, L = 8 A = 2, and α = 1/3, what is the value of Y?
(For K and L, round to the nearest whole number) ______
2. If Y = 300, L = 10, and α = 1/3, what is the marginal product
of labor? ______
3. Using the values for Y and α above, if K = 900, what is the
marginal product of capital?...

(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.

Normalize the cobb douglas production function Y = F (K,L) =
K1/2L1/2 in terms of output per unit of
labor. Note that this function does not have technology change.
Your answer should be in terms of y = f(k) =
Answer is y = (K/L)1/2 = k1/2
Please show step by step how to do this including the
derivate and exponent laws you use

Suppose that a firm has the Cobb-Douglas production function Q =
12K ^ (0.75) L^ (0.25). Because this function exhibits (constant,
decreasing, increasing) returns to scale, the long-run average cost
curve is (upward-sloping, downward-sloping, horizontal), whereas
the long-run total cost curve is upward-sloping, with (an
increasing, a declining, a constant) slope.
Now suppose that the firm’s production function is Q =
KL. Because this function exhibits (constant, decreasing,
increasing) returns to scale, the long-run average cost curve is
(upward-sloping, downward-sloping,...

Given the Cobb-Douglas production function q = 2K 1 4 L 3 4 ,
the marginal product of labor is: 3 2K 1 4 L 1 4 and the marginal
product of capital is: 1 2K 3 4 L 3 4 .
A) What is the marginal rate of technical substitution
(RTS)?
B) If the rental rate of capital (v) is $10 and the wage rate
(w) is $30 what is the necessary condition for cost-minimization?
(Your answer should be...

In the Cobb-Douglas production function :
the marginal product of labor (L) is equal to β1
the average product of labor (L) is equal to β2
if the amount of labor input (L) is increased by 1 percent,
the output will increase by β1 percent if the amount of Capital
input (K) is increased by 1 percent,
the output will increase by β2 percent
C and D

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 4 minutes ago

asked 4 minutes ago

asked 9 minutes ago

asked 10 minutes ago

asked 10 minutes ago

asked 10 minutes ago

asked 18 minutes ago

asked 18 minutes ago

asked 19 minutes ago

asked 19 minutes ago

asked 23 minutes ago

asked 23 minutes ago