Question

Consider that the production function Q= F(K,L) = 3K + 9L

Determine the mix of output that minimizes costs when the wage is $20 and the price of capital is $30.

Answer #1

Consider a firm which has the following production function
Q=f(L,K)=4?LK
(MPL=2?(K/L) and MPK=2?(L/K).
(a) If the wage w= $4 and the rent of capital r=$1, what is the
least expensive way to produce 16 units of output? (That is, what
is the cost-minimizing input bundle (combination) given that
Q=16?)
(b) What is the minimum cost of producing 16 units?
(c) Show that for any level of output Q, the minimum cost of
producing Q is $Q.

Suppose that the production function for Hannah and Sam’s home
remodeling business is
Q=F(L,K)Q=F(L,K)
Q=10L0.2K0.3.Q=10L0.2K0.3.
The wage rate is $1,500 per week and the cost of renting a unit of
capital is $1,000 per week. What is their cost function?
Instructions: Enter your answer as a whole
number.
C(Q) = Q2.

Suppose that Hannah and Sam have the production function
Q=F(L,K)Q=F(L,K)
Q=10L0.5K0.5.Q=10L0.5K0.5.
The wage rate is $1,000 per week and a unit of capital costs $4,000
per week.
a. True or false? If we plot L along the horizontal axis
and K along the vertical axis, then Hannah and Sam's
output expansion path is a straight line that passes through the
origin and has a slope of 0.25.
TrueFalse
b. What is their cost function? Choose from the options
below.
A:400QB:200Q2C:2,000Q0.5D:200Q+400Q2A: ...

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...

Consider a firm using the production technology given by q =
f(K, L) = ln(L^K)
If capital is fixed at K = 2 units in the short run, then what
is the profit maximizing allocation of output if the price of
output and respective input prices of labor and capital are given
by (p, w, r) = (2, 1, 5)?

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 ,...

Consider the following production function: x = f(l,k) =
Albkbwhere x is the output, l is the labour
input, k is the capital input, and A, b are positive constants.
(a) Set up the cost minimization problem and solve for the first
order conditions using the Lagrange Method. Let w be the wage rate
and r the rental rate of capital.
(b) Using your answer in (a), find how much labour and capital
would the firm use to produce x...

1. Consider the production
function q=K2L0.5
a) Find the cost minimizing quantities of K and L for q = 100, r
as the price of K and w as the price of L.
b) Find the cost minimizing quantities of K and L for q = 1000,
r as the price of K and w as the price of L. Explain whether or not
the output expansion [change from part a) to part b)] is labor
saving or capital saving.

firm can manufacture a product according to the production
function
Q = F (K, L) = K0.75 L 0.25 a. What is this type of function
called? Are the inputs perfect substitutes or should they be used
in a fixed proportion instead? © (3pts) b. Suppose capital is fixed
at 81 units. If the firm can sell its output at a price of $200 per
unit and wage is $50, how many units of labor should the firm hire
in...

Suppose that Hannah and Sam have the production function
Q=F(L,K) Q=10L0.5K0.5. The wage rate is $1,000 per week and a unit
of capital costs $4,000 per week.
a. True or false? If we plot L along the horizontal axis and K
along the vertical axis, then Hannah and Sam's output expansion
path is a straight line that passes through the origin and has a
slope of 0.25.
b. What is their cost function? Choose from the options
below.
A:400Q
B:200Q^2...

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