Question

What is the expansion path for the firm with the production function of f(L, K) = (L+1)K

Answer #1

The production function is given as . The different equilibrium points of cost minimization, or profit maximization, of different quantities and isocost lines corresponds to the expansion path for the firm.

Suppose price of labor is w while price of capital is r, hence the cost fucntion will be as . The optmila bundle will be where the marginal rate of technical substitution (MRTS) will be equal to the slope of the isocost line. The MRTS can be found as or (as MRTS will be for a constant quantity) or or . The slope of the isocost line can be found as or or or . Hence, the optimal bundle will be at where , ie or , which is the expansion path. It can be further written as , as the equation of the expansion path.

A firm’s production function is Q(L,K) = K^1/2 + L. The firm
faces a price of labor, w, and a price of capital services, r.
a. Derive the long-run input demand functions for L and K,
assuming an interior solution. If the firm must produce 100 units
of output, what must be true of the relative price of labor in
terms of capital (i.e. w/r) in order for the firm to use a positive
amount of labor? Graphically depict this...

Suppose one firm has production function f(K, L) =√K+√L, and
another firm has the production function f(K, L) = (√K+√L)^(.3).
Will these firms have the same supply functions?
Show your work

If a firm has the production function f(L,K) =(L+1)K, and
currently uses no units of labor, but K=3 units of capital, what is
its marginal rate of
substitution?Aretherevaluesofwandrsuchthatthischoiceoffactorinputs
is optimal?

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.

A firm has production function y = f(K,L), where y is output, K
is capital, and L is labour. We have:
a. f(K,L) = K^0.4 + L^0.4
b. f(K,L) = (K^0.4)(L^0.4)
What are the firm's production function degree of
homogeneity?
I know the answer is 0.4 for A and for B it is 0.8.
But I don't know how to get those answers. I know m = degree of
homogeneity. I'm guessing they found A from m = 0.4. For...

For a firm with production function f(L,K)=√L+√K, find its cost
function for arbitrary values of w and r. That is,find a formula
for the cost of producing q units that includes q,and also w and
r,as variables. Also find marginal and average cost,and draw a plot
that shows both cost functions in the same graph.

For a firm with production function f(L,K)=√L+√K, find its cost
function for arbitrary values of w and r. That is,find a formula
for the cost of producing q units that includes q,and also w and
r,as variables. Also find marginal and average cost,and draw a plot
that shows both cost functions in the same graph.

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...

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: ...

(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...

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