Question

2. A firm has production function Q = k^1/2L^1/2 and faces a wage for the labor input w = 1 and a rental price of capital r = 9

a. The policy of the Federal Reserve brings the rental price of capital to r = 4 Graph the change of the cost minimizing equlibrium explaining the type of substitution that is happening.

b. Compute the new cost function. Suppose a monopoly and show graphically if after this change in the cost function is going to produce more or less.

Answer #1

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 the firm's production function is Q = K 1/3L 2/3 . a. If
the rental rate of capital R = $30 and the wage rate W = $40, what
is the cost-minimizing capital-to-labor ratio? b. If the rental
rate of capital R is $35 and the wage rate W is $70, how many units
of labor and capital should the firm use to produce 12 units of
output?

Suppose that firm face the following production function: Q =
2L^1/2 K^1/2 and firm has K upper bar (is fixed) units of capital
in short run. Suppose also that price of labor (W) is 16 and
pricepf capital (r) is 1 and firm's objective output is 144. At
what level K upper bar short run total cost would be equal to the
long run total cost?

Given production function: Q=L3/5K1/5.
Where L is labor, K is capital, w is wage rate, and r is rental
rate.
What kinds of returns to scale does your firm face?
Find cost minimizing level of L and K, and long run cost
function.

The firms production function is: Q=2L^2/3 K^1/3
A) Suppose the firm wants to determine the cost minimizing
combination for L and K for any given values of q, w, and r. Solve
for the the firms factor demand functions for L and K (i.e. express
the optimal quantity of L and K in terms of W, r and Q)
B) Using these factor demand functions, solve for the firm's
long run cost function.

A firm produces a product with labor and capital. Its production
function is described by Q = min(L, K). Let w and r be the prices
of labor and capital, respectively.
a) Find the equation for the firm’s long-run total cost curve as
a function of quantity Q and input prices, w and r.
b) Find the solution to the firm’s short-run cost minimization
problem when capital is fixed at a quantity of 5 units (i.e., K =
5). Derive...

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.

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.

A firm’s production function is Q = min(K , 2L), where Q
is the number of units of output produced using K units of capital
and L units of labor. The factor prices are w = 4 (for labor) and r
= 1 (for capital). On an optimal choice diagram with L on the
horizontal axis and K on the vertical axis, draw the isoquant for Q
= 12, indicate the optimal choices of K and L on that isoquant,...

Suppose a firm has a production function q = f(L, K) =2L + 4K,
and the factor prices are w = $2 and r = $2. What is the minimum
cost at which the firm is able to produce 20 units of output?
a. $10 b. $30 c. $45 d. $100 e. $50
please explain why

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