Question

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?

Answer #1

Suppose a firm has a production function given by q = 3L +
K.
The firm can purchase labor, L at a price w = 24, and capital, K
at a price of r = 5.
What is the firm’s total cost function?

Suppose that a firm's production function is Q =
10L1/2K1/2. The cost of a unit of labor (i.e.
the wage) is $20 and the cost of a unit of capital is $80.
a. What are the cost minimizing levels of capital and labor if
the firm wishes to produce 140 units of output?
b. Illustrate your answer for part (a) on a well-labeled diagram
that shows the firm's production isoquant and isocost equation.

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...

The firm’s production function is given by q =
4K0.5L0.5, where q denotes the output
(measured as the number of research reports per month). The firm
hires people (“labor”, measured in hours of work) and rents office
space (“capital”, measured in sq. feet). The marginal product of
labor is given by MPL = 2K0.5L–0.5
and the marginal product of capital is given by MPK =
2L0.5K–0.5.
1. Find the cost-minimizing levels of capital (K*)
and labor (L*) required to produce...

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.

Suppose a firm's production function is given by LaTeX:
Q\left(L,K\right)=4L^{0.65}K^{0.35}Q ( L , K ) = 4 L^0.65 K^0.35.
The wage is w= 25/ hour and the rent for capital is r= 25/hour. To
produce 350 units per hour, what is the minimum hourly cost of
production? Enter to the nearest $0.1. [number only, no $ sign]

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?

Suppose that a firm has production function F(L, K) = L1/4 K3/4
for producing widgets, the wage rate for labor is w = $32, and the
rental rate of capital is r = $6. Suppose the firm has an order to
produce 40 units of output.
a) Carefully write out the firm’s cost minimization problem,
using information specific to this problem.
b) Express two equations—specific to this problem—that the
optimal solution satisfies.
c) Solve these two equations for L* and...

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 a firm’s production function is given by Q = L 1/2 , K
1/2.
a) Suppose the firm has a fixed cost FC=6, the price
of labor is w = 64 and the price of capital is r = 4. Derive the
firm’s total cost function, TC(Q).
b) What is the firm’s marginal cost?
c) Graph the firm’s isoquant for Q = 20 units of
output. On the same graph, sketch the firm’s isocost line
associated with the total...

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