Question

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?

Answer #1

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.

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...

A firm produces output according to the production function.
Q=sqrt(L*K) The
associated marginal products are MPL = .5*sqrt(K/L) and MPK =
.5*sqrt(L/K)
(a) Does this production function have increasing, decreasing, or
constant marginal
returns to labor?
(b) Does this production function have increasing, decreasing or
constant returns to
scale?
(c) Find the firm's short-run total cost function when K=16. The
price of labor is w and
the price of capital is r.
(d) Find the firm's long-run total cost function...

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

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 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 a firm’s production function is given by Q = L1/2*K1/2.
The Marginal Product of Labor and the Marginal Product of Capital
are given by:
MPL = (K^1/2)/2L^1/2 & MPK = (L^1/2)/2K^1/2)
a) (12 points) If the price of labor is w = 48, and the price of
capital is r = 12, how much labor and capital should the firm hire
in order to minimize the cost of production if the firm wants to
produce output Q = 10?...

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?

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...

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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