Question

**14. A firm’s production function is Q =
12*L ^{0.5}*K^{0.5}. Input prices are $36 per labor
unit and $16 per capital unit. The product’s price is P = $10.
(Given: MP(L) = 6*L^{-0.5}*K^{0.5}; and MP(K) =
6*L^{0.5}*K^{-0.5})**

In the short run, the firm has a fixed amount of capital, K = 9. Calculate the firm’s profit-maximizing employment of labor. (Note: short term profit maximization condition: MPR(L) = MC(L) )

In the long run, suppose the firm
could adjust both labor and capital. Calculate the least cost input
proportions (i.e. K/L or L/K). (Note : In the long run the least
cost input condition : MP(L)/P_{L} =
MP(K)/P_{K}.)

Answer #1

3. Consider the production function, Q = [L0.5 +
K0.5] 2 . The marginal products are given as
follows: MPL = [L0.5 + K0.5] L-0.5
and MPK = [L0.5 + K0.5] K-0.5 and
w = 2, r = 1.
A). what is the value of lambda
B). Does this production function exhibit increasing, decreasing
or constant returns to scale?
C).Determine the cost minimizing value of L
D).Determine the cost minimizing value of K
E).Determine the total cost function
F).Determine the...

1. A firm production function is given by q(l,k) =
l0.5·k0.5, where q is number of units of
output produced, l the number of units of labor input used and k
the number of units of capital input used. This firm profit
function is π = p·q(l,k) – w·l – v·k, where p is the price of
output, w the wage rate of labor and v the rental rate of capital.
In the short-run, k = 100. This firm hires...

A firm has production function
q=10*(L0.5)*(K0.5). In the short
term, capital K is fixed at 9.
(a) What is the multiplicative constant term in the firm's
short-run inverse demand for labor?
(b) What is the multiplicative constant term in the firm's
short-run direct demand for labor?
(c) What is the multiplicative constant term in the firm's
long-run inverse demand for labor?

A firm’s production function is q = 10KL with per unit input
prices for labor w = 3 and capital r = 2. Support your answers with
a graph of isoquant-isocosts.
a. Calculate the least-cost input combination of L and K to
produce 60 units of output.
b. Suppose the wage decreases to $2. How does this affect input
use holding constant output at 60?
c. What are the total costs of producing the two output levels
in parts (a)...

A firm produces good Q using inputs L & K. The firm’s
production function is X = 20L^0.5 + 11K. The
price of K is $P_K a unit and the price of L is $P_L a unit, and in
the short‐run, the capital input is
fixed at 3 units.
a. If the firm needs an output of X_1 in the short‐run, what is the
firm’s total cost and marginal
cost of production?
b. What is the firm’s fixed cost and...

A competitive firm’s production function is
Q = 5 + 20L - .5L2 + 40K – K2,
and its demand function is
PQ = MRQ = d = $6.
The input prices of L and K are PL = $6 and
PK = $12. Use Excel to find the profit-maximizing and
cost minimizing amounts of L and K to employ.
L = _______
K = _____
Find the cost minimizing ratios of
marginal product to input prices:
Ratios...

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...

Firm B’s production function is q = min {8L,
10K} where L is the quantity of labor and
K is the quantity of capital used to produce output
q. Let PL and PK
denote price of labor and price of capital, respectively. Derive
Firm B’s long-run total cost function. Show your work.

A firm produces output (y), using capital (K) and labor (L). The
per-unit price of capital is r, and the per-unit price of labor is
w. The firm’s production function is given by, y=Af(L,K), where A
> 0 is a parameter reflecting the firm’s efficiency.
(a) Let p denote the price of output. In the short run, the
level of capital is fixed at K. Assume that the marginal product of
labor is diminishing. Using comparative statics analysis, show that...

A firm’s production function is Q = K^0.5L^0.5. The
prices of the applied inputs are pK = $2, pL = $2. The firm would
like to know the maximum output that can be produced for $8,000.
Find the combination of inputs that maximizes output for a cost of
$8,000, the amount of output that can be produced, and identify the
expansion path.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 3 minutes ago

asked 13 minutes ago

asked 14 minutes ago

asked 26 minutes ago

asked 27 minutes ago

asked 34 minutes ago

asked 36 minutes ago

asked 36 minutes ago

asked 36 minutes ago

asked 45 minutes ago

asked 57 minutes ago

asked 58 minutes ago