Question

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 variable cost?

Answer #1

A firm produces good X and has a production function X =
2L^0.25K^0.25, where L and K are the inputs.
Assume that the price of L is $6 and the price of capital is $12.
Let the firm have a target output
of X1 units.
a. Find the firm’s conditional demand for labor and capital.
b. Find the firm’s total cost function.
c. What is the firm’s marginal cost?

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...

A firm uses two inputs, capital K and labor L, to produce output
Q that can be sold at a price of $10. The production function is
given by Q = F(K, L) = K1/2L1/2 In the short run, capital is fixed
at 4 units and the wage rate is $5, 1. What type of production
function is F(K, L) = K1/2L1/2 ? 2. Determine the marginal product
of labor MPL as a function of labor L. 3. Determine the...

A firm has the following production function:
q=5LK^0.5+2L^2K-L^3K
What is its short-run production function if capital is fixed at
K=9?
What are the firm’s marginal product of labour and average
product of labour in the short run?
Show that the firm’s elasticity of output with respect to labour
in the short run is a function of marginal product of labour and
average product of labour. Calculate the short-run elasticity of
output with respect to labour

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...

14. A firm’s production function is Q =
12*L0.5*K0.5. 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*K0.5; and MP(K) =
6*L0.5*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...

a firm produces a product with labor and capital as inputs. The
production function is described by Q=LK. the marginal products
associated with this production function are MPL=K and MPK=L. let
w=1 and r=1 be the prices of labor and capital, respectively
a) find the equation for the firms long-run total cost curve
curve as a function of quantity Q
b) solve the firms short-run cost-minimization problem when
capital is fixed at a quantity of 5 units (ie.,K=5). derive the...

Consider a firm using the production technology given by q =
f(K, L) = ln(L^K)
If capital is fixed at K = 2 units in the short run, then what
is the profit maximizing allocation of output if the price of
output and respective input prices of labor and capital are given
by (p, w, r) = (2, 1, 5)?

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...

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...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 19 minutes ago

asked 20 minutes ago

asked 25 minutes ago

asked 28 minutes ago

asked 30 minutes ago

asked 35 minutes ago

asked 51 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago