Question
In: Economics
A firm produces a product with labor and capital as inputs. Its production function is described...
A firm produces a product with labor and capital as inputs. Its production function is described by Q(L,K) = L^1/2 K^1/2. Let w and r be the prices of labor and capital, respectively.
a. Derive the firm’s long-run total cost and long-run marginal cost functions.
b. Assume capital is fixed at 4 units in the short-run and derive the firm’s short-run total cost and short-run average variable cost functions.
c. Rewrite your short-run and long-run total cost functions (for the grader) and then graphically depict both on the same graph.
d. In general, how do the long-run total cost and short-run total cost of producing each level of output compare? Explain when and why the short-run total cost would equal the long-run total cost.
Solutions
Rahul Sunny answered 2 years agoRelated Solutions
8.13) A firms produces a product with labor and capital. its production function is described by...
8.13) A firms produces a product with labor and capital. its
production function is described by Q=L+K. The marginal products
associated with this production function are MPL =1 and MPK=1. Let
w=1, and r=1 be the prices of labor and capital respectively.
a) fund the equation for the firms long-run total cost curve as
a function of quantity Q when the prices of labor and capital are
w=1 and r=1.
b) find the solution to the firms short-run cost-minimization
problem...
Assume a firm has 2 inputs in its production function, labor and capital, and can adjust...
Assume a firm has 2 inputs in its production function, labor
and capital, and can adjust the amount of either one of these
inputs in order to increase output. Assume the marginal product of
a unit of capital is always twice as high as the marginal product
of a unit of labor (this is true regardless of how much labor and
how much capital the firm employs). If the firm wanted to expand
output, would they ever do so by...
Suppose there are two inputs in the production function, labor and capital, and these two inputs...
Suppose there are two inputs in the production function, labor
and capital, and these two inputs are perfect substitutes. The
existing technology permits 5 machines to do the work of 2 workers.
So the production function is f(E, K) = 2K + 5E. The firm wants to
produce q units of output, where q > 0 is some number. Suppose
the price of capital is $10 per machine per hour. What combination
of inputs will the firm use if the...
Suppose there are two inputs in the production function, labor and capital, and these two inputs...
Suppose there are two inputs in the production function, labor
and capital, and
these two inputs are perfect substitutes. The existing
technology permits 3 machines to do the work of 2
worker. So F(E,K)=2K+3E. The firm wants to produce 60 units of
output. Suppose the price of capital is
$10 per machine per hour. What combination of inputs will the
firm use if the wage rate is $10 or $15 or
$20 per hour? What if the firm wants to...
A firm uses two inputs in production: capital and labor. In the short run, the firm...
A firm uses two inputs in production: capital and labor. In the
short run, the firm cannot adjust the amount of capital it is
using, but it can adjust the size of its workforce.
--
If the cost of renting capital increases, which of the following
curves will be affected? (Check all answers that apply).
--
Average variable cost
Marginal cost
Average fixed cost
Average total cost
2 points
QUESTION 2
If the cost of hiring workers increases, which...
Suppose there are two inputs in the production function, labor and capital, which are substitutes. The...
Suppose there are two inputs in the production function, labor
and capital, which are substitutes. The current wage is $10 per
hour and the current price of capital is $25 per hour.
Given the following information on the marginal product of
labor and the marginal product of capital, find the firm’s
profit-maximizing input mix (i.e. number of workers and units of
capital) in the long-run. Show your work and explain.
L
MPL
K
MPK
1
125
1
130
2
100...
a) The standard economic model of a production function where capital and labor are inputs into...
a) The standard economic model of a production function where
capital and labor are inputs into production, with both earning a
return according to their marginal contribution to the value of
output
b) The Marxian approach of production as a labor process, where
the value added is distributed between the capitalist and the
worker.
What is the most important difference in conclusions drawn from
the the two approaches to production?
Consider a firm which produces according to the following production function by using labor and capital:...
Consider a firm which produces according to the following
production function by using labor and capital:
f(l,k) = k1/4 / 1/2
(a) Solve the cost minimization problem of this firm for the
given wage rate, w and the rental rate of capital,v.
(b) Derive the cost function of the firm.
(c) Solve the profit maximization of the firm for a given price
p, and derive the supply function.
(d) Derive the profit function of the firm.
(e) Suppose demand for...
Consider a firm which produces according to the following production function by using labor and capital:...
Consider a firm which produces according to the following
production function by using labor and capital: f(l,k) =
K1/2 L1/2
(a) Solve the cost minimization problem of this firm for the
given wage rate, w and the rental rate of capital,v. Derive the
long-run total cost function of the firm.
(b) Derive the short-run total cost, the short-run average cost,
the short- run marginal cost function of the firm under the
assumption that capital is the fixed input.
(c) What...
Consider a production function of two inputs, labor and capital, given by Q = (√L +...
Consider a production function of two inputs, labor and capital,
given by Q = (√L + √K)2. Let w = 2 and r = 1. The marginal products
associated with this production function are as follows:MPL=(√L +
√K)L-1/2MPK=(√L + √K)K-1/2
a) Suppose the firm is required to produce Q units of output.
Show how the cost-minimizing quantity of labor depends on the
quantity Q. Show how the cost-minimizing quantity of capital
depends on the quantity Q.
b) Find the equation...
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