Question
In: Economics
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 wage rate is $15 or $25 or $35 per hour?
Solutions
Rahul Sunny answered 2 years agoRelated Solutions
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...
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...
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...
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?
Capital and labor are the only two inputs for the following production process. Capital is fixed...
Capital and labor are the only two inputs for the following
production process. Capital is fixed at 4 units, which costs 50
dollars each unit per day. Workers can be hired for 100 each per
day. Complete the following table and plot the marginal cost (MC),
average total cost (ATC), average variable cost (AVC), average
fixed cost (AFC) on the same graph.
The quantity of labor input
Total output per day
AFC
AVC
ATC
MC
0
0
1
100...
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...
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...
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 that production of widgets requires capital and labor. The production function is constant returns to...
Suppose that production of widgets requires capital and labor.
The production function is constant returns to scale and capital
investment is sunk. There are no other barrier to entry. Is the
investment in sunk capital a barrier to entry? Explain. What will
the market equilibrium be if there are many possible entrants?
Suppose that an economy has a Cobb-Douglas production function with three inputs. K is capital (the...
Suppose that an economy has a Cobb-Douglas production function
with three inputs. K is capital (the number of machines), L is
labor (the number of workers), and H is human capital (the number
of college degrees among workers). Markets for output and factors
of production are both competitive. The production function is Y =
K^1/3*L^1/3*H^1/3
1. Prove that this technology shows constant returns to
scale.
2. Solve the competitive firm’s profit maximization problem by
deriving the first-order conditions.
3. An...
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