Question
In: Economics
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 this good is given by the following relation: p = 272−2q
Now, solve for the market equilibrium price level (where demand equals supply) if w = 1 and v = 2. (f) Decide whether the production function exhibits constant, increasing or decreasing returns to scale.
Solutions
Rahul Sunny answered 8 months agoRelated Solutions
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...
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...
Consider the following production function using capital (K) and labor (L) as inputs. Y = 10.K0.5L0.5....
Consider the following production function using capital (K) and
labor (L) as inputs. Y = 10.K0.5L0.5. The marginal product of labor
is (MPL=) 5.K0.5/L0.5, and marginal product of capital (MPK) =
5.L0.5/K0.5.a. If K = 100 and L=100 what is the level of output
Y?b. If labor increases to 110 while K=100, what is the level of
output?c. If labor increases to 110 while K=100, what is the
marginal product of labor?d. If labor increases to 120 while K=100,
what...
A firm produces plastic water bottles according to the production function ? = ?(?,?) = ?...
A firm produces plastic water bottles according to the
production function ? = ?(?,?) = ? 2?, where ? is the number of
water bottles produced, ? is the quantity of labor employed and ?
is the quantity of capital. The associated marginal product
functions are ??? = 2?? and ??? = ? 2 . The cost per unit of labor
and capital are ? = $4 and ? = $2, respectively.
1) If this firm wants to produce a...
A firm produces output using capital (K) and labor (L). Capital and labor are perfect complements...
A firm produces output using capital (K) and labor (L). Capital
and labor are perfect complements and 1 unit of capital is used
with 2 units of labor to produce 1 unit of output. Draw an example
of an isoquant. If wages and rent are $2 and $3, respectively, what
is the Average Total Cost?
A firm has a production function given by Q=4KL where K, L and Q
denote capital, labor, and output, respectively. The firm wants to
produce...
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...
A firm produces gizmos according to the production function Q =10KL , where Q is the...
A firm produces gizmos according to the production function Q
=10KL , where Q is the quantity of gismos produced, K is the
quantity of capital rented and L is the quantity of labour hired.
The manager has been given a production target: Produce 9,000
gizmos per day. He is informed that the daily rental price of
capital is $400 per unit and the wage rate is $200 per day. a)
Currently, the firm has 10 units of capital. How...
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...
2. A firm uses labor and machines to produce output according to the production function f...
2. A firm uses labor and machines to produce output according to
the production function f (L,K) = 2 L K ,where L is the number of
units of labor used and K is the number of machines. The cost of
labor is $40 per unit and the cost of using a machine is $10. The
Long Run Decision of the Firm
(a) Write down the equation for an isocost line for this firm.
What is the slope of these...
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...
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- what are the fundamental similarity and differences between gap and dgap?
- Maria Gonzales is a 57-year-old operating room nurse who works full-time at a local hospital. She...
- Use the bond term's below to answer the question Maturity 7 years Coupon Rate 4% Face...
- What experience have you had with Organization Development or with Change Management? Describe the organization, the...
- 1. Renfro Rentals has issued bonds that have a 12% coupon rate, payable semiannually. The bonds...
- Given an array of positive integers a, your task is to calculate the sum of every...
- Define “culture.” Software is defined by the Merriam-Webster Dictionary as "the programs that run on a...
ADVERTISEMENT