Question
In: Economics
Schmutz Auto Wash provides car washes. Its production function is ? = 2?1/2(? - 1)1/2 where...
Schmutz Auto Wash provides car washes. Its production function
is ? = 2?1/2(? - 1)1/2
where ? is cars washed per day, ? is daily hours of labor input,
and ? is daily usage of capital inputs. The price of a unit of
capital input is $48. The price of a unit of labor input is $16. In
the short run, Schmutz has 4 units of capital input installed (so ?
= 4).
a). Find Schmutz’s short run daily total cost function, short run daily variable cost function, and short run daily fixed costs.
b). Find Schmutz’s short run marginal cost function, short run average variable cost function, and short run total cost function.
c). Suppose that the market for car washes is perfectly competitive and the going market price of a car wash is ?. Find Schmutz’s short run daily supply function, including its shutdown price.
d). Find Schmutz’s short run daily quantity supplied, producer surplus, and profit if ? = 40.
Solutions
Rahul Sunny answered 2 years agoRelated Solutions
Schmutz Auto Wash provides car washes. Its production function is ? = 2?1/2(? - 1)1/2 where...
Schmutz Auto Wash provides car washes. Its production function
is ? = 2?1/2(? - 1)1/2
where ? is cars washed per day, ? is daily hours of labor input,
and ? is daily usage of capital inputs. The price of a unit of
capital input is $48. The price of a unit of labor input is $16. In
the short run, Schmutz has four units of capital input installed
(so ? = 4).
a). Find Schmutz’s short run daily total...
1. A profit-maximizing, monopolistically competitive car wash washes 40 cars per day, and its total cost...
1. A profit-maximizing, monopolistically competitive car wash
washes 40 cars per day, and its total cost $200 and currently makes
an economic profit of $280. In the long run, everything else equal,
the
a. car wash will wash less than 40 cars
per day.
b. car wash will charge more than $12 per
wash.
c. car wash will need to hire new workers
to wash more cars.
d. car wash will wash more than 50 cars...
A car wash firm calculates that its daily production (in number of cars washed) depends on...
A car wash firm calculates that its daily production (in number
of cars washed) depends on the number n of workers it
employs according to the formula
P = 40n − 0.05n2 cars.
Calculate the marginal product of labor at an employment level
of 50 workers. HINT [See Example 3.]
This means that, at an employment level of 50 workers, the
firm's daily production will increase at a rate of cars
per additional worker it hires.
A competitive firm has a production function ?(?, ?) = (? + ?)1/2 where ? and...
A competitive firm has a production function ?(?, ?) = (? +
?)1/2 where ? and ? stand for inputs capital and labour
respectively. The price of capital is ?, and the price of labour is
?. Which of the following is true?
Regardless of ? and ?, cost minimisation requires that ? =
?.
If ? > ?, contingent demand for labour is 0.
The technology has increasing returns to scale.
If ? < ?, profit maximisation requires that...
A car wash has two stations, 1 and 2. The service time at station 1 is...
A car wash has two stations, 1 and 2. The service time at
station 1 is exponentially distributed with parameter λ1, and the
service time at station 2 is exponentially distributed with
parameter λ2.When a car arrives at the car wash, it begins service
at station 1, provided station 1 is free; otherwise, the car waits
until station 1 is available. Upon completing service at station 1,
the car then proceeds to station 2, provided station 2 is free;
otherwise,...
1. Consider the following table that provides information for a firm’s short-run production function and its...
1. Consider the following table that provides information for a
firm’s short-run production function and its product demand, given
by the column labeled D1.
Labor
Output
Price
(D1)
0
0
$10.00
1
16
10.00
2
31
10.00
3
45
10.00
4
58
10.00
5
69
10.00
6
78
10.00
Based on that information, calculate Total Revenue (TR),
Marginal Revenue Product (MRP), Marginal Product of Labor (MP) and
Value of the Marginal Product (VMP), then answer the following
questions:
Assume that...
US Inc. has decided to expand its operations to owning and operating car washes. The following...
US Inc. has decided to expand its operations to owning and
operating car washes. The following is an excerpt from the
conversation between the chief executive officer, John Porter and
the vice president of finance, Mc.Call :
John : Mc.Call, have you given any thought to how we're going to
manage the acquisition of Swiffer Car Wash?
Mc.Call: Well, the two basic options, as I see it, are to issue
either preferred stock or bonds. The equity market is a...
Bolster Inc. has decided to expand its operations to owning and operating car washes. The following...
Bolster Inc. has decided to expand its operations to owning and
operating car washes. The following is an excerpt from the
conversation between the chief executive officer, Mike O'Brian, and
the vice president of finance, John Ibison:
Mike: John, have you given any thought to how we're going to
manage the acquisition of Swiffer Car Wash?
John: Well, the two basic options, as I see it, are to issue
either preferred stock or bonds. The equity market is a little...
9. a. Suppose that a firm’s production function is q=9x^1/2 in the short run, where there...
9. a.
Suppose that a firm’s production function is q=9x^1/2 in the short
run, where there are fixed costs of $1000, and x is the
variable input whose cost is $4000 per unit. What is the total cost
of producing a level of output q? In other words, identify
the total cost function C(q).
b. Write down the
equation for the supply curve.
c. If price is
$1000, how many units will the firm produce? What is the level of...
A competitive firm has the production function Q = (Lw + Lb) 1/2 , where Lw...
A competitive firm has the production function Q = (Lw + Lb) 1/2
, where Lw and Lb are the respective numbers of white and black
workers employed. The price of output is constant at P = 36. The
market wage is wb = 3 for black workers and ww = 9 for white
workers. If a firm has a discrimination coefficient of d > 0,
then it behaves as if the wage is wb(1 + d) for black workers...
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