Question
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-0.05n^2 cars. Calculate the marginal product of labor for the 51st worker and interpret the answer in context
Homework Answers
Answer #1
Marginal product of Labor(MPL) is the additional output produced when hire one additional unit of worker.
Mathematically MPL = dP/dn where P represents total output and n represents number of workers
Here, Production function is given by :
Now for, n = 51, we have dP/dn = 40 - 0.1*51 = 34.9
Hence, marginal product of labor for the 51st worker is 34.9
Interpretation : When he hire 51st worker, the number of cars washed will increase by 34.9 units.
Not the answer you're looking for?
Similar Questions
1. Schmutz Auto Wash provides car washes. Its production function is ? = 2?1/2(? - 1)1/2...
1. 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 one unit of capital input installed (so
? = 1).
a). Find Schmutz’s short run daily...
4. The table below shows the number of cars produced by a car manufacturer. Car production...
4. The table below shows the number of
cars produced by a car manufacturer. Car production depends on the
number of workers as follows:
Assume that all
other inputs other than labor are fixed. a. Complete the table by
calculating MPL and APL.
Over what range of labor are there increasing returns to scale?
diminishing returns to scale? Negative returns to scale?
Over what range of labor is MPL greater than
APL? What is happening to APL as employment
increases...
A firm has a production function Y = (K0.3)*(N0.7). Given this production function, the marginal product...
A firm has a production function Y =
(K0.3)*(N0.7). Given this production
function, the marginal product of labor is given by
MPN
=0.7*(K0.3)*(N-0.3). Suppose that
the firm uses 1 unit of capital for production, that is, K = 1.
Additionally, suppose that the market wage is w = 0.35.
Questions:
a) Calculate the optimal number of workers the firm will
hire. Round your answer to the closest integer.
b) Suppose that the government subsidizes employment by
0.05 per worker (s...
1. Consider a firm with the following production function: Q= 60 L^2 K^1/2 -4L^3 The firm...
1. Consider a firm with the following production function:
Q= 60 L^2 K^1/2 -4L^3
The firm is operating in the short run with a fixed capital
stock of K=4
Use this to answer the following questions:
2. Suppose the firm in the previous question is able to increase
its capital to K ¯ = 9.
After what quantity of labor does diminishing marginal returns
now occur?
What is the maximum output the firm can now produce?
After what number of...
A firm has a daily production function q = 2.5L^1/3K^1/3. Currently, the firm rents 8 pieces...
A firm has a daily production function q = 2.5L^1/3K^1/3.
Currently, the firm rents 8 pieces of equipment. The amount of
equipment is fixed in the short run. The unit wage rate is $25
while the rental cost of capital is $100.
Find the short run production function.
Find the number of workers the firm wishes to employ to produce
q units (the short run conditional demand for labor).
Find the firm’s short run total cost
Find the firm’s short...
5. A competitive firm has a production function described as follows. “Weekly output is the square...
5. A competitive firm has a production function described as
follows. “Weekly output is the square root of the minimum of the
number of units of capital and the number of units of labor
employed per week.” Suppose that in the short run this firm must
use 16 units of capital but can vary its amount of labor
freely.
a) Write down a formula that describes the marginal product of
labor in the short run as a function of the...
The production function for a firm is Q = −0.6L 3 + 18L 2K + 10L...
The production function for a firm is Q = −0.6L 3 + 18L 2K + 10L
where Q is the amount of output, L is the number of labor hours per
week, and K is the amount of capital.
(a)Use Excel to calculate the total short run output Q(L) for L
= 0, 1, 2...20, given that capital is fixed in the short run at K =
1.
(b) Use Excel to calculate the total long run output Q(L) for...
1. In the short run, the firm ________ change the number of workers it employs but...
1. In the short run, the firm ________ change the number of
workers it employs but ________ change the size of its plant.
A) can; can B) can; cannot C) cannot; can D) cannot; cannot
2.Jill runs a factory that makes lie detectors in Little Rock,
Arkansas. This month, Jill's 34 workers produced 690 machines.
Suppose Jill adds one more worker and, as a result, her factory's
output increases to 700. Jill's marginal product of labor from the
last worker...
A firm produces an output with the production function Q=K*L2, where Q is the number of...
A firm produces an output with the production function Q=K*L2,
where Q is the number of units of output per hour when the firm
uses K machines and hires L workers each hour. The marginal product
for this production function are MPk =L2 and MPl = 2KL. The factor
price of K is $1 and the factor price of L is $2 per hour.
a. Draw an isoquant curve for Q= 64, identify at least three
points on this curve....
LeBron Factory Number of Workers Number of Machines Output (chairs produced per hour) Marginal Product of...
LeBron
Factory
Number
of
Workers
Number
of
Machines
Output
(chairs
produced
per hour)
Marginal
Product of
Labor
Cost of
Workers
Cost of
Machines
Total
Cost
?1
?2
?5
?2
?2
?10
?3
?2
?20
?4
?2
?35
?5
?2
?55
?6
?2
?70
?7
?2
?80
Refer to Table above.
First, complete the missing information in the Table
above.
1.Each worker at the
LeBron Chair Factory costs $12 per hour. The cost of each machine
is $20 per day regardless...
ADVERTISEMENT
Need Online Homework Help?
Get Answers For Free
Most questions answered within 1 hours.
ADVERTISEMENT
Active Questions
asked 14 minutes ago
asked 24 minutes ago
asked 32 minutes ago
asked 43 minutes ago
asked 45 minutes ago
asked 1 hour ago
asked 1 hour ago
asked 1 hour ago
asked 2 hours ago
asked 2 hours ago
asked 2 hours ago
asked 2 hours ago