ECON 350 - CLASSICAL
ECONOMICS - Law of Diminishing
Returns
Question Bank - Set 1
Liberty University
Question 1
Question
A company that produces computer chips has a factory with fixed capital like
machinery and buildings. The company decides to increase the number of work-
ers in the factory. However, they notice that as the number of workers increases,
the additional output produced by each additional worker decreases after a cer-
tain point. Explain the concept of the Law of Diminishing Returns in this
context.
Solution
The Law of Diminishing Returns states that as additional units of a variable
input (such as labor) are added to fixed amounts of other inputs (like machin-
ery and buildings), the marginal product of the variable input will eventually
decrease.
Step 1: Initially, when additional workers are hired, the total output of com-
puter chips will increase at an increasing rate. This is because each new worker
can specialize in a specific task, leading to higher efficiency and productivity.
Step 2: However, there comes a point when adding more workers does not
lead to the same increase in production. This is because there is a limited
capacity in the factory - the fixed inputs like machinery and buildings can only
support a certain number of workers efficiently.
Step 3: As a result, the productivity of each additional worker decreases.
They may start getting in each other’s way, causing inefficiencies or delays in
the production process. This leads to a diminishing marginal product of labor.
Step 4: At a certain point, adding more workers may even lead to a decrease
in overall production due to overcrowding or lack of resources to support the
increased workforce. This is the point where the Law of Diminishing Returns
sets in.
Step 5: In order to maximize production efficiency, a company must find
the optimal number of workers that can work effectively with the fixed capital
in the factory. Beyond this optimal point, adding more workers will result in
diminishing returns and decreased productivity.
Question 2
Question
Suppose a firm is producing bicycles in a factory. The number of workers in the
factory is fixed at 10. Initially, with 10 workers, the firm is able to produce 100
bicycles per day. When the firm hires an additional worker, the daily production
increases to 110 bicycles. However, when another worker is hired (so there are
now 12 workers in total), the daily production only increases to 115 bicycles.
Explain this phenomenon in the context of the Law of Diminishing Returns.
Solution
The Law of Diminishing Returns states that as more units of a variable input
(in this case, workers) are added to a fixed input (in this case, the factory and
machinery), the marginal product of the variable input will eventually decrease.
Step 1: Initially, with 10 workers, the firm produces 100 bicycles per day.
This implies each worker is able to produce 10 bicycles per day (100
10 = 10).
Step 2: When the firm hires an additional worker, the daily production
increases to 110 bicycles. This means the 11th worker contributes 10 additional
bicycles to the daily production.
Step 3: However, when another worker is hired (12 workers in total), the
daily production only increases to 115 bicycles. This means the 12th worker
contributes only 5 additional bicycles to the daily production.
This phenomenon is in line with the Law of Diminishing Returns. As more
workers are added to the fixed factory and machinery, the marginal productiv-
ity of each additional worker decreases. The fixed resources can only support a
certain number of workers efficiently before the additional workers start becom-
ing less productive due to overcrowding, inefficient division of labor, or other
factors.
Question 3
Question
Suppose a company is producing furniture and currently employs 100 workers in
their factory. The company notices that as they hire more workers beyond 100,
the additional output produced by each additional worker starts to decrease.
2
If the company’s total output is initially increasing at a constant rate, explain
how the law of diminishing returns manifests in this scenario.
Solution
The law of diminishing returns is a principle in economics that states that as
more of a variable input (such as labor) is added to a fixed input (such as
capital), the marginal product of the variable input will eventually decrease.
Step 1: Initially, the company’s total output is increasing at a constant
rate. This means that each additional worker hired contributes just as much
output as the worker before.
Step 2: However, as the company hires more workers beyond the initial
100, the law of diminishing returns comes into play. The fixed input (capital)
does not increase, so adding more workers eventually leads to inefficiencies and
lower marginal product of labor.
Step 3: The diminishing returns can manifest in various ways, such as over-
crowding in the workplace, communication issues, or lack of physical resources
to support more workers. As a result, the additional output produced by each
additional worker starts to decrease.
Step 4: This leads to a situation where the company’s total output still
increases, but at a decreasing rate. Eventually, the total output may even
decrease if the company continues to hire more workers without improving other
factors of production.
Step 5: To maximize efficiency and output, the company should carefully
assess the optimal number of workers to hire based on the law of diminishing re-
turns. Balancing the marginal cost of labor with the marginal revenue generated
from additional output is crucial for profitability.
Question 4
Question
A company produces bicycles in a factory. The company finds that with each
additional worker hired, the total number of bicycles produced increases, but at
a decreasing rate. The initial increase in production is high, but after a certain
point, the increase becomes smaller and smaller until it eventually becomes
negative. Explain how the Law of Diminishing Returns applies to this situation.
Solution
The Law of Diminishing Returns, also known as the Law of Diminishing Marginal
Returns, states that as one input variable is increased while other inputs are
held constant, the overall output will reach a point where the marginal increase
in output decreases with each additional unit of input.
3
Step 1: Concept of Diminishing Returns Initially, when a company
hires additional workers to produce bicycles, the total number of bicycles pro-
duced increases rapidly. This is because the fixed capital (such as machinery
and equipment) can be efficiently utilized with more labor. As the number of
workers increases, the efficiency of production also increases, leading to a rapid
increase in output.
Step 2: Diminishing Marginal Returns However, after a certain point,
adding more workers becomes less efficient. This is because there is a limit
to how many workers can effectively work in the factory without causing over-
crowding or inefficiencies. At this stage, the marginal increase in output starts
decreasing, and the company experiences diminishing marginal returns.
Step 3: Negative Returns If the company continues to add more workers
beyond the point of diminishing returns, the output may actually start to de-
crease. This is known as negative returns. At this point, the additional workers
may start interfering with each other’s productivity, causing chaos and reducing
the total output of bicycles.
In conclusion, the Law of Diminishing Returns helps businesses understand
the relationship between input and output and guides them in optimizing pro-
duction processes to achieve maximum efficiency and profitability.
Question 5
Question
A company produces shoes in a factory. The company initially hires 10 workers
and is able to produce 100 pairs of shoes per day. As the company hires more
workers, the production increases according to the Law of Diminishing Returns.
The production function is given by P(w) = 100w−5w2, where wis the number
of workers and P(w) is the number of pairs of shoes produced per day.
If the company hires 20 workers, what is the rate of change in production
with respect to the number of workers at that point?
Solution
Step 1: Find the rate of change in production with respect to the number of
workers using the derivative of the production function.
The rate of change in production with respect to the number of workers (w)
can be found by taking the derivative of the production function P(w):
dP
dw =d
dw (100w−5w2)
Step 2: Differentiate the production function with respect to w.
dP
dw = 100 −10w
4
Step 3: Substitute w= 20 into the derivative to find the rate of change in
production.
dP
dw
w=20
= 100 −10(20) = 100 −200 = −100
Therefore, the rate of change in production with respect to the number of
workers when the company hires 20 workers is −100 pairs of shoes per worker.
Question 6
Question
A manufacturing company is producing a certain electronic device. The com-
pany has observed that, as more workers are hired to assemble the electronic
devices, the marginal product of each additional worker begins to decrease. Af-
ter analyzing the production data, the company has determined that the point
of diminishing returns occurs when 10 workers are hired. At this point, the
marginal product of the 10th worker is 20 units. If the company continues
to hire workers beyond the point of diminishing returns, what is the expected
marginal product for the 12th worker?
Solution
Let’s denote the marginal product of the nth worker as MPn. We are given that
MP10 = 20 units. To find the expected marginal product for the 12th worker,
let’s follow these steps:
Step 1: Understand the Law of Diminishing Returns. According to the
Law of Diminishing Returns, as additional units of a variable input (in this
case, workers) are added to fixed inputs (such as the production facilities and
equipment), the marginal product of each additional unit of the variable input
will eventually start to decrease.
Step 2: Calculate the expected marginal product for the 12th worker. Since
the point of diminishing returns occurred at the 10th worker, hiring additional
workers beyond this point will result in a decrease in the marginal product.
Assuming that the marginal product decreases linearly beyond the point of
diminishing returns, we can set up a linear equation using the given information:
Let kbe the constant rate of decrease in marginal product beyond the point of
diminishing returns.
Thus, we have the equation: M P10 −k= 20
And for the 12th worker: M P12 =MP10 −2k
Step 3: Solve for the expected marginal product for the 12th worker. Sub-
stitute the value of MP10 into the equation: 20 −k= 20
Solve for k:k= 0
Therefore, the expected marginal product for the 12th worker is: MP12 =
MP10 −2k= 20 −2(0) = 20 units.
5
Question 7
Question
A company produces electronic gadgets using a fixed amount of capital and
labor. After a certain point, the company experiences diminishing returns as
it hires more labor. Suppose the company’s production function is given by
Q= 10L−0.5L2−30, where Qis the quantity of gadgets produced and Lis the
number of laborers hired. Calculate the number of laborers that will maximize
the company’s production and the corresponding maximum quantity of gadgets
produced.
Solution
Step 1: To find the number of laborers that will maximize the company’s pro-
duction, we need to find the critical points of the production function. This
occurs when the first derivative is equal to 0.
dQ
dL = 10 −L= 0
L= 10
Step 2: To determine whether this critical point is a maximum or minimum,
we need to analyze the second derivative.
d2Q
dL2=−1
Since the second derivative is negative, the critical point corresponds to a max-
imum.
Step 3: Substituting L= 10 back into the production function Q= 10L−
0.5L2−30 to find the maximum quantity of gadgets produced.
Q= 10(10) −0.5(10)2−30
Q= 100 −50 −30
Q= 20
Therefore, to maximize production, the company should hire 10 laborers,
resulting in a maximum of 20 gadgets produced.
Question 8
Question
A firm is running a production process where it employs both labor and capital.
Initially, the firm increased the amount of labor it hires while keeping the amount
of capital constant. As a result, the total output increased rapidly at first, then
at a decreasing rate, and eventually started to decrease. Explain this situation
in terms of the Law of Diminishing Returns.
6
Solution
Step 1: The Law of Diminishing Returns states that as more of a variable
input is added to a fixed input, the marginal product of the variable input will
eventually decrease.
Step 2: Initially, when the firm increased the amount of labor while keeping
the amount of capital constant, the total output increased rapidly because each
additional unit of labor could specialize in a specific task, leading to greater
efficiency and productivity.
Step 3: However, as the firm continued to hire more labor, the marginal
product of labor started to decrease. This is because the fixed input (capital)
became a limiting factor, causing the additional labor to be less productive or
efficient.
Step 4: The diminishing returns set in when the firm reached a point where
the marginal product of labor became negative. At this stage, the firm was
experiencing negative returns, where adding more labor actually decreased the
total output.
Step 5: This situation can be explained using the concept of the Total Prod-
uct Curve, where initially the curve rises steeply (increasing returns), then slopes
more gently (diminishing returns), and eventually starts to decline (negative re-
turns).
Step 6: In conclusion, the situation described is a classic example of the
Law of Diminishing Returns, where the firm experienced diminishing marginal
product of labor as more labor was added to a fixed amount of capital in the
production process.
Question 9
Question
A company is producing smartphones in a factory. The company notices that
as they increase the number of workers in the factory (keeping all other factors
constant), the production of smartphones initially increases but eventually starts
to decrease. Explain this phenomenon in the context of the Law of Diminishing
Returns.
Solution
The Law of Diminishing Returns is a fundamental concept in economics that
states that as a firm increases the amount of one input while keeping other
inputs constant, the marginal product of that input will eventually decrease.
This law helps to explain the shape of the production function.
Step 1: Initially, as more workers are added to the factory, the production
of smartphones increases due to the division of labor and specialization. Each
additional worker contributes positively to the overall production and efficiency
increases.
7
Step 2: At a certain point, however, the Law of Diminishing Returns sets in.
This occurs when the fixed factors of production (such as factory size, machinery,
etc.) cannot be easily increased or adjusted. As more and more workers are
added, the fixed factors become a bottleneck, leading to inefficiencies.
Step 3: Eventually, the production of smartphones will start to decrease as
each additional worker contributes less than the worker before. This is because
the fixed factors are being overutilized and there is not enough resources to
support the increasing number of workers.
Step 4: In the context of the smartphone factory, this phenomenon would
be observed when the factory becomes overcrowded, machinery is being over-
worked, or other constraints prevent the additional workers from being as pro-
ductive as the initial workers.
In conclusion, the Law of Diminishing Returns explains why an increase in
one input (workers in this case) while holding other inputs constant will even-
tually lead to diminishing marginal returns and a decrease in overall production
efficiency.
Question 10
Question
A company is producing smartphones using two factors of production: labor
(L) and capital (K). The total product of smartphones (Q) produced per day is
given by the function Q= 10L0.5K0.5.
If the company has a fixed amount of capital (K) and is currently using
25 units of labor, determine whether the company is experiencing diminishing
returns to labor. Justify your answer.
Solution
Step 1: Calculate the marginal product of labor (MPL) and the average product
of labor (APL) using the given total product function.
MPL = ∂Q
∂L = 0.5·10 ·K0.5·L−0.5= 5K0.5L−0.5
APL = Q
L=10L0.5K0.5
L= 10L−0.5K0.5
Step 2: Substitute the given values into the MPL and APL equations. Given:
Kis fixed and L= 25 units.
MPL = 5K0.5·25−0.5= 5K0.5·1
5√K=√K
APL = 10 ·25−0.5K0.5= 10 ·1
5√K·K0.5= 2√K
8
Step 3: Check if the MPL is decreasing as more units of labor are hired. If
MPL decreases, the company is experiencing diminishing returns to labor.
∂MPL
∂L = 0
Since the derivative of MPL with respect to labor is zero, the company is not
currently experiencing diminishing returns to labor when using 25 units of labor.
Question 11
Question
Suppose a farmer is cultivating a field and applying fertilizer. Initially, the
farmer observes that as more fertilizer is added, the crop yield increases. How-
ever, at a certain point, the farmer notices that the crop yield starts to increase
at a decreasing rate, indicating the onset of diminishing returns. Define the Law
of Diminishing Returns and explain how it manifests in the cultivation of this
field.
Solution
The Law of Diminishing Returns states that as more units of a variable in-
put (e.g., fertilizer, labor) are added while keeping other inputs constant, the
marginal product of that input will eventually decrease. This means that the
additional output gained from each additional unit of input will diminish over
time.
Step 1: Initially, the farmer observes increasing crop yield as more fertilizer
is added. This is because the initial application of fertilizer helps in providing
essential nutrients to the plants, promoting growth and increasing yields.
Step 2: However, as the farmer continues to add more fertilizer beyond
a certain point, the crop yield starts to increase at a decreasing rate. This is
due to the Law of Diminishing Returns. At this stage, the soil may become
saturated with nutrients, leading to reduced effectiveness of additional fertilizer
in improving crop yield.
Step 3: Moreover, excessive application of fertilizer can lead to environ-
mental issues such as water pollution and soil degradation. This highlights the
importance of optimizing input levels to achieve maximum output efficiency
without causing harm to the environment.
Step 4: In summary, the manifestation of the Law of Diminishing Returns
in the cultivation of the field shows how increasing a variable input beyond
a certain point can result in diminishing marginal returns. This highlights
the significance of input optimization and sustainable agricultural practices to
enhance productivity while minimizing negative impacts.
9
Question 12
Question
A company is producing wheat using a fixed amount of land. The company ini-
tially invested in labor and capital to cultivate the land, resulting in an increase
in wheat production. However, after some time, the company noticed diminish-
ing returns to labor and capital as they continued to invest more resources into
the cultivation process. Explain the concept of the Law of Diminishing Returns
in the context of wheat production.
Solution
The Law of Diminishing Returns, also known as the Law of Diminishing Marginal
Returns, states that as more and more of a variable input (such as labor or cap-
ital) is applied to a fixed input (such as land), the marginal product of the
variable input will eventually decrease. This means that each additional unit of
the variable input will yield less additional output than the previous unit.
Step 1: Initially, when the company invested in labor and capital to cul-
tivate the fixed amount of land, the productivity of the land increased. This
is because the combination of land, labor, and capital was able to efficiently
produce wheat beyond the natural output of the land itself.
Step 2: However, as the company continued to invest more resources (labor
and capital) into the cultivation process, they began to experience diminishing
returns. The additional units of labor and capital added to the fixed amount
of land eventually led to a point where the marginal product of each additional
unit of labor or capital decreased.
Step 3: This decline in marginal product occurs due to factors such as
overcrowding of labor, capital becoming less complementary with the fixed land
input, and inefficiencies in the production process. As a result, the company
reaches a point where each additional unit of labor or capital contributes less
to overall wheat production than before.
Step 4: In practical terms, the Law of Diminishing Returns implies that
there is an optimal level of input (labor and capital) that maximizes output on
a fixed amount of land. Going beyond this optimal level leads to diminishing
returns, where the additional input costs outweigh the additional output gained.
In summary, the Law of Diminishing Returns highlights the concept that
beyond a certain point, the addition of more variable inputs to a fixed input will
result in diminishing marginal returns, ultimately affecting overall productivity.
Question 13
Question
A company employs 50 workers to produce a certain product. As more workers
are hired, the production initially increases at an increasing rate, but eventually
10
reaches a point where the increase in production diminishes with each addi-
tional worker hired. Explain, in detail, how the Law of Diminishing Returns is
illustrated in this scenario.
Solution
To illustrate the Law of Diminishing Returns, we can consider the scenario of
a company hiring workers to produce a certain product. Initially, when the
company hires more workers, production increases at an increasing rate because
there are more people to work on producing the product.
Step 1: Increasing Returns Stage At the beginning, the company may
have 50 workers and by hiring more workers, say 10 more, the production in-
creases significantly. This is because each additional worker contributes posi-
tively to the production process. Tasks can be divided more efficiently among
the workers, leading to a higher output of the product.
Step 2: Diminishing Returns Stage However, as the company continues
to hire more workers beyond a certain point, there may not be enough resources
(machinery, space, materials) available to support the increasing number of
workers effectively. This leads to a scenario where each additional worker hired
contributes less and less to the production process.
Step 3: Negative Returns Stage Eventually, the company may reach a
point where hiring even more workers results in a decrease in production. This
is known as the negative returns stage. The limited availability of resources and
the diminishing contribution of each additional worker lead to inefficiencies in
the production process, causing a decrease in the overall output of the product.
In this scenario, the Law of Diminishing Returns is clearly illustrated as the
company experiences increasing returns initially, followed by diminishing and
eventually negative returns as more workers are hired beyond a certain point.
Question 14
Question
A company operates a factory that produces smartphones. Initially, the com-
pany hires 50 workers and the output of smartphones per day increases signifi-
cantly. However, after hiring additional workers, the company notices that the
increase in output is not as significant as before. Explain this phenomenon using
the Law of Diminishing Returns.
Solution
The Law of Diminishing Returns states that as one input variable is increased,
while all other variables are held constant, the marginal contribution of the
input variable will eventually decline. This phenomenon can be observed in the
production process of the company.
11
Step 1: Understand the concept Initially, when the company hires 50
workers, the factory operates efficiently as each worker contributes positively to
the output of smartphones. This is known as the stage of increasing returns to
scale.
Step 2: Diminishing returns However, as the company hires more work-
ers, there may not be enough resources (machines, workspace, etc.) to support
each additional worker effectively. In this case, the productivity of each new
worker may start to decrease, leading to diminishing returns.
Step 3: Negative returns If the company continues to hire more workers
beyond a certain point, the excessive number of workers may start to interfere
with each other’s productivity. This stage is known as negative returns or
declining marginal productivity.
Step 4: Optimal level of production To maximize output and efficiency,
the company must find the optimal number of workers that will ensure the high-
est level of productivity without experiencing diminishing or negative returns.
By understanding the Law of Diminishing Returns, the company can make
informed decisions about the number of workers to hire and optimize its pro-
duction process.
Question 15
Question
A firm is currently producing 100 units of a product per day with two workers.
The production function is given by Q= 10L−0.2L2, where Qis the quantity of
the product produced, and Lis the number of workers employed. Determine the
marginal product of labor, average product of labor, and total product when
the third worker is hired. Explain whether the law of diminishing returns is
evident in this scenario.
Solution
Step 1: Calculate the marginal product of labor (MPL) when the firm hires the
third worker. Given the production function Q= 10L−0.2L2, the marginal
product of labor is the derivative of the production function with respect to L.
MPL = dQ
dL = 10 −0.4L
Step 2: Calculate the average product of labor (APL) when the firm hires
the third worker. The average product of labor is the total product divided by
the number of workers. For two workers:
Q= 10(2) −0.2(2)2= 20 −0.8 = 19.2
Average product of labor for two workers:
APL2=19.2
2= 9.6
12
Step 3: Determine the total product when the firm hires the third worker.
For three workers:
Q= 10(3) −0.2(3)2= 30 −1.8 = 28.2
Step 4: Evaluate the law of diminishing returns. When the third worker
is hired, the marginal product of labor decreases from 10 to 9.2, indicating
diminishing returns. Additionally, the average product of labor decreases from
9.6 to 9.4 when the third worker is hired, further supporting the presence of
diminishing returns in this scenario.
Question 16
Question
Suppose a company is producing smartphones and has a fixed capital stock of
machinery and a fixed number of workers. Initially, the company hires additional
workers and experiences increasing marginal product of labor. However, after
a certain point, the marginal product of labor starts to decrease. Explain the
concept of the Law of Diminishing Returns in the context of this scenario.
Solution
The Law of Diminishing Returns is an economic principle that states as ad-
ditional units of a variable input are added to fixed inputs in the production
process, the marginal product of the variable input will eventually decrease.
Step 1: Initially, as the company hires additional workers, the fixed capital
stock remains the same, which leads to an increase in production due to spe-
cialization and division of labor. This causes the marginal product of labor to
increase.
Step 2: However, as more and more workers are hired, the fixed capital
stock becomes a constraint. The company reaches a point where the efficiency of
adding more workers diminishes. This is because the fixed factors (machinery)
cannot be expanded or improved to keep up with the increasing number of
workers.
Step 3: Due to this imbalance between variable input (workers) and fixed
input (machinery), the marginal product of labor starts to decrease. The ad-
ditional workers now begin to get in each other’s way, leading to inefficiencies,
duplication of effort, and eventually a decrease in output per additional unit of
labor.
Step 4: The Law of Diminishing Returns highlights the importance of main-
taining a balance between all inputs in the production process to achieve optimal
efficiency. This principle is essential for businesses to make informed decisions
regarding resource allocation and production levels to maximize profits.
13
Question 17
Question
A company is producing widgets in a factory. The company notices that when
they increase the number of workers in the factory, the total output of widgets
increases at a decreasing rate. If the company continues to add more workers
beyond a certain point, the total output of widgets may even start to decrease.
Explain the concept of the Law of Diminishing Returns in the context of widget
production.
Solution
The Law of Diminishing Returns is a concept in economics that states that
as one input factor is increased while keeping all other factors constant, the
marginal output will eventually decrease. This means that there is a limit to
the efficiency gains achievable by increasing a single input.
Step 1: Initially, when the company adds more workers to the factory,
the total output of widgets increases. This is because each additional worker
contributes to an increase in production due to the division of labor and spe-
cialization.
Step 2: However, as the number of workers continues to increase, there is a
point where the factory becomes overcrowded and each additional worker may
start to get in the way of others, causing inefficiencies. This leads to a situation
where the marginal output of each additional worker starts to decrease.
Step 3: Beyond a certain point, adding more workers may actually lead to
a total decrease in output. This could be due to overcrowding, lack of resources,
or other factors that limit the ability of the workers to be productive.
Step 4: In the context of widget production, the company will need to
identify the optimal number of workers that maximizes output without expe-
riencing diminishing returns. This requires careful planning and analysis to
ensure efficient use of resources.
Step 5: Overall, the Law of Diminishing Returns highlights the importance
of understanding the relationship between input and output in production pro-
cesses. It serves as a reminder that increasing a single input factor indefinitely
may not always lead to proportionate increases in output.
Question 18
Question
Suppose a company is producing bicycles in a factory. The company initially
hires 10 workers and experiences increasing returns to scale. However, after
adding more workers, the company eventually reaches a point where it experi-
ences diminishing returns to scale.
14
If the company hires 20 workers and the total output increases by 200 bicycles
per day, but when the company hires 30 workers the total output increases by
only 100 bicycles per day, what can you conclude about the law of diminishing
returns in this scenario?
Solution
To understand the concept of diminishing returns in this scenario, we need to
analyze the increase in total output as the company hires more workers.
Step 1: Calculate the increase in output per worker when the company
hires 20 workers. Let xbe the increase in output per worker. With 10 workers,
the total output is 10x. When 20 workers are hired, the total output increases
by 200 bicycles per day, so:
20x= 10x+ 200
10x= 200
x= 20
Therefore, the increase in output per worker when the company hires 20
workers is 20 bicycles per day.
Step 2: Calculate the increase in output per worker when the company
hires 30 workers. Using the increase per worker of 20 bicycles per day, with 10
workers the total output is 10(20) = 200. When 30 workers are hired, the total
output increases by 100 bicycles per day, so:
30(20) = 200 + 100
600 = 300
Contradiction
Step 3: Conclusion The contradiction between the calculated increase in
output per worker when the company hires 20 workers versus 30 workers implies
that the company is experiencing diminishing returns to scale. As more workers
are added beyond a certain point (from 20 to 30 workers in this case), the
additional output per worker decreases, indicating diminishing marginal returns.
Question 19
Question
A company produces smartphones and is currently operating with one unit of
labor. The company’s production function is given by Q= 10L−0.5L2, where Q
is the quantity of smartphones produced and Lis the number of units of labor
employed. Determine the level of labor that maximizes output and explain
whether the law of diminishing returns applies in this scenario.
15
Solution
Step 1: Calculate the marginal product of labor (MPL) by taking the derivative
of the production function with respect to labor:
MPL = dQ
dL = 10 −L
Step 2: Set the marginal product of labor equal to zero to find the labor
level that maximizes output:
10 −L= 0 ⇒L= 10
Step 3: Calculate the second derivative of the production function to deter-
mine the concavity of the function:
d2Q
dL2=−1
Step 4: Since the second derivative is negative, the production function is
concave down at L= 10. This indicates that the law of diminishing returns
applies, as increasing labor beyond 10 units will result in diminishing marginal
returns.
Question 20
Question
Suppose a company is producing bicycles in a factory. Initially, they hired 10
workers and experienced a 20
Solution
Let’s denote the production increase as a function of the number of workers
hired. We have: - When 10 workers were hired, the production increased by 20-
When 20 workers were hired, the production only increased by 5
Let’s assume the production increase is given by the function f(n) = an +b,
where nis the number of workers hired.
Step 1: Set up the system of equations Using the information given,
we have the system of equations:
f(10) = 10a+b= 20
f(20) = 20a+b= 5
Step 2: Solve the system of equations Subtracting the first equation
from the second, we get:
20a+b−(10a+b)=5−20
16
10a=−15
a=−3
2
Substitute aback into the first equation to solve for b:
10(−3
2) + b= 20
−15 + b= 20
b= 35
Therefore, the production increase function is f(n) = −3
2n+ 35.
Step 3: Find the point of diminishing returns The Law of Diminishing
Returns states that the point of diminishing returns is when the production
increase starts to decrease. This occurs when the derivative of the production
increase function is 0.
Differentiating f(n) = −3
2n+ 35 with respect to n, we get:
f′(n) = −3
2
Setting f′(n) = 0, we find:
−3
2= 0
Therefore, the company started experiencing the Law of Diminishing Re-
turns from the beginning, as the marginal increase in production was decreasing
from the start.
Question 21
Question
Suppose a farmer has a field where he plants corn. The farmer hires additional
labor to plant and harvest the corn. Initially, as more labor is added, the
output of corn increases. However, there comes a point where adding more labor
leads to diminishing returns. Assume that the farmer is currently experiencing
diminishing returns. Explain why the Law of Diminishing Returns occurs in
this situation.
Solution
To understand why the Law of Diminishing Returns occurs in this situation,
let’s break it down into steps:
Step 1: Initially, when the farmer adds more labor to the field, the output
of corn increases. This is because each additional worker can specialize in a
specific task and contribute efficiently to the overall production.
17
Step 2: However, as the farmer continues to hire more labor, the field may
become overcrowded. Each additional worker may not have enough space or
resources (such as tools or land) to work efficiently. This leads to a situation
where the marginal product of each additional worker starts to decrease.
Step 3: The diminishing returns occur because the fixed input (land) be-
comes a constraint. There is a limited amount of land available, so adding
more labor eventually leads to a situation where the marginal product of labor
decreases.
Step 4: In essence, the Law of Diminishing Returns states that as more
units of a variable input (labor) are added to a fixed input (land), the marginal
product of the variable input will eventually diminish. This occurs due to the
inefficiencies that arise from overcrowding and competition for limited resources.
Therefore, in the scenario of the farmer experiencing diminishing returns, the
Law of Diminishing Returns occurs because of the fixed input (land) constraint
and the inefficiencies that arise from adding more variable input (labor) beyond
a certain point.
Question 22
Question
A company has a factory where they produce electronic devices. The factory
has limited space and resources, which means that there is a maximum number
of workers that can efficiently work in the factory.
After conducting an analysis, the company found that the optimal number
of workers in the factory is 50. However, due to an increase in demand, the
company decided to hire 20 additional workers, bringing the total number of
workers to 70.
Explain how the Law of Diminishing Returns applies in this scenario and
discuss the potential consequences of hiring more workers than the optimal
number.
Solution
The Law of Diminishing Returns states that as more units of a variable input
(in this case, workers) are added to a fixed quantity of capital, the marginal
product of the variable input will eventually decrease.
Step 1: When the company had 50 workers, they were operating at the
optimal level where each additional worker contributed positively to the over-
all production output. However, when the company hired 20 more workers,
increasing the total to 70, they exceeded the optimal number.
Step 2: As a consequence of hiring more workers than the optimal number,
the factory may experience inefficiencies. The additional 20 workers may start
to get in each other’s way, causing congestion, delays, and reduced productivity.
18
The factory may also face resource constraints, such as space and equipment
shortage, which can further hinder the efficiency of the production process.
Step 3: Another consequence of hiring more workers than necessary is
increased costs. The company will have to pay additional wages, provide train-
ing, and potentially invest in expanding the factory space or purchasing more
equipment to accommodate the extra workers. This can lead to a decrease in
profitability and potentially financial losses.
In conclusion, the scenario described demonstrates the application of the Law
of Diminishing Returns, where hiring more workers beyond the optimal number
can result in inefficiencies, increased costs, and reduced overall productivity.
Question 23
Question
A manufacturing company has a production process that involves three stages:
labor, capital, and raw materials. The company currently employs 100 workers,
10 machines, and 500 units of raw materials. The company’s total output is
1000 units. It is observed that by adding an additional worker, the output
increases to 1050 units. However, by adding another worker, the output only
increases to 1070 units. Explain this phenomenon in the context of the Law of
Diminishing Returns.
Solution
The Law of Diminishing Returns states that as increments of one input are
added while holding all other inputs constant, at some point the marginal in-
crease in output will diminish. This phenomenon can be observed in the scenario
described.
Step 1: Calculate the marginal product of labor for each additional worker
added. The marginal product of labor (MPL) is the additional output produced
by adding one more unit of labor while holding all other inputs constant. We
can calculate MPL using the formula:
MP L =∆Q
∆L
where: - ∆Qis the change in total output - ∆Lis the change in labor input
For the first additional worker:
MP L1=1050 −1000
1= 50
For the second additional worker:
MP L2=1070 −1050
1= 20
19
Step 2: Analyze the results in the context of the Law of Diminishing Re-
turns. The Law of Diminishing Returns implies that as more units of an input
are added, the marginal product of that input will eventually diminish. In this
scenario, we observe that the marginal product of labor decreases from 50 to 20
as we add more workers. This indicates that each additional worker contributes
less to the total output as more workers are hired.
Therefore, the phenomenon observed, where the total output increases by
less when going from 1050 to 1070 units compared to going from 1000 to 1050
units, is a clear demonstration of the Law of Diminishing Returns in action.
Question 24
Question
An agricultural firm is analyzing the production of wheat on one of its farms.
The firm notices that as they add more workers to the wheat field, the addi-
tional output from each new worker begins to decline. After conducting further
analysis, they establish that the total product of labor is given by the function
Q(L) = 50L−2L2, where Qrepresents the total output of wheat (in bushels)
and Lis the number of workers employed. Find the number of workers that
maximizes total output and calculate the maximum total output.
Solution
Step 1: To find the number of workers that maximizes total output, we need to
find the critical points of the function Q(L). Step 2: Calculate the derivative of
Q(L) with respect to L. Step 3:
Q′(L) = d
dL(50L−2L2) = 50 −4L
Step 4: Set Q′(L) = 0 to find critical points.
50 −4L= 0
4L= 50
L=50
4
Step 5: The critical point is at L= 12.5, but since we can’t have a fraction of a
worker, we need to test the endpoints of the possible range of workers. Consider
L= 12 and L= 13. Step 6: Calculate the total output for L= 12.
Q(12) = 50(12) −2(12)2= 600 −288 = 312
Step 7: Calculate the total output for L= 13.
Q(13) = 50(13) −2(13)2= 650 −338 = 312
Step 8: The maximum total output occurs at L= 12, with a total output of
312 bushels of wheat.
20
Question 25
Question
A company is currently producing 500 units of a product per day with 10 work-
ers. The company is considering hiring additional workers. After some analysis,
the company’s production manager estimates that the marginal product of the
11th worker will be 70 units per day. However, the marginal product of each
subsequent worker will decrease by 10 units per day. If the company’s goal
is to maximize output while minimizing costs, how many workers should the
company hire?
Solution
The Law of Diminishing Returns states that as additional units of a variable
input (workers in this case) are added to fixed inputs (capital, technology, etc.),
the marginal product of the variable input will eventually decrease.
Let’s denote: - MPi: Marginal product of the i-th worker in units per day -
T Pi: Total product when employing iworkers - T Ci: Total cost of employing i
workers
We are given: - MP11 = 70 units per day - Each subsequent worker’s
marginal product decreases by 10 units per day
To maximize output while minimizing costs, the company should hire work-
ers up to the point where the marginal product of the last worker hired equals
the wage the company is paying. This is because if the marginal product of the
last worker hired is greater than the wage, it is profitable to hire that worker. If
the marginal product of the last worker hired is less than the wage, it is better
not to hire any more workers.
Let’s assume the daily wage per worker is wunits.
Step 1: Calculate Marginal Product Function
We can express the marginal product of the i-th worker in terms of ias
follows:
MPi= 70 −10(i−11)
Step 2: Calculate Total Product Function
The total product produced by employing iworkers can be expressed as the
sum of marginal products up to the i-th worker:
T Pi=
i
X
k=1
MPk
Step 3: Calculate Total Cost Function
The total cost of employing iworkers is given by:
T Ci=w·i
Step 4: Determine Optimal Number of Workers
21
To determine the optimal number of workers to hire, we need to find the
point at which the marginal product of the last worker hired equals the wage.
This can be represented by the equation:
MPi=w
Substitute the marginal product function into the equation and solve for i:
70 −10(i−11) = w
70 −10i+ 110 = w
10i= 180 −w
i=180 −w
10
Since the number of workers must be a whole number, the company should
hire 180−w
10 workers to maximize output while minimizing costs.
Question 26
Question
A company is producing electronic devices and has a production function given
by Q= 5L2
3K1
3, where Qrepresents the number of devices produced, Lis the
amount of labor input, and Kis the amount of capital input. The company
currently has fixed capital and is considering increasing only the amount of
labor input. Determine whether the production function exhibits the Law of
Diminishing Returns as the amount of labor input increases.
Solution
1. To determine whether the production function exhibits the Law of Dimin-
ishing Returns, we need to calculate the marginal product of labor (M P L) and
the average product of labor (AP L) for different levels of labor input.
2. The marginal product of labor can be calculated by taking the partial
derivative of the production function with respect to labor:
MP L =∂Q
∂L =10
3L−1
3K1
3
3. Next, we can calculate the average product of labor by dividing the total
product (Q) by the amount of labor input:
AP L =Q
L= 5L2
3K1
3/L = 5L1
3K1
3
4. Now, let’s investigate the behavior of MP L and AP L as the amount of
labor input (L) increases without changing the amount of capital input (K).
22
5. As Lincreases, let’s evaluate the expressions for M P L and AP L at a
particular level of Land observe any trends in their values.
6. If M P L starts to decrease as Lincreases, while AP L is also diminishing,
then the production function exhibits the Law of Diminishing Returns.
7. If M P L starts to decrease after a certain level of L, it indicates that
each additional unit of labor input contributes less to the total output, which
is a typical characteristic of the Law of Diminishing Returns. Similarly, if AP L
reaches a maximum value and starts to decrease with further increases in L, it
also supports the presence of the Law of Diminishing Returns.
Therefore, by analyzing the behavior of MP L and AP L as the amount
of labor input increases, we can determine whether the production function
exhibits the Law of Diminishing Returns.
Question 27
Question
Suppose a company is producing a certain product and currently employs 100
workers in its production process. The company notices that as they hire more
workers, the output of the product increases at a decreasing rate. After ana-
lyzing the situation, they find that the marginal product of labor is decreasing
beyond a certain point. Explain the concept of the Law of Diminishing Returns
in this scenario.
Solution
The Law of Diminishing Returns states that if one input in the production
process is increased while holding all other inputs constant, a point will even-
tually be reached at which the marginal product of that input will begin to
decrease. In this scenario, the company is experiencing diminishing returns in
their production process as they hire more workers.
Step 1: Marginal Product of Labor The marginal product of labor is
the additional output gained by adding one more unit of labor while holding all
other inputs constant. The company notices that the marginal product of labor
is decreasing beyond a certain point, which signifies the onset of diminishing
returns.
Step 2: Increasing Labor Initially, as the company hires more workers,
the total output of the product increases. Each new worker contributes posi-
tively to the total output, leading to an increasing marginal product of labor.
Step 3: Diminishing Marginal Returns However, due to limited re-
sources such as machinery, workspace, or raw materials, there comes a point
where adding more workers no longer leads to a proportional increase in out-
put. This is the stage of diminishing marginal returns, where each additional
worker contributes less to the total output than the previous worker.
23
Step 4: Production Inefficiency Beyond the point of diminishing returns,
the company may experience production inefficiency. This could result in higher
production costs, lower product quality, and decreased overall profitability.
In conclusion, the Law of Diminishing Returns highlights the concept that
as one input is increased while keeping other inputs constant, the marginal
product of that input will eventually decrease, leading to diminishing returns in
the production process.
Question 28
Question
A manufacturing company is producing smartphones in a factory. The company
has a fixed amount of capital (machinery, equipment, etc.) and labor available
for production. Initially, as more labor is added, the production of smartphones
increases at an increasing rate. However, after a certain point, adding more
labor does not increase production as much. Explain the concept of the Law of
Diminishing Returns in the context of this scenario.
Solution
The Law of Diminishing Returns is a fundamental principle in economics that
states that as one input factor (e.g., labor) is increased while other factors (e.g.,
capital) are held constant, the marginal output eventually decreases. In the
production of smartphones, this law can be observed as follows:
Step 1: Increasing Labor Input Initially, the company experiences in-
creasing returns to scale as more workers are added to the production process.
With a fixed amount of capital, each additional worker can specialize in their
tasks and make the production process more efficient, leading to a greater in-
crease in the number of smartphones produced.
Step 2: Constant Returns to Scale At a certain point, the company
reaches a stage where the addition of more labor starts to result in diminishing
marginal returns. This means that each additional unit of labor contributes
less to the overall production output. The fixed amount of capital may not be
sufficient to support a large workforce effectively, leading to inefficiencies and
decreased productivity.
Step 3: Negative Returns If the company continues to add more and
more labor beyond the point of diminishing returns, it may eventually reach
a stage of negative returns. This means that the marginal output of each ad-
ditional unit of labor is now negative, resulting in an overall decrease in the
total production of smartphones. This stage is highly inefficient and indicates
a misallocation of resources.
In summary, the Law of Diminishing Returns highlights the importance of
optimizing input factors in production processes to achieve maximum efficiency
24
and output. It serves as a warning against over-reliance on any single input
factor without considering the broader context of production.
Question 29
Question
A company is producing chairs in a factory. The company notices that as they
increase the number of workers in the factory, the production of chairs per day
increases initially but at a decreasing rate. Define the law of diminishing returns
and explain how it applies to the production of chairs in the factory.
Solution
The law of diminishing returns, also known as the law of diminishing marginal
returns, states that as the input of one factor of production is increased while
other factors are held constant, the marginal output of that factor will eventually
decrease.
Step 1: Initially, when the company increases the number of workers in
the factory, the production of chairs per day increases. This is because each
additional worker adds more output to the total production and specialization
of labor occurs.
Step 2: However, as the company continues to add more workers, a point
is reached where the factory becomes crowded, and each additional worker may
lead to inefficiencies. For example, there may not be enough space or resources
for each worker to be as productive as before.
Step 3: Eventually, the production of chairs per day will start to increase
at a decreasing rate. This is an indication that the law of diminishing returns
is kicking in. The marginal output of each additional worker is decreasing, and
the overall efficiency of the factory is diminishing.
Step 4: In extreme cases, adding more workers may even lead to a decrease
in the total production of chairs per day. This would be a clear manifestation
of the law of diminishing returns, where the additional workers are now causing
more harm than good to the production process.
Therefore, the law of diminishing returns is applicable to the production of
chairs in the factory as the company observes a decrease in the marginal output
of each additional worker beyond a certain point, leading to a decrease in the
efficiency of the production process.
Question 30
Question
A company produces widgets in a factory where labor and capital are the two
main factors of production. The production function is given by Q= 5L0.5K0.5,
25
where Qis the total output, Lis the amount of labor, and Kis the amount of
capital. If the company currently uses 16 units of labor and 9 units of capital,
determine the marginal product of labor.
Solution
Step 1: To find the marginal product of labor, we first need to find the total
product of labor with 16 units of labor and then find the total product of labor
with 17 units of labor.
Step 2: With 16 units of labor and 9 units of capital, the total output is
calculated by substituting L= 16 and K= 9 into the production function.
Q= 5(16)0.5(9)0.5= 5(4)(3) = 60
Step 3: Next, we determine the total product of labor with 17 units of labor
by substituting L= 17 and K= 9 into the production function.
Q′= 5(17)0.5(9)0.5= 5(4.123)(3) ≈61.85
Step 4: The marginal product of labor is then calculated as the change in
total output over the change in labor inputs.
MPL=∆Q
∆L=Q′−Q
17 −16 ≈61.85 −60
1≈1.85
Therefore, the marginal product of labor when the company uses 16 units
of labor is approximately 1.85.
Question 31
Question
In an agricultural setting, a farmer notices that as more fertilizer is applied to
a field, the increase in crop yield starts to diminish. Suppose the production
function for a specific crop is given by Q= 10L−0.5L2, where Qis the total crop
yield and Lis the amount of labor input. Determine the point at which the law
of diminishing returns sets in, and explain the concept behind this phenomenon.
Solution
1. To find the point at which the law of diminishing returns sets in, we need
to differentiate the production function with respect to Land set the derivative
equal to zero: dQ
dL = 10 −L= 0
L= 10
26
2. Therefore, the point at which the law of diminishing returns sets in is
when L= 10. At this point, the marginal product of labor will start to decrease.
3. The concept behind the law of diminishing returns is that as more units
of a variable input (in this case, labor) are added to a fixed input (in this case,
the field), at some point the marginal product of the variable input will start
to decrease. This is due to factors such as limited resources, inefficiencies, and
diminishing returns to scale. In the case of the farmer, increasing the amount
of labor beyond a certain point may lead to overcrowding, overworking the
field, and suboptimal use of resources, causing the marginal product of labor to
decrease.
Question 32
Question
A company initially has a farm with 100 workers which produces 1000 units of a
certain crop per month. The company decides to hire more workers to increase
production. After hiring 50 additional workers, the production increases to 1500
units per month. However, when they hire another 50 workers (a total of 200
workers), the production only increases to 1600 units per month.
Given this scenario, explain the concept of the Law of Diminishing Returns
and discuss how it applies to this situation.
Solution
The Law of Diminishing Returns states that as additional units of a variable
input (in this case, workers) are added to fixed inputs (such as land or ma-
chinery), there is a point at which the marginal product of the variable input
will decrease. This means that each additional unit of the variable input will
contribute less to the total output.
Step 1: Calculate the marginal product of labor for each additional batch
of workers.
The initial production is 1000 units with 100 workers. The addition of 50
workers increased production to 1500 units, so the marginal product of these 50
workers is:
Marginal Product of Labor = Change in Output
Change in Labor =1500 −1000
50 =500
50 = 10
Similarly, the addition of another 50 workers increased production to 1600
units, so the marginal product of these 50 workers is:
Marginal Product of Labor = 1600 −1500
50 =100
50 = 2
Step 2: Analysis of the Law of Diminishing Returns in this scenario
27
In this scenario, we observe diminishing marginal returns in the production
of the crop. The initial set of 50 workers increased production by 10 units each,
but the next set of 50 workers only increased production by 2 units each.
This diminishing return occurs because as more workers are hired, the fixed
inputs (such as land or machinery) become a constraint on the ability of each
additional worker to contribute. Eventually, this leads to the point where each
additional worker contributes less to the total output, resulting in diminishing
marginal returns.
Therefore, the Law of Diminishing Returns is clearly evident in this situation
where the increase in output is not proportional to the increase in the number
of workers hired.
Question 33
Question
A company produces widgets in a factory with a fixed size. The company noticed
that initially, as they increased the number of workers in the factory, the total
number of widgets produced was increasing at an increasing rate. However, after
a certain point, the total number of widgets produced started increasing at a
decreasing rate. Explain this phenomenon in terms of the Law of Diminishing
Returns.
Solution
The Law of Diminishing Returns states that as additional units of a variable
input are applied to a fixed input, at some point the marginal product of the
variable input will decrease. This can be explained using the concept of Total
Product, Marginal Product, and Average Product.
Let’s denote: - T P as Total Product, the total output or quantity of wid-
gets produced. - MP as Marginal Product, the additional output produced by
adding one more unit of the variable input. - AP as Average Product, the total
output per unit of the variable input.
Initially, when additional workers are hired, the company experiences in-
creasing returns - this means the Marginal Product is increasing. As more
workers are added, specialization, division of labor, and efficient use of fixed
resources lead to a higher output per additional worker.
Step 1: Increasing Marginal Product. Initially, the company experiences
increasing Marginal Product, meaning each additional worker contributes sig-
nificantly to the total number of widgets produced. This is due to optimal
utilization of fixed resources and division of labor which enhance productivity.
Step 2: Constant Marginal Product. After a certain point, the company
reaches a stage where adding more workers does not increase productivity at
the same rate. This is a result of fixed inputs (e.g., limited space, machinery)
28
being shared among an increasing number of workers. As a result, the Marginal
Product remains constant.
Step 3: Decreasing Marginal Product. Eventually, the company reaches a
point where the Marginal Product starts to decrease. This happens because
adding more workers leads to overcrowding and inefficiencies due to the fixed
resources becoming overburdened. Each additional worker might interfere with
the work of others or limit the available resources per worker, causing a drop in
productivity.
In conclusion, the Law of Diminishing Returns explains the phenomenon
where, after a certain point, adding more units of a variable input (workers) to
a fixed input (factory size) results in decreasing Marginal Product and, conse-
quently, decreasing total output (widgets produced) at an increasing rate.
Question 34
Question
In a manufacturing plant, the production of smartphones follows the law of
diminishing returns. The total output (Q) of smartphones produced per day is
given by the function:
Q(K, L) = 10K0.5L3
4
Where Krepresents the units of capital (machinery) used and Lrepresents the
units of labor. If the plant has 10 units of capital and 16 units of labor, calculate
the marginal product of labor.
Solution
Step 1: Calculate the total product of smartphones with 10 units of capital and
16 units of labor. Substitute these values into the production function:
Q(10,16) = 10(10)0.5(16)3
4
Q(10,16) = 10(3.162)(32)
Q(10,16) = 1009.44
Step 2: Calculate the total product of smartphones with 10 units of capital
and 15 units of labor.
Q(10,15) = 10(10)0.5(15)3
4
Q(10,15) = 10(3.162)(27.386)
Q(10,15) = 860.21
Step 3: Calculate the marginal product of labor using the formula:
MP L =Q(K, L)−Q(K, L −1)
29
MP L = 1009.44 −860.21
MP L = 149.23
Therefore, the marginal product of labor when the plant has 10 units of
capital and 16 units of labor is 149.23 smartphones per additional unit of labor.
Question 35
Question
A company is producing a certain product with a fixed amount of capital. Ini-
tially, the company hired 10 workers and the total product produced was 500
units. When the company hired 5 more workers, the total product increased
to 700 units. However, when the company hired another 5 workers, the total
product only increased to 720 units. Determine whether the law of diminishing
returns is present in this scenario.
Solution
Step 1: Calculate the marginal product of labor for each additional worker. Let
T P represent the total product and Lrepresent the number of workers. When
10 workers were employed: T P1= 500 units When 15 workers were employed:
T P2= 700 units When 20 workers were employed: T P3= 720 units
Step 2: Calculate the marginal product of labor using the formula:
MPL=∆T P
∆L
For the first increase of 5 workers:
MPL1=700 −500
15 −10 =200
5= 40
For the second increase of 5 workers:
MPL2=720 −700
20 −15 =20
5= 4
Step 3: Analyze the results. The law of diminishing returns states that as
additional units of a variable input (labor) are added to a fixed amount of an-
other input (capital), the marginal product of the variable input will eventually
decrease. In this scenario, the marginal product of labor decreases from 40 to 4
as more workers are hired. Therefore, the law of diminishing returns is present
in this scenario.
30
MP L = 1009.44 −860.21
MP L = 149.23
Therefore, the marginal product of labor when the plant has 10 units of
capital and 16 units of labor is 149.23 smartphones per additional unit of labor.
Question 35
Question
A company is producing a certain product with a fixed amount of capital. Ini-
tially, the company hired 10 workers and the total product produced was 500
units. When the company hired 5 more workers, the total product increased
to 700 units. However, when the company hired another 5 workers, the total
product only increased to 720 units. Determine whether the law of diminishing
returns is present in this scenario.
Solution
Step 1: Calculate the marginal product of labor for each additional worker. Let
T P represent the total product and Lrepresent the number of workers. When
10 workers were employed: T P1= 500 units When 15 workers were employed:
T P2= 700 units When 20 workers were employed: T P3= 720 units
Step 2: Calculate the marginal product of labor using the formula:
MPL=∆T P
∆L
For the first increase of 5 workers:
MPL1=700 −500
15 −10 =200
5= 40
For the second increase of 5 workers:
MPL2=720 −700
20 −15 =20
5= 4
Step 3: Analyze the results. The law of diminishing returns states that as
additional units of a variable input (labor) are added to a fixed amount of an-
other input (capital), the marginal product of the variable input will eventually
decrease. In this scenario, the marginal product of labor decreases from 40 to 4
as more workers are hired. Therefore, the law of diminishing returns is present
in this scenario.
30
