Math / Data & Statistics

QuestionCompleted: 7 of 8 My score: $7.5 / 8$ pts (93.75\%) Part 2 of 2
Suppose a firm produces hardware that plays video games using workers according to the table below. Suppose also that its output sells for $\$ 100$ per unit. \begin{tabular}{cc} \hline Workers & Output \\ \hline 0 & 0 \\ 1 & 24 \\ 2 & 36 \\ 3 & 42 \\ 4 & 45 \\ 5 & 47 \\ \hline \end{tabular}
Is the firm experiencing the effects predicted by the law of diminishing returns? The firm is experiencing diminishing returns. What is the value of the marginal product of the third worker? The third worker's value of the marginal product is $\$ \square$ . (Enter your response as an integer.)

Studdy Solution

STEP 1

What is this asking? We need to check if the firm's output growth is slowing down as they hire more workers, and figure out how much extra money the third worker brings in. Watch out! Don't mix up total output with extra output from each worker.
We're interested in how much more stuff is made when adding each worker.

STEP 2

1. Calculate Marginal Product
2. Calculate Value of Marginal Product
3. Check for Diminishing Returns

STEP 3

Let's calculate the marginal product!
This tells us the extra output we get from each additional worker.
It's like checking how much more hardware each new worker helps create.

STEP 4

For the first worker, the marginal product is simply their output: $\text{MP}_1 = 24$ .

STEP 5

For the second worker, it's the difference between the output with two workers and the output with just one: $\text{MP}_2 = 36 - 24 = 12$ .

STEP 6

Similarly, the third worker's marginal product is $\text{MP}_3 = 42 - 36 = 6$ .

STEP 7

The fourth worker adds $\text{MP}_4 = 45 - 42 = 3$ units.

STEP 8

Finally, the fifth worker contributes $\text{MP}_5 = 47 - 45 = 2$ units.

STEP 9

Now, let's find the value of the marginal product (VMP).
This tells us how much extra money each worker generates.
Since each unit sells for $\$100$ , we just multiply the marginal product by the price.

STEP 10

So, the third worker's VMP is $\text{VMP}_3 = \text{MP}_3 \cdot \text{Price} = 6 \cdot \$100 = \$600$ .

STEP 11

Let's see if the law of diminishing returns is happening here.
This law says that as we add more workers, the extra output from each new worker will eventually start to decrease.

STEP 12

Looking at the marginal products we calculated: $24, 12, 6, 3, 2$ , we see they are indeed decreasing!
Each new worker adds less to the total output than the one before.
So, yes, diminishing returns are at play!

STEP 13

The value of the marginal product of the third worker is $\$600$ .
The firm is experiencing diminishing returns, as the marginal product of each worker decreases as more workers are hired.

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Studdy Solution

STEP 1

STEP 2

1. Calculate Marginal Product
2. Calculate Value of Marginal Product
3. Check for Diminishing Returns

STEP 3

Let's calculate the marginal product!
This tells us the extra output we get from each additional worker.
It's like checking how much more hardware each new worker helps create.

STEP 4

For the first worker, the marginal product is simply their output: $\text{MP}_1 = 24$ .

STEP 5

For the second worker, it's the difference between the output with two workers and the output with just one: $\text{MP}_2 = 36 - 24 = 12$ .

STEP 6

Similarly, the third worker's marginal product is $\text{MP}_3 = 42 - 36 = 6$ .

STEP 7

The fourth worker adds $\text{MP}_4 = 45 - 42 = 3$ units.

STEP 8

Finally, the fifth worker contributes $\text{MP}_5 = 47 - 45 = 2$ units.

STEP 9

Now, let's find the value of the marginal product (VMP).
This tells us how much extra money each worker generates.
Since each unit sells for $\$100$ , we just multiply the marginal product by the price.

STEP 10

So, the third worker's VMP is $\text{VMP}_3 = \text{MP}_3 \cdot \text{Price} = 6 \cdot \$100 = \$600$ .

STEP 11

Let's see if the law of diminishing returns is happening here.
This law says that as we add more workers, the extra output from each new worker will eventually start to decrease.

STEP 12

Looking at the marginal products we calculated: $24, 12, 6, 3, 2$ , we see they are indeed decreasing!
Each new worker adds less to the total output than the one before.
So, yes, diminishing returns are at play!

STEP 13

The value of the marginal product of the third worker is $\$600$ .
The firm is experiencing diminishing returns, as the marginal product of each worker decreases as more workers are hired.

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Studdy Solution

STEP 1

STEP 2

1. Calculate Marginal Product2. Calculate Value of Marginal Product3. Check for Diminishing Returns

STEP 3

Let's **calculate the marginal product**!This tells us the *extra* output we get from *each additional* worker.It's like checking how much *more* hardware each new worker helps create.

STEP 4

For the *first* worker, the marginal product is simply their output: MP1=24\text{MP}_1 = 24MP1​=24.

STEP 5

For the *second* worker, it's the difference between the output with two workers and the output with just one: MP2=36−24=12\text{MP}_2 = 36 - 24 = 12MP2​=36−24=12.

STEP 6

Similarly, the *third* worker's marginal product is MP3=42−36=6\text{MP}_3 = 42 - 36 = 6MP3​=42−36=6.

STEP 7

The *fourth* worker adds MP4=45−42=3\text{MP}_4 = 45 - 42 = 3MP4​=45−42=3 units.

STEP 8

Finally, the *fifth* worker contributes MP5=47−45=2\text{MP}_5 = 47 - 45 = 2MP5​=47−45=2 units.

STEP 9

Now, let's find the **value of the marginal product (VMP)**.This tells us how much extra *money* each worker generates.Since each unit sells for $100\$100$100, we just multiply the marginal product by the price.

STEP 10

So, the *third* worker's VMP is VMP3=MP3⋅Price=6⋅$100=$600\text{VMP}_3 = \text{MP}_3 \cdot \text{Price} = 6 \cdot \$100 = \$600VMP3​=MP3​⋅Price=6⋅$100=$600.

STEP 11

Let's see if the **law of diminishing returns** is happening here.This law says that as we add more workers, the *extra* output from each new worker will eventually start to decrease.

STEP 12

Looking at the marginal products we calculated: 24,12,6,3,224, 12, 6, 3, 224,12,6,3,2, we see they are indeed decreasing!Each new worker adds less to the total output than the one before.So, yes, diminishing returns are at play!

STEP 13

The value of the marginal product of the third worker is $600\$600$600.The firm *is* experiencing diminishing returns, as the marginal product of each worker decreases as more workers are hired.

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1. Calculate Marginal Product
2. Calculate Value of Marginal Product
3. Check for Diminishing Returns

Let's calculate the marginal product!
This tells us the extra output we get from each additional worker.
It's like checking how much more hardware each new worker helps create.

For the first worker, the marginal product is simply their output: $\text{MP}_1 = 24$ .

For the second worker, it's the difference between the output with two workers and the output with just one: $\text{MP}_2 = 36 - 24 = 12$ .

Similarly, the third worker's marginal product is $\text{MP}_3 = 42 - 36 = 6$ .

The fourth worker adds $\text{MP}_4 = 45 - 42 = 3$ units.

Finally, the fifth worker contributes $\text{MP}_5 = 47 - 45 = 2$ units.

Now, let's find the value of the marginal product (VMP).
This tells us how much extra money each worker generates.
Since each unit sells for $\$100$ , we just multiply the marginal product by the price.

So, the third worker's VMP is $\text{VMP}_3 = \text{MP}_3 \cdot \text{Price} = 6 \cdot \$100 = \$600$ .

Let's see if the law of diminishing returns is happening here.
This law says that as we add more workers, the extra output from each new worker will eventually start to decrease.

Looking at the marginal products we calculated: $24, 12, 6, 3, 2$ , we see they are indeed decreasing!
Each new worker adds less to the total output than the one before.
So, yes, diminishing returns are at play!

The value of the marginal product of the third worker is $\$600$ .
The firm is experiencing diminishing returns, as the marginal product of each worker decreases as more workers are hired.