(Transcript of audio with descriptions. Transcript includes narrator headings and description headings of the visual content)
(Speaker)
In this part you are asked to use the table to determine the marginal cost, individual marginal benefit, and marginal social benefit for security services.
(Description)
The table consists of 6 columns: Quantity of security guards, Total cost, Marginal cost, Total benefit to each resident, Individual marginal benefit, Marginal social benefit.
The columns, Marginal cost, Individual marginal cost, Marginal social benefit, are blank.
The table consist of 5 rows.
The first row: Quantity of security guards is, 0, Total cost is, 0 dollars, Total individual benefit to each resident is, 0 dollars.
The second row: Quantity of security guards is, 1, Total cost is, 150, Total individual benefit to each resident is, 10.
The third row: Quantity of security guards is, 2, Total cost is, 300, Total individual benefit to each resident is, 16.
The fourth row: Quantity of security guards is, 3, Total cost is, 450, Total individual benefit to each resident is, 18.
The fifth row: Quantity of security guards is, 4, Total cost is, 600, Total individual benefit to each resident is, 19.
The following text is written above the table:
In the box below calcualte the marginal cost, the individual marginal benefit for each resident, and the marginal social benefit.
(Speaker)
First, we are going to calculate the marginal cost of hiring each additional security guard. As we increase the quantity of security guards from zero to one, the total cost increases from zero dollars to 150 dollars.
Remember, the marginal cost is the change in total cost. So in this case, the marginal cost is 150 dollars.
(Description)
A cell at the intersection of the first row and the column Marginal cost is, equals 150 minus 0 equals 150 dollars.
(Speaker)
We can see the marginal cost will actually be 150 dollars for each additional security guard as total costs increase by 150 dollars as we move from one to two to three to four security guards.
(Description)
A cell at the intersection of the third row and the column Marginal cost is, equals 300 minus 150 equals 150.
A cell at the intersection of the fourth row and the column Marginal cost is, equals 450 minus 300 equals 150.
A cell at the intersection of the fifth row and the column Marginal cost is, equals 600 minus 450 equals 150.
(Speaker)
Next, we are going to calculate the individual marginal benefit, or the additional benefit, to each resident. The marginal benefit is calculated in a similar way as marginal cost. As we hire the first security guard, the total benefit increases from zero to 10 dollars. So the marginal benefit of the first security guard is 10 dollars.
(Description)
A cell at the intersection of the second row and the column Individual marginal benefit is, equals 10 minus 0 equals 10 dollars.
(Speaker)
You notice that as we hire more security guards, the marginal benefit decreases. Hiring the second security guard provides a marginal benefit of 6 dollars to each resident.
(Description)
A cell at the intersection of the third row and the column Individual marginal benefit is, equals 16 minus 10 equals 6.
(Speaker)
Hiring the third and fourth security guards provide a benefit of 2 dollars and 1 dollar, respectively.
(Description)
A cell at the intersection of the fourth row and the column Individual marginal benefit is, equals 18 minus 16 equals 2.
A cell at the intersection of the fifth row and the column Individual marginal benefit is, equals 19 minus 18 equals 1.
(Speaker)
In the final column, you are asked to calculate marginal social benefit. The problem states that each resident will receive the same marginal benefit. If there are 100 residents, then the marginal social benefit of hiring the first security guard is 1 thousand dollars. We found the marginal social benefit by simply multiplying the individual marginal benefit by the total number of residents.
(Description)
A cell at the intersection of the second row and the column Marginal social benefit is, equals 10 dollars times 100 equals 1000 dollars.
(Speaker)
We can also do this for the case of the second, third, and fourth security guards. Doing so yields a marginal social benefit or 600 dollars, 200 dollars, and 100 dollars, respectively.
(Description)
A cell at the intersection of the third row and the column Marginal social benefit is, equals 6 times 100 equals 600.
A cell at the intersection of the fourth row and the column Marginal social benefit is, equals 2 times 100 equals 200.
A cell at the intersection of the fifth row and the column Marginal social benefit is, equals 1 times 100 equals 100.