Work It Out, Chapter 10, Step 1

(Transcript of audio with descriptions. Transcript includes narrator headings and description headings of the visual content)

(Speaker)
This problem is going to analyze the individual's decision to maximize utility subject to an income constraint. In particular, you're going to solve for Brenda's consumption of bagels and cups of coffee that maximizes her utility given in the table seen here.

(Description)
The table is labeled Consumption bundle. It consists of 3 columns: Quantity of bagels, Quantity of coffee (cups), Total utility (utils). The table consists of 11 rows. The first row: 0, 0, 0. The second row: 0, 2, 28. The third row: 0, 4, 40. The fourth row: 1, 2, 48. The fifth row: 1, 3, 54. The sixth row: 2, 0, 28. The seventh row: 2, 2, 56. The eight row: 3, 1, 54. The ninth row: 3, 2, 62. The tenth row: 4, 0, 40. The eleventh row: 4, 2, 66. The following text is briefly written above the table: Brenda likes to have bagels and coffee for breakfast. The accompanying table shows Brenda’s total utility from various consumption bundles of bagels and coffee. The following text is briefly written below the table: Suppose Brenda knows she will consume 2 cups of coffee for sure. However, she can choose to consume different quantities of bagels. She can choose either 0, 1, 2, 3, or 4 bagels.

(Speaker)
In the first part of the problem, we are told that Brenda is going to consume two cups of coffee. We need to find total utility and marginal utility for each combination of bagels and coffee.

(Description)
An additional table is shown to the right of the original one. It is also labeled Consumption Bundle and it has the same columns with the additional fourth column on the right side, which is labeled as Marginal utility (utils). Cells in columns Total utility (utils) and Marginal utility (utils) are blank except for the first cell of Marginal Utility (utils) column, which is dashed. All values in cells of the column Quantity of Coffee (cups) are equal 2. The column Quantity of Bagels has the following values starting from the first row: 0, 1, 2, 3, 4, respectively. The table consists of 5 rows. The values in these cells correspond to the values in the left table. The following text is written above the tables: Find Brenda’s total utility and calculate her marginal utility from bagels as she goes from consuming 0 bagel to 1 bagel, from 1 bagel to 2 bagels, from 2 bagels to 3 bagels, and from 3 bagels to 4 bagels. Assume she consumes two cups of coffee.

(Speaker)
You will notice that we kept only rows where Brenda is consuming two bagels. To find total utility, we need to simply look at the table. When Brenda consumes zero bagels and two cups of coffee, she will have 28 utils of utility.

(Description)
The corresponding data in the second row of the left table is briefly highlighted. The number 28 is written in the first row and Total utility (utils) column of the right table. The first row of the right table is also briefly highlighted.

(Speaker)
Next, we want to find the total and marginal utility for Brenda as she consumes one bagel and two cups of coffee. Total utility is found from the larger table. For Brenda, she will have 48 utils of total utility. To calculate marginal utility, we're going to simply take the change in total utility as Brenda increases her bagel consumption from zero to one bagel. This gives her a marginal utility of 20 utils, the difference in total utility.

(Description)
The corresponding data in the fourth row of the left table is briefly highlighted. The cells in the second row of the right table now have the following values: 1, 2, 48, equals 48 minus 28 equals 20. This row is briefly highlighted.

(Speaker)
We can repeat the process as she increases her consumption to two bagels. Brenda’s total utility increases to 56 utils. And her marginal utility for the second bagel is 56 minus 48, or 8 utils.

(Description)
The corresponding data in the seventh row of the left table is briefly highlighted. The cells in the third row of the right table now have the following values: 2, 2, 56, equals 56 minus 48 equals 8. This row is briefly highlighted.

(Speaker)
Finally, we can complete the table by finding her total utility as she increases her bagel consumption to three and four bagels. Her total utility increases to 62 and 66 utils, respectively. Her marginal utility of the third bagel is 62 minus 56, or 6 utils. And her marginal utility for the fourth bagel is 66 minus 62, or 4 utils.

(Description)
The corresponding data in the ninth and the eleventh rows of the left table is briefly highlighted. The cells in the third row of the right table now have the following values: 3, 2, 62, equals 62 minus 56 equals 6. This row is briefly highlighted. The cells in the fourth row of the right table now have the following values: 4, 2, 66, equals 66 minus 62 equals 4. This row is briefly highlighted.