(Transcript of audio with descriptions. Transcript includes narrator headings and description headings of the visual content)
(Speaker)
This problem is going to ask you a series of questions related to the cost of production for Kate's Katering.
In the table, you are given the number of meals Kate can produce and her variable costs at each level of output. Further in the problem, you are given Kate's fixed cost of 100 dollars per day.
(Description)
The following text is written:
Kate’s Katering provides catered meals, and the catered meals industry is perfectly competitive. Kate’s machinery costs $100 per day and is the only fixed input. Her variable cost consists of the wages paid to the cooks and the food ingredients. The variable cost per day associated with each level of output is given in the accompanying table.
The table below this text is provided.
The table consists of 2 columns: Quantity of meals, VC.
The table consists of 6 rows.
The first row: Quantity of meals is, 0, VC is, 0 dollars.
The second row: Quantity of meals is, 10, VC is, 200 dollars.
The third row: Quantity of meals is, 20, VC is, 300 dollars.
The fourth row: Quantity of meals is, 30, VC is, 480 dollars.
The fifth row: Quantity of meals is, 40, VC is, 700 dollars.
The sixth row: Quantity of meals is, 50, VC is, 1000 dollars.
(Speaker)
In part A, you are asked to calculate Kate’s total cost, marginal cost, average variable cost, and average total cost.
We are going to start by extending our table to make this a little easier.
(Description)
The following columns are added to the right sight of the table: TC of meal, MC of meal, AVC of meal, ATC of meal. Cells in these columns are blank.
The following text is written above the table:
Calculate the total cost, the marginal cost, the average variable cost, and the average total cost for each quantity of output.
(Speaker)
We are going to start first by calculating Kate’s total cost. Recall in the problem you are told Kate spends 100 dollars per day on machinery. This is her fixed cost. The table provides you with the variable cost. So Kate’s total cost is found by adding 100 dollars to variable cost for all levels of production.
(Description)
The following text is written above the table:
Fixed cost are given as 100 dollars, we can use this to find total cost.
Recall that TC equals VC plus FC
A cell at the intersection of the first row and the column TC of meal is, equals 0 plus 100 equals 100 dollars.
A cell at the intersection of the second row and the column TC of meal is, equals 200 plus 100 equals 300 dollars.
A cell at the intersection of the third row and the column TC of meal is, equals 300 plus 100 equals 400 dollars.
A cell at the intersection of the fourth row and the column TC of meal is, equals 480 plus 100 equals 580 dollars.
A cell at the intersection of the fifth row and the column TC of meal is, equals 700 plus 100 equals 800 dollars.
A cell at the intersection of the sixth row and the column TC of meal is, equals 1000 plus 100 equals 1100 dollars.
These cells are briefly highlighted.
Then the values in column TC of meal are simplified to the following ones, starting from the first row: 100 dollars, 300 dollars, 400 dollars, 580 dollars, 800 dollars, 1100 dollars, respectively.
(Speaker)
For example, if Kate produces 30 meals, her variable cost will be 480 dollars. And her fixed costs are 100 dollars. Adding these together gives Kate a total cost of 580 dollars.
Next, we're going to use our calculation of total cost to find Kat marginal cost. Remember, the definition of marginal cost is the change in total cost divided by the change in quantity.
As Kate increases her production from 0 to 10 meals, her total cost will increase from 100 dollars to 300 dollars. Marginal cost of the first 10 meals is 300 dollars minus 100 dollars divided by 10 minus 0, or 200 dollars divided by 10, or 20 dollars.
(Description)
The following text is written above the table:
Marginal cost is calculated as the change in Total Cost divided by the change in Quantity.
A cell at the intersection of the first row and the column MC of meal is, dashed.
A cell at the intersection of the second row and the column MC of meal is, equals the change in Total Cost divided by the change in Quantity equals StartFraction 300 minus 100 Over 10 minus 0 EndFraction equals 200 divided by 10 equals 20. This cell is briefly highlighted.
(Speaker)
We are going to repeat this process as Kate increases her production to 20, 30, 40, and 50 meals. Since her production is always increasing by increments of 10, the denominator will be 10.
(Description)
A cell at the intersection of the third row and the column MC of meal is, equals the change in Total Cost divided by the change in Quantity equals StartFraction 400 minus 300 Over 10 minus 0 EndFraction equals 100 divided by 10 equals 10.
A cell at the intersection of the fourth row and the column MC of meal is, equals the change in Total Cost divided by the change in Quantity equals StartFraction 580 minus 400 Over 10 minus 0 EndFraction equals 180 divided by 10 equals 18.
A cell at the intersection of the fifth row and the column MC of meal is, equals the change in Total Cost divided by the change in Quantity equals StartFraction 800 minus 580 Over 10 minus 0 EndFraction equals 220 divided by 10 equals 22.
A cell at the intersection of the sixth row and the column MC of meal is, equals the change in Total Cost divided by the change in Quantity equals StartFraction 1100 minus 800 Over 10 minus 0 EndFraction equals 300 divided by 10 equals 30.
These cells are briefly highlighted.
Then the values in column MC of meal are simplified to the following ones, starting from the first row: blank, 20.00 dollars, 10.00 dollars, 18.00 dollars, 22.00 dollars, 30.00 dollars, respectively.
(Speaker)
Now that we have finished calculating marginal costs, you will notice that marginal costs initially decrease. But as production continues to increase, so do marginal costs.
The last part of the problem requires you to calculate the average variable cost and average total cost. Both measures are calculated in a similar fashion.
Starting with 10 meals, average variable cost is found by dividing variable cost at 10 meals, 200 dollars by 10 meals. When Kate produces 10 meals, her average variable cost is 20 dollars.
(Description)
The following text is written above the table:
AVC and ATC are calculated by dividing VC and TC by quantity at each level of output.
AVC equals VC divided by Q
ATC equals TC divided by Q
A cell at the intersection of the first row and the column AVC of meal is, dashed.
A cell at the intersection of the second row and the column AVC of meal is, equals VC divided by Q equals 200 divided by 10 equals 20. This cell is briefly highlighted.
(Speaker)
We can find average total cost by dividing total cost of producing 10 meals, 300 dollars, by 10. When Kate produces 10 meals, her average total cost is 30 dollars per meal.
(Description)
A cell at the intersection of the first row and the column ATC of meal is, dashed.
A cell at the intersection of the second row and the column ATC of meal is, equals TC divided by Q equals 300 divided by 10 equals 30. This cell is briefly highlighted.
(Speaker)
Finally, we can calculate the remainder of Kate’s average variable and average total cost.
(Description)
A cell at the intersection of the third row and the column AVC of meal is, equals 300 divided by 20 equals 15.
A cell at the intersection of the third row and the column ATC of meal is, equals 400 divided by 20 equals 20.
A cell at the intersection of the fourth row and the column AVC of meal is, equals 480 divided by 30 equals 16.
A cell at the intersection of the fourth row and the column ATC of meal is, equals 580 divided by 30 equals 19.33.
A cell at the intersection of the fifth row and the column AVC of meal is, equals 700 divided by 40 equals 17.50.
A cell at the intersection of the fifth row and the column ATC of meal is, equals 800 divided by 40 equals 20.00.
A cell at the intersection of the sixth row and the column AVC of meal is, equals 1000 divided by 50 equals 20.00.
A cell at the intersection of the sixth row and the column ATC of meal is, equals 1100 divided by 50 equals 22.00.
These cells are highlighted.
(Speaker)
In both cases, you will notice that both averages initially decrease but eventually increase. Average variable costs increase after 20 meals. you should note that at this point marginal costs are now greater than average variable cost. Average total costs begin to increase after 30 meals, which is also the point where marginal costs are greater than average total cost.