We saw in the chapter opener that some colleges and private companies have launched online courses that anyone with an Internet connection can take. The most successful of these massive open online courses (MOOCs) have attracted tens of thousands of students. Suppose that your college offers a MOOC and spends a total of \(\$ 200,000\) on one-time costs to have instructors prepare the course material and buy additional server capacity. The college administration estimates that the variable cost of offering the course will be \(\$ 20\) per student per course. This variable cost is the same, regardless of how many students enroll in the course. a. Use this information to fill in the missing values in the following table: $$ \begin{array}{c|c|c|c|c} \hline \text { Number of } & & \\ \begin{array}{c} \text { Students } \\ \text { Taking the } \\ \text { Course } \end{array} & \begin{array}{c} \text { Average } \\ \text { Total Cost } \end{array} & \begin{array}{c} \text { Average } \\ \text { Variable } \\ \text { Cost } \end{array} & \begin{array}{c} \text { Average } \\ \text { Fixed Cost } \end{array} & \begin{array}{c} \text { Marginal } \\ \text { Cost } \end{array} \\ \hline 1,000 & & & & \\ \hline 10,000 & & & & \\ \hline 20,000 & & & & \\ \hline \end{array} $$ b. Use your answer to part (a) to draw a cost curve graph to illustrate your college's costs of offering this course. Your graph should measure cost on the vertical axis and the quantity of students taking the course on the horizontal axis. Be sure your graph contains the following curves: average total cost, average variable cost, average fixed cost, and marginal cost.

Step by step solution

01

Fill out the Average Total Cost (ATC)

The total cost consists of fixed costs and variable costs. The fixed cost is given as $200,000, which does not change with the number of students. The variable cost per student is $20. Hence, the ATC for a given number of students can be calculated by the equation: ATC = (Fixed Costs + Variable Costs per student * Number of students) / Number of Students So the ATC for 1,000 students would be \((200,000 + 20*1,000) / 1,000 = \$220\), for 10,000 students it would be \((200,000 + 20*10,000) / 10,000 = \$40\), and for 20,000 students it would be \((200,000 + 20*20,000) / 20,000 = \$30\).

02

Fill out the Average Variable Cost (AVC)

The AVC is simply the variable cost per student which is given as $20 for all the students. This does not change with the number of students.

03

Fill out the Average Fixed Cost (AFC)

The AFC is the fixed cost divided by the number of students. So for 1,000 students, it would be $200,000 / 1,000 = $200, for 10,000 students it would be $200,000 / 10,000 = $20, and for 20,000 students it would be $200,000 / 20,000 = $10.

04

Fill out the Marginal Cost (MC)

The MC is equivalent to the variable cost in this case because the variable cost is constant per student. So the MC is $20 for all the students.

05

Draw the cost curve graph

Use the calculated data to draw a graph with the number of students on the x-axis and cost on the y-axis. This graph should contain four curves: the ATC starting at $220 for 1,000 students and decreasing to $30 for 20,000 students, the AVC as a horizontal line at $20, the AFC starting at $200 for 1,000 students and decreasing to $10 for 20,000 students, and the MC as a horizontal line at $20.

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