The Admissions Director (AD) wants to determine the optimum number of students for each ECO561 class. You are provided with the following data:
Tuition is $1250 per student.
Instructor Pay $2500
Other incidental (variable) costs - $1000.00
Variable cost increases by 10% per each additional student
How many students will you recommend to the AD?
What would be the profit for the given number of students?
Is this a profit maximizing number of students?
Now assume that variable cost increases by 15% for each additional student, what is the new profit maximizing number of students?
What is the relevance of the marginal rule (MR = MC) in your decision making?
To determine the optimum number of students for each ECO561 class, we need to consider the costs and revenue associated with each student and find the number that maximizes profit. Let's break down the steps to get the answers to each question:
1. How many students will you recommend to the AD?
- To answer this question, we need to compare the revenue generated by each additional student with the variable costs incurred for that student. We know that tuition is $1250 per student, instructor pay is $2500, and other incidental costs are $1000. The variable cost increases by 10% for each additional student.
Let's calculate the variable cost for each student, considering the 10% increase:
- For the first student: $1000
- For the second student: $1000 + ($1000 * 10%) = $1100
- For the third student: $1100 + ($1100 * 10%) = $1210
- For the fourth student: $1210 + ($1210 * 10%) = $1331
- And so on...
We will compare the revenue created by each additional student with the respective variable cost to determine the number of students to recommend.
2. What would be the profit for the given number of students?
- Once we determine the number of students recommended, we can calculate the revenue and costs associated with that number of students to find the profit. The formula for profit is: Profit = (Revenue - Total Costs).
3. Is this a profit-maximizing number of students?
- To determine if this is the profit-maximizing number of students, we need to analyze how profit changes with each additional student. If adding more students increases profit, it means we haven't reached the maximum yet. However, if adding more students decreases profit, it means we have surpassed the profit-maximizing number.
4. Now assume that variable cost increases by 15% for each additional student, what is the new profit-maximizing number of students?
- To find the new profit-maximizing number of students, we follow the same steps as before, but now with the increased variable cost of 15% per additional student. We calculate the variable cost for each student considering the 15% increase and compare it with the revenue generated to find the optimal number of students.
5. What is the relevance of the marginal rule (MR = MC) in your decision making?
- In decision making, the marginal rule (MR = MC) is used to determine the level of output that maximizes profit. Marginal Revenue (MR) represents the change in total revenue caused by producing one additional unit, while Marginal Cost (MC) represents the change in total cost caused by producing one additional unit. If MR is greater than MC, producing one more unit will increase profit. However, if MR is less than MC, producing one more unit will decrease profit. By equating MR and MC, we are finding the level of output where profit is maximized.