In: Economics
As a budding entrepreneur, you have purchased a small bagel shop. You have engaged in a market study to categorize your customers’ willingness to pay for a meal (coffee+bagel) into 8 equal sized groups: ($5.00, $4.50, $4.00, $3.50, $3.00, $2.50, $2.00, $1.50). All of your costs are fixed except labor and materials, which cost $2.25 per meal sold.
a) What price should you charge for a meal? (Hint: you don’t need to know the number of customers to answer this or part b)
b) Suppose your market research tells you that the four lowest value groups are all students. Should you offer a student discount? If so, how much?
c) If there are 100 daily customers from each consumer group, what is your shop’s profit gain from offering a discount to students relative to offering the same price to all customers?
d) If the fixed costs associated with the shop are salaries, a franchise fee, and rent, which are renewed and paid annually and average $500 per day, should the shop stay open in the long run? Does your answer depend on whether or not the shop offers a student discount?
a) Assume each group has 1 consumer.
Suppose, if the price was $5 the one unit is sold. TR=$5. The total cost of this unit will be $2.25. Therefore, profit=$2.75
Now, if P=$4.5, then two units are sold. One unit to the person with the willingness to pay $5 and another to the person with the willingness to pay $4.5. This means TR=$9 (2*4.5). The total cost of 2 units is $4.5(2.25*2). Therefore, profit=$4.5
Using the above logic the following table has been constructed which shows that the profit-maximizing price is $4.00
Q | P | TR (PQ) | TC (2.25Q) | Profit |
1 | 5.00 | 5.00 | 2.25 | 2.75 |
2 | 4.50 | 9.00 | 4.50 | 4.50 |
3 | 4.00 | 12.00 | 6.75 | 5.25 |
4 | 3.50 | 14.00 | 9.00 | 5.00 |
5 | 3.00 | 15.00 | 11.25 | 3.75 |
6 | 2.50 | 15.00 | 13.50 | 1.50 |
7 | 2.00 | 14.00 | 15.75 | -1.75 |
8 | 1.50 | 12.00 | 18.00 | -6.00 |
b) To capture 1 student, the meal price has to be $3. This would mean an additional revenue of $3.
So TR= initial 12 + new 3= $15 and total cost = initial 6.75 + new 2.25 = $9. Therefore, profit = 15-9 = $6
To capture 2 students, the meal price has to be $2.5. This would mean an additional revenue of $5
So, TR = $17 and total cost will increase by 2*2.5 = 5. So total cost= 11.75. Therefore, profit = 17-11.75 = $ 5.25
Using the above logic we find that the profit is maximized in case 1 where one student is attracted using a student discount as shown in the table below. So the student discount should be 25% (reducing 4 to 3 means a 25% discount)
TR | TC | Profit |
15.00 (attract 1 student) | 9.00 | 6.00 |
17.00 (attract 2 students) | 11.25 | 5.75 |
18.00 (attract 3 students) | 13.50 | 4.50 |
18.00 (attract 4 students) | 15.75 | 2.25 |
c) If there are 100 students the profit without any discount is profit is simply (profit from 1 person * 100) = 5.25*100= 525. Similarly, after discount profit is 6*100 = 600
Profit gain = 600 - 525 = $75
d) Fixed cost = 500. The firm should exit if it is unable to meet its fixed cost from the profits. In both cases with and without the discount, the profit earned is sufficient enough to cover the fixed cost. Without the discount, the profit is 525 and with the discount, it is 600. So the fixed cost is covered well irrespective of discount.