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California, there are seven bathing suit stores that provide service to beach-going customers
California, there are seven bathing suit stores that provide service to beach-going customers. Each of the stores vigorously competes with each other and they are faced with the same schedule of costs. Additionally, each of the stores faces an identical bathing suit demand curve in the Santa Barbara market. Swim N Style is a typical store out of those seven and it faces the following demand and cost schedule.
A recent marketing survey shows that Santa Barbara exhibits a high growth in bathing suit market. Consequently, seventeen new bathing suit stores now enter the market, joining the seven that already existed. Therefore, the demand schedule facing Swim N Style (and all other stores) falls, while the cost schedules for both old and new stores remain constant. The following represents the new demand schedule.
UPDATED DEMAND SCHEDULE
| Suits sold (per hour) | Price |
| 1 | $31.50 |
| 2 | $28.50 |
| 3 | $25.50 |
| 4 | $22.50 |
| 5 | $19.50 |
| 6 | $16.50 |
| 7 | $13.50 |
| 8 | $10.50 |
| 9 | $7.50 |
| 10 | $4.50 |
QUESTION: Suppose the number of swimsuits sold remained constant under the increased competition, but the number of stores was reduced so that each was operating at its point of minimum average cost. How many stores would now be in operation? Why? Show the detailed calculations and explain the reason.
Expert Solution
The point where the minimum average cost occurs is the sales level at which the firm's average cost per unit is the lowest (i.e. which maximizes each firm's gross margin). Since this point is not provided, let's assume that this point is 8 suits per hour. We then need to determine how many suits are sold per hour in total (i.e. among all stores). Again, this information is not provided, but we can assume it is 152 swim suits.The number of stores in operation is thus computed as follows:
= Total swim suits sold per hour / Number of swim suits sold by each firm
= 152 / 8
=19 firms
Therefore, there are 19 firms in operation. Since there are 7 stores and 17 new ones (7+17), this gives us a total of 24 stores. Based on the above calculation, 5 of these stores (24-19) will thus have to close.
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