### Affect since there are many competing sandwich retailers

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An early-bird entrepreneur decides each morning whether to work at his local Brooklyn artisanal bakery, or instead to assemble gourmet sandwiches to sell to office workers for lunch on Wall Street.1 The owner of the bakery will pay him \$300 a day, and has enough local demand at the bakery to keep him busy every day of the year. If he spends the working day making sandwiches, he must pay \$12.50 per day for the cost of a parking space for the hour it takes to deliver the sandwiches to office buildings.2,3 The per day variable cost of this enterprise depends on the cost of ingredients and on how many sandwiches he makes (the cost of making each additional sandwich increases with the total number of sandwiches since the entrepreneur must exert more and more effort to get them done in time for delivery). The average variable cost (in dollars per sandwich) is 2.5 + .005q, where q is the total number of sandwiches.

1. Upon waking, the entrepreneur learns that the price (which he has no ability whatsoever to affect since there are many competing sandwich retailers around) is \$7 per sandwich; how many sandwiches should he make per day (if any)? What is his economic profit?

2. Suppose the next day the price drops to \$4.99 per sandwich. How many sandwiches will the entrepreneur make on this day, and what is his economic profit? Now assume the price is again \$7, and expected to remain at this level indefinitely. But instead of \$12.50 per day in parking costs, the entrepreneur has the option of purchasing a time-share in a parking space in the parking garage of one of the main office buildings on Wall Street that will allow him to park free of any additional charge on any day he wishes. There are approximately 250 working days per year when the entrepreneur can expect to find demand for his sandwiches and, since he dislikes Manhattan, he does not anticipate using the parking space for any purposes other than for sandwich delivery. The owner of the parking space offers him this deal for an annual charge of \$3125 per calendar year.

3. If the entrepreneur agrees to this time share parking deal and purchases the space, how many sandwiches will he make on the first day of the year, and what is his economic profit?

4. On the morning of the last day of the year for which the annual parking charge has been paid, the sandwich price unexpectedly falls to \$4.99. How many sandwiches will the entrepreneur make that day, and what is his economic profit?

5. Explain why the answer to part (2) differs from the answer to part (4).

6. Suppose in part (4) that the fall in sandwich prices had occurred on the second day of the year instead of the last day of the year. How would that have changed your response to part (4)?

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