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Ice Cream and Shut Down Decisions

About an hour north of New York City along the Hudson River sits a small town called Cold Spring. During the summer, New Yorkers escape the steamy city to Cold Spring and hit up the antique shops or hike Breakneck Ridge. With a population of only 2,000 people and five ice cream shops, they probably have the highest per capita ice cream in history. My favorite shop is called Moo Moo’s. During the summer and fall months, the line to buy ice cream flows down the street. Everyone wants some of their thick, creamy, homemade deliciousness. To me, their cake batter ice cream is the best. My friends rave about the s’mores ice cream.

But, what happens to Moo Moo’s in the winter? Where do all of those New Yorkers go? Yes, some people will still come up to cross-country ski at Fahenstalk Park, eat brunch at Hudson Hil’s, or stock up on fancy soaps at the Cold Spring Apothecary. But, mostly, the streets are quiet. And, shockingly, people are not thinking about ice cream while sporting their furry boots and down-lined coats. What should Moo Moo’s do? Should the stay open?

To think about this problem, we need to examine a business’s profit. In other words, how much do firms make? Well, that depends on how much money they are bringing in and how much is flowing out. In the winter, we can imagine that revenue for poor Moo Moo’s must go way down. Revenue is price x quantity. Price is the same as it was in the summer (unless they think to lower the price) and quantity falls dramatically. So, it is safe to assume that revenue has shrunk. Some ice cream shops put out signs advertising hot chocolate, but Moo Moo’s is strictly ice cream, so it is forced to depend on revenue from ice cream.

What about costs? Well, they have to pay people to scoop ice cream and maybe to even make the ice cream. On top of that, they have to pay for the building (prime real-estate along the waterfront), the freezers in the store, all of the equipment, and electricity/heat. So, if you are in charge of running Moo Moo’s what would you do? That depends! Let’s break this down. For simplicity, we’ll assume that there are just two costs: those of the workers and that for the rent. The cost to hire workers is their variable costs (costs that vary with the amount of ice cream sold) and rent is considered their fixed costs (they have to pay it regardless).

If Moo Moo’s is operating, its profit is: