No Such Thing as a Free Lunch: Principles of Economics (Part 38)

"It is really gratifying, for example, to visit India now and see that because they've had good educational institutions, and they've had a focus on it, there are more and more people in India participating in the world economy."
Bill Gates

 Case Study in Marginal Analysis: An Ice Cream Parlor

by

Charles Lamson

The following is the description of the decisions made in 2000 by the owner of a small ice cream parlor in Ohio. After being in business for one year, this entrepreneur had to ask herself, should I stay in business? 

The cost figures on which she based her decisions are presented next. These numbers are real, but they do not include one important item: the managerial labor provided by the owner. In her calculations, the entrepreneur did not include a wage for herself, but we will assume an opportunity cost of $30,000 per year ($2,500 per month).

Fixed Costs

The fixed components of the store's monthly costs include the following:

Not all the items on this list are strictly fixed, however. Electricity costs, for example, would be slightly higher if the store produced more ice cream and stayed open longer, but the added cost would be minimal.

Variable Costs

The ice cream store's variable costs include two components: (1) behind-the-counter labor costs, and (2) cost of making ice cream. The store employs high school students at a wage of $5.15 per hour. Including the employer's share of the Social Security tax, the gross cost of each hour of labor is $5.54 per hour. There are two employees working in the store at all times. The full cost of producing ice cream is $3.27 per gallon. Each gallon contains approximately 12 servings. Customers can add toppings free of charge, and the average cost of the toppings taken by a customer is about $.05:

Gross labor costs.................................................... $5.54/hour

Cost of producing one

  gallon of ice cream

  (12 servings per gallon) .............................................. $3.27

 Average cost of added

  toppings per serving................................................... $0.05

Revenues 

The store sells ice cream cones, sundaes, and floats. The average price of a purchase at the store is $1.45. The store is open 8 hours per day, 26 days a month and serves an average of 240 customers per day:

 Average purchase......................................................... $1.45

 Days open per month.................................................... 26

 Average number of customers per day......................... 240

From the preceding information, it is possible to calculate the stores average monthly profit. Total revenue is equal to 240 customers * $1.45 per customer * 26 open days in an average month: TR =  $9,048 per month.

Profits

The store sells 240 servings per day. Because there are 12 servings of ice cream per gallon, the store uses exactly 20 gallons per day (240 servings/12). Total costs are $3.27 * 20 or $65.40 per day for ice cream and $12 per day for toppings (240 * $0.05). The cost of variable labor is $5.54 * 8 hours * 2 workers, or $88.64 per day. Total variable costs are therefore $166.04 ($65.40 + $12 + $88.64) per day. The store is open 26 days a month, so the total variable cost per month is $4,317.04. 

Adding fixed costs of $3,435 to variable costs of $4,317.04, we get total cost of operation of $7,752.04 per month. Thus, the firm is averaging a profit of $1,295.96 per month ($9,048 - $7,752.04). This is not an "economic profit" because we have not accounted for the opportunity cost of the owner's time and efforts. In fact, when we factor in an implicit wage of $2,500 per month for the owner, we see that the store is suffering losses of $1,204.04 per month ($1,295.96 - $2,500).

Should the entrepreneur stay in business? if she wants to make $2,500 per month and she thinks that nothing about her business will change, she must shut down in the long run. However, two things keep her going: (1) a decision to stay open longer and (2) hope for more customers in the future.

Opening Longer Hours: Marginal Costs and Marginal Revenues

The store's normal hours of operation are noon until 8 p.m. On an experimental basis, the owner extends its hours until 11 p.m. for one month. The following table shows the average number of additional customers for each of the added hours:

Assuming that the late customers spend an average of $1.45, we can calculate the marginal revenue and the marginal cost of staying open longer. The marginal cost of one serving of ice cream is $3.27 divided by 12 = $0.27 + $0.05 (for topping) = $0.32 (See table that follows.)

Marginal analysis tells us that the store should stay open for two additional hours. Each day that the store stays open from 8 to 9 p.m. it will make an added profit of $59.45 - $24.20, or $35.25. Staying open from 9 to 10 p.m. adds $29 - $17.48 or $11.52, to profit. Staying open the third hour, however, decreases profits because the marginal revenue generated by staying open from 10 to 11 p.m. is less than the marginal cost. The entrepreneur decides to stay open for two additional hours per day. This adds $46.77 ($35.25 + $11.52) to profit each day, a total of $1,216.02 per month.

By adding the two hours, the store turns an economic loss of $1,204.04 per month into a small ($11.98) profit after accounting for the owners implicit wage of $2,500 per month.

The owner decided to stay in business. She went on to serve over 300 customers per day, and the price of a dish of ice cream rose to $2.50 while costs did not change very much. In 2001, she cleared a profit of nearly $10,000 per month. 

*CASE & FAIR, 2004, PRINCIPLES OF ECONOMICS, 7TH ED., PP. 186-187*

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