A couple of students have asked about the Roo Cup (given my rant) and why Kangaroo Express would sell soda for 25¢ per cup, especially during the summer when demand is expected to be higher. Here is my explanation.
Assume that the weekly demand for sodas purchased by the average soda consumer at Kangaroo Express (KE) can be defined by the following equation:
P = 3.75 - .875Q
where P is the price and Q is the quantity of sodas sold per week to the average soda customer. Let’s also assume that (and this is my guess, not an official statement from KE) the marginal cost to KE of a soda is constant and is 25¢ (i.e., KE’s cost of producing one more soda).
If KE can charge only one price, it maximizes profits by setting its output where the marginal cost of producing one more soda (i.e., 25¢) is equal to the marginal revenue earned from selling it to the average customer. We calculate marginal revenue using our demand equation above so that:
MR = 3.75 - 1.75Q
Setting marginal revenue equal to marginal cost and solving for Q we get:
.25 = 3.75 - 1.75Q ⇒ 1.75Q = 3.5 ⇒ Q = 2 & P = $2
If KE can charge only one price, the company maximizes its profit per customer by setting its price at $2 and the average KE customer buys two sodas each week. (This is shown in Table 1 below and in the diagram Graph 1 below.)
First, the company doesn’t want to price below its marginal cost of producing a soda, so that last row is not feasible and is there only to show that any price below 25¢ results in a loss.
Second, there are people who are not willing to purchase even one cup at $2.00, but might be willing to pay, say, $1 for a cup. But KE doesn’t want to price at $1.00 per cup because then it’s not maximizing profits, it’s maximizing revenue. What it would like to do is charge customers their willingness to pay for each cup. In other words, charge the average customer $2.88 for the first cup, $2.00 for the second, $1.13 for the third, and 25¢ for the fourth. It stops at 25¢ because that is its cost of producing that marginal cup of soda. If KE could do this, its profit per customer would be as follows:
So instead of earning just $3.50 in profit per customer per week, if KE could effectively price discriminate it would earn $5.26 per customer. KE wants to get more of the consumer surplus as shown in Graph 1 below.
Consumer surplus is the value consumers receive in excess of what they paid for some good or service. In the graph above, and from the charts above, the average consumer was willing to pay up to $2.88 for the first cup, but only paid $2.00 for it. His or her surplus from the first cup was $0.88. Total consumer surplus when the price of soda is $2.00 per cup is illustrated in Graph 1 as the triangular area from above the price line (of $2.00) and below the demand curve. By KE pricing at $2 and selling just two cups, it gives up that surplus to the consumer. It would like to have that.
Notice also that at $2.00 per cup, the average customer is willing to purchase only 2 cups per week. But that average customer would be willing to purchase 3 cups per week if the price was $1.13, and 4 cups per week if the price was just 25¢, KE’s marginal cost of producing soda. That triangle area to the right of 2 cups per week that is above the marginal cost curve but below the demand curve is surplus that neither KE nor the customer obtains when KE prices soda at $2.00 per cup. KE would like to have that, too.
Lastly, it’s also the case that, since I’ve used the average customer, there are customers who are not willing to purchase any cups at $2.00/cup, but might purchase at least one if soda was priced at, say, 50¢ per cup. (Really, somebody paying any price between 25¢ and $2.00 per cup for a soda benefits both KE and that consumer.) KE wants those sales as well, if it can get them.
How can KE get more consumer surplus that is currently enjoyed by current consumers and the lost surplus due to the price being $2.00. Easy!
Notice that the total surplus to the average consumer in excess of KE’s marginal costs of producing each cup (i.e., 25¢) is the area below the demand curve and above the red marginal cost curve. In other words, if KE priced its soda at 25¢ per cup, the average customer buys 4 sodas per week for $1.00 per week. KE earns no profit and consumer surplus is measured by the triangle $0.25 to $3.75 to 4 cups per week. Using geometry (i.e., 1/2 base times height) we can see that total consumer surplus is 3.5 x 2 = $7.00. The average consumer values 4 sodas net of KE’s cost of producing 4 sodas and the price they paid for them at $7.00.
The Roo Cup works this way: Consumers pay $7.00 for a plastic cup that cost KE probably $0.20 to manufacture, allowing them unlimited refills for 25¢ each throughout the summer months. Now you can see that what KE did was found a successful means of a) extracting all the consumer surplus without having to charge different prices. (An impossible task given it doesn’t have the necessary information to assess consumers’ value per cup and it cannot prevent customers with low values for a soda from buying cups at low prices and then turning around and selling them to higher valued soda consumers for less than what KE would have sold it to them.) And b) more importantly, it brought in customers who weren’t willing to pay $2.00 per cup for soda, but find attractive paying $7.00 for the Roo Cup and then 25¢ per refill to refill it all summer. These are people who aren’t even included as the average customer, but now find themselves going to Kangaroo once, twice, three times and more each week to refill their cup. While there, they buy milk, a hot dog, cigarettes, etc., The company maximized its profit, the customer feels like she got a bargain, and the deal generated a whole lot of free publicity for Kangaroo Express.