Welcome back to week nine of the Power of Markets course. In this second session we'll finish up our coverage of price discrimination. One example of third degree price discrimination to leave you with is how colleges charge tuition. In general, for a college with 1,000 entering freshmen per year They're probably at least 400 different prices the college will charge to the incoming students for the same basic education. And colleges have found price discrimination for a size of about 1,000 entering students per year can generate at least $500,000 a year in added revenue. What colleges have done recently is even pay attention who visits the campus or not. Visiting the campus is an indication that you're more eager to study at that college. And on average you'll probably pay a higher price if you visit the campus. They'll also look at your intended major. Pre-meds on average are viewed as having higher lifetime incomes. And colleges are able to charge them higher prices, the higher tuition coming in to the college education process. So sometimes it doesn't pay to be as earnest. At least when it comes to college education and the price you end up paying for it. What we'll do in this session is look at another form of second degree price discrimination. Again, second degree price discrimination is where the price you pay depends on the volume you buy. And in particular, we'll look at two-part tariffs. Where in cases like buying an iPhone, or joining Sams Club or Costco, you pay and entry fee, and then you pay a per unit price for the products you actually buy from those sellers. And in general, we'll see that the price tends to be above marginal cost. When first used two parts price discrimination but also less than the monopolistic price. Now let, lets start with a very simple case. We will look at telephone service and assume that there is only one type of consumer. And demand curve d and panel a, lets assume for simplicity That costs are constant. So marginal cost equals average total cost flat line. Two part pricing, would involve charging price equal to marginal cost per unit. But then an entry fee That's equal to the shaded ar-, the blue area, area T. So, in this case, two part pricing actually mimics perfect, or first degree, price discrimination. All potential consumer surplus gets converted into producer profits. The entry fee is just high enough to make the consumer indifferent. Between being able to buy Q units at a price equal to marginal cost, or not buy any units at all. Again, a very simple case, but now by having two instruments, a per unit price and an entry fee. The producer has, these two instruments to be able to operate on consumers. And in this simple case, is able to convert all perspective consumer surplus, into producer surplus. Outputs also efficient, every unit that gets produced, that's valued above marginal cost and to being produced in this market. But all the games from the market being there [INAUDIBLE] to the producer. Now just to test our understanding of the budget constraint indifference curve analysis. Lets look at panel b. How we can analyze two part pricing from that perspective. What the entry fee involves. Is determining and we are using the composite convention where we are putting minutes of local phone service on the horizontal axis and spending on all other goods on the vertical axis. What the entry fee involves is figuring out how much can we parallel shift down. The initial budget constraint of A, Z. How much income can we take away from the consumer and leave her indifferent from being able to purchase two units of phone service and Not having any phone service whatsoever. And the maximum we can take away from her is the vertical distance a to a prime. That's the size, the maximum that the consumer would end with a corner solution at point a. Purchasing no minutes of local phone service. And yet be just as well off is, she is at point e consuming q units of cellular phone service. Now lets look at a more complex case. What if we have different consumers, different demand curves and not just the same demand curve for each consumer? And let's at particular, in particular this case of Martha that has a demand curve of DM, and Donald that has a demand curve of DD. And we'll show how in general it pays in this very simple case to charge a price above marginal cost per unit and not a price at marginal cost. Again, a very simple case for marginal cost And average total costs are flat or constant. If we charged a, a price and this is a particular case where the demand curve Donald has for phone service is double what Martha her demand for phone service. The total demand curve. Is the summation of Donald's demand curve, and Martha's demand curve for phone service. Now lets think about raising the per unit price, from P to P prime. Just slightly above marginal cost. What that's going to do is lower the amount of the entry fee we can charge and lets assume to that the fees gotta be the same across the two consumers, Martha and Donald. A richer examples where we can different entry fees, different size entry fees to different consumers. But lets assume you are constrained. To charge the same entry fee to the two consumers. So one, one of the decisions this cellular phone service will have make to pay is does it pay not to serve Martha and charge a higher entry fee to dialed with a bigger demand curve. Or does it pay to keep both of them around but then be constrained by how much consumer surplus gets generated by this market from Martha. At the extreme of your charging a price equal to marginal cost. The most, the largest entry fee you can charge and keep both consumers is the blue shaded area. Now let's say, now let's try to raise the price above marginal cost. That per unit price increase, the gain in profit, so profit would increase by the amount we sell Q1. Times the higher price, how much the higher price exceeds the former price we charge P. So, there's an increase in per unit profit that's equal to P prime, J, K. In P. It's equal to that rectangular area. If we charge a higher price per unit. Against that we have got a way the lower entry fee we can charge and that lower entry fee, if we want to keep both consumers. That lower entry fee is p prime s r p times 2. So we picked up P prime J K P but then we lose out 2 times P prime S R P. And since Donald's demand curve is twice as large as Martha's. That two times p prime SRP is the same as P prime, LMP. So the change in profit, the delta in profit equals a positive LJKM, equals this trapezoidal area there. So in general and again it's tricky because what if we can charge different entry fees but in, in this case where you got to charge the same entry fee and paste a, a, a charge in general a price higher than incremental cost. And then take a little bit of a hit in entry fee you can charge. Now it also turns out that the price will tend to be below the monopoly price. Again, the same setting with Donald and Martha. Donald's demand curve twice as large. If we charged the monopoly price. And if we couldn't engage in price discrimination, we would look to where marginal revenue equals marginal cost. And for a linear demand curve, remember from a few sessions ago, it's half the distance to the demand curve. So we charge a level of Q and charge a price of P. And if we charge the monopoly price and wanted to keep both consumers, the maximum entry fee we could charge was that blue shaded area. Now let's say we wanted price below the monopoly level. To P prime. For small decrements in price, right around the profit maximizing price level, the lost revenue on the units you've already sold, is roughly offset by the additional revenue picked up from additional units. So we would lose, by lowering price to P prime. We would lose P, J, K, P prime, but we'd gain. Revenue on the incremental units, k f, q1, q. And for small changes in price quantity. This would roughly offset each other. But by lowering that price to p prime. We also pick up a higher entry fee. Though we can charge these two consumers. Twice that shaded in area. And because the demand curve for Donald is twice the amount for Martha. The gain and profit would be that trapezoidal area. PLMP prime. So in terms of the additional entry fee that would give us It pays to charge below a monopoly price. One final point, the costs associated with setting up price discrimination, or systems of price discrimination. Disneyland found this out they used to have a system where they would charge you an entry fee up to 1980. And then charge you a price depending on which ride you took, and the highest per unit prices were for the most desirable rides. So if you wanted to ride Space Mountain, that required an e-ticket. What Disneyland found out, was that it was too expensive to end up running and monitoring this system of price discrimination. They still deploy, different forms of price discrimination. Season passes, senior citizen discounts, and nowadays you can also buy a pass that, gives you expedited access, to rides. But the old form for the prices vary depending on the ride, proved to be too costly to monitor. So against the gains, of price discrimination, we have to weigh. The class of implementing a system and running a system like that. And the final point to keep in mind from this session 2 part tarifs, that one extreme can mimic perfect price discrimination. In general, the per unit price, we want to set it above marginal cost and the price will also be below the per unit price below the monopoly price. Where exactly in between will depend on, the, different types of customers, their demand curve, tradeoffs you need to make and, especially if you can charge even different entry fees by different customer classes.
