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GREG HUTKO: Hi, and welcome back to the 14.01 problem-solving videos. Today I'm going to do Fall 2010 Problem Set 7, Problem Number 2. And we're going to work through both parts A and B to begin with, so I'm going to read the beginning part of the problem.

Suppose Napster's considering selling music via email. There are two types of users, students and non-students. Each non-student has an inverse demand function of 200 minus x and each student has an inverse demand function of 160 minus x, where x is the number of songs delivered by email, p is measured in cents.

The marginal cost to Napster of sending an additional song via email is 0. Suppose Napster can identify all users as either students or non-students.

If Napster offers a fixed number of songs per year to each person, what is the profit maximizing level of songs offered to a student and a non-student. In other words, what is the equilibrium level of output for each type of person under first degree price discrimination?

Part B is going to ask us, given the equilibrium level of outputs that we've calculated, what is the dollar price charged to students and non-students per year?

Now what this problem is really asking us about, it's asking us about a situation in economics called a two-part tariff.

Now in some cases, when you have two groups of consumers that have differing demand functions, a monopolist can actually capture the vast majority of the consumer surplus. Or in most cases, all the consumer surplus if he can differentiate between the two groups.

So in this case, Napster is probably going to set up a situation where they can differentiate between students and non-students. So if they can discriminate by a student by having them enter their school ID or their school email address, then they'd be able to do the situation that we're doing for parts A and B.

The two parts of a two-part tariff, the first part is an access fee that's equal to the consumer surplus. So you can say to a consumer, sure, you can have this set bundle of songs, this set number of songs. But you're going to have to pay all of the potential benefit that it would bring you. So if it's going to bring

you 160 units of benefit, we're going to take that from you and we're going to give it to the producers instead.

The second part, in addition to the access fee, the producer has to decide the price per unit when the consumer is consuming the bundle.

And they also have to decide how many songs to bundle. The way the producer makes this decision is by setting the price per unit equal to the marginal cost.

So they're basically going to say, I'm going to throw in as many songs into this bundle, get you using as many of the songs as possible, or listening to the songs as possible. But I'm going to only thrown in as many songs until it starts costing me more than it could potentially bring me by capturing your consumer surplus.

So we're going to set the price per unit equal to the marginal cost equal to 0 in this problem.

Now looking at our graph, I've tossed up the demand curves for the student and the non-students. And what's going to happen in this problem is in the equilibrium case, our supply curve is actually straight along the x-axis because our marginal cost is equal to 0. So if this was a competitive equilibrium, the producer's surplus would be equal to 0.

Suppose Napster's considering selling music via email. There are two types of users, students and non-students. Each non-student has an inverse demand function of 200 minus x and each student has an inverse demand function of 160 minus x, where x is the number of songs delivered by email, p is measured in cents.

The marginal cost to Napster of sending an additional song via email is 0. Suppose Napster can identify all users as either students or non-students.

If Napster offers a fixed number of songs per year to each person, what is the profit maximizing level of songs offered to a student and a non-student. In other words, what is the equilibrium level of output for each type of person under first degree price discrimination?

Part B is going to ask us, given the equilibrium level of outputs that we've calculated, what is the dollar price charged to students and non-students per year?

Now what this problem is really asking us about, it's asking us about a situation in economics called a two-part tariff.

Now in some cases, when you have two groups of consumers that have differing demand functions, a monopolist can actually capture the vast majority of the consumer surplus. Or in most cases, all the consumer surplus if he can differentiate between the two groups.

So in this case, Napster is probably going to set up a situation where they can differentiate between students and non-students. So if they can discriminate by a student by having them enter their school ID or their school email address, then they'd be able to do the situation that we're doing for parts A and B.

The two parts of a two-part tariff, the first part is an access fee that's equal to the consumer surplus. So you can say to a consumer, sure, you can have this set bundle of songs, this set number of songs. But you're going to have to pay all of the potential benefit that it would bring you. So if it's going to bring

you 160 units of benefit, we're going to take that from you and we're going to give it to the producers instead.

The second part, in addition to the access fee, the producer has to decide the price per unit when the consumer is consuming the bundle.

And they also have to decide how many songs to bundle. The way the producer makes this decision is by setting the price per unit equal to the marginal cost.

So they're basically going to say, I'm going to throw in as many songs into this bundle, get you using as many of the songs as possible, or listening to the songs as possible. But I'm going to only thrown in as many songs until it starts costing me more than it could potentially bring me by capturing your consumer surplus.

So we're going to set the price per unit equal to the marginal cost equal to 0 in this problem.

Now looking at our graph, I've tossed up the demand curves for the student and the non-students. And what's going to happen in this problem is in the equilibrium case, our supply curve is actually straight along the x-axis because our marginal cost is equal to 0. So if this was a competitive equilibrium, the producer's surplus would be equal to 0.

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