## Price Discrimination

There are many pricing policies or pricing tactics that firms use to extract higher profits than the single monopoly price. The common methods are** price discrimination**, **perfect price discrimination**, **price discrimination** based on customer attributes, **price discrimination** based on customer’s self selection, and bundling.

Price discrimination is a price strategy where firms with market powers can increase their profits by simply charging different prices for different units of the exact same good. Typically monopolists seek to maximize profit by setting marginal revenue (MR) equal to marginal cost (MC). Under this model however, consumer’s are receiving consumer surplus, thus the good or service is actually worth more to the consumer than what they are paying. Monopolies also do not operate at the competitive market rate, meaning consumers that would normally purchase the good at a lower price are now abstaining from purchasing the good or service. By lowering the price to consumers with these demand preferences, while maintaining a price above their own marginal cost, more profit could be brought in.

By following a **price discrimination** policy a price can be set on an individual consumer or group of consumers basis, instead of a simple flat price, hence the discrimination. Under a competitive market a price set above marginal cost will lead to zero sales, making monopolies or any other instance of a firm with market power being the only type of firm that can ideally practice this policy.

In simple terms, when looking at a typical demand curve, it has a downwards slope. As price increases, demand decreases for consumers. Therefore while 100 consumers may be willing to pay for product 1 when it is priced $50, 30 consumers will be willing to pay up to $80. The 30 consumers will of course agree to pay $30 less than their willingness to pay (consumer surplus). By discriminating and charging $50 to consumers that at most will be willing to pay $50 and by charging $80 to consumers that at most will be willing to pay $80, more profit is made by the firm with market power.

While in many businesses it is looked down upon to offer one person a different price than another, many industries practice **price discrimination** and the pricing policy is accepted. When one goes to a movie theater, there is usually a price for students (those with less disposable income) that is less than the price for a regular admission ticket. Amusement parks and professional sporting events tend to follow similar pricing policies. Again, to effectively practice** price discrimination** the firm must have some market power.

**price discrimination** example:

An amusement park offers tickets to adults and college students.It has a marginal cost of $3 for each ticket.

The demand function for students is: Qds = 500 – 100p

where Qds = quantity demand for students

To find the profit maximizing firm price for students Marginal revenue must be set equal to marginal cost, MR=MC.

To do this find the inverse demand function. Subtract the price to the other side of the “=” sign and subtract the Qds to the other side of the “e” sign and divide by 100.

Inverse of Qds is = Ps = 5 – .01Qs

This makes marginal revenue equal to

5 – .01Qs-.01Qs

or

MR = 5-.02Qs

Now MR is to be set to MC

5-.02Qs = 3

-.02Qs = -2

Qs = 100

Therefore the monopolist will maximize its profits with students by selling 100 tickets.

By substituting 100 into Qs in the price function, the price of the tickets for students is determined.

Ps = 5 – .01Qs

Ps=5-.01(100)

Ps = 5-1

Ps = 4

Therefore the price for students should be $4 which will yield 100 ticket sales.

Profits for students would be (price – marginal cost) x quantity

or (4-3)x100

$100

Now the same must be done for adult ticket consumers.

If their demand function was

Qda = 800-100p the inverse demand function would be Pa= 8 -.01Qa

with a marginal revenue (MR) of 8-.02Qa

By setting this to the $3 marginal cost we get

8-.02Qa=3

Qa = 250

The price would be 8 – .01(250)

or $5.50

Profit for adults would be (price – marginal cost) x quantity

(5.5 – 3) x 250

$625

To compare profits in **price discrimination** versus non-**price discrimination** the profits must be found by finding the profit maximizing firm levels without **price discrimination**. To do this the market demand function is needed. The market demand function is the sum of the students and the adult’s demand functions.

Qda = 800-100P when price >5 (at P =5 no students will demand any tickets)

Qd = 1300-200p when price <= 5 (sum of both students and adults)

The next step is to find the inverse demand functions.

P = 8-.01Q when Q is < 500

P= 6.5 -.005Q when Q >= 500

Like earlier, the marginal revenue MR needs to then be found.

P= 8 – .02Q when Q < 500

P = 6.5 – .01Q when Q >= 500

Set these to the Marginal cost of $3

8 – .02Q = 3

Q = 250 P = 5.5

Profit = 2.5 x 250 = $625

6.5 – .01Q = 3

Q = 350 P = 4.75

Profit = 1.75 x 350 = $612.50

The profits earned by **price discrimination** and non **price-discrimination** must then be compared.

**Price discrimination**: $100 + $625 = $725

Non-**price discrimination**: $612.50 or $625

Regardless of which price is set for the profit maximizing firm, when practicing **price discrimination** more profit is yielded. $725-625 results in a $100 higher profit margin for **price discriminating** firms.

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