Lecture notes on monop price discrim by JH PDF

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Lecture 4: Monopoly and Price Discrimination Some questions for this lecture: 1. Why is a Young Person’s railcard 33% off? Why not 25%? Or 50% 2. Why is spreadsheet and word processor software bundled together so that it is cheaper to buy them together than buy each individually? 3. You are a software company with high fixed costs and marginal costs of zero. A consultant says you must charge a high price to cover your fixed costs. Another says charge a low one since you have zero marginal costs. What do you do?

1

The Monopolist’s problem

The economic problem for a monopolist is to select a quantity of output or a price for each unit of output in order to maximise profit. When there are other firms around, as we shall see next, then firms have to worry about the reaction of other firms. For the moment, let us assume that there are no other firms and so the problem for the monopolist is to worry about the reaction of consumers only to his own prices, not those of other firms. When is it reasonable to assume no other firms are around? This is when a firm has some (at least small degree of) market power. That is, it faces a demand curve that is not infinitely elastic. So, it could be a market in which there is literally only one single firm; a single supermarket in a particular region for example or a firm that has exclusive rights to a particular market e.g. a TV company showing a particular film or sport. Or it could be a firm with a slightly differentiated product from other products; a particular mobile phone company for example. Let us take a very simple case. Suppose the monopolist knows both his own costs and the demand curve, and that these are given by the following equations: Demand Curve:

P = a – bQ

Cost function:

TC = F + cQ

Where Q is output (offered for sale) and P is price. Note that a, b, c, and F are numbers that describe the possibilities of demand (a and b), technology and cost (c and F). In our model these possibilities are fixed and beyond manipulation by the firm. For example, in the model the firm cannot simply choose to reduce marginal cost (c) – it must work with the level of marginal cost given by the existing technology and availability of inputs. At a later stage we will consider what happens when the firm can influence the level of marginal cost, but for the time being we assume that the monopolist only has the power to decide Q (and thereby P). (Note from the total cost function that average cost = c + F/Q and marginal cost = c.)

Business Economics Lecture 4 – Page 1

1.1

Mathematical approach

If you like maths, here is the solution to the monopolist’s problem. If you don’t, see the next section The profit of the monopolist is Total Revenue minus Total Cost. Total revenue is simply PQ, and total cost is cQ + F. Thus Profit:

 = (P – c)Q – F = (a – bQ – c)Q – F

The monopolist’s problem is to choose output (Q) to maximise profit (). Recall from high school algebra, that to choose a Q to maximise  we need to set /Q=0 which gives

  a  2 bQ  c  0 Q which in turn implies

Q = (a – c)/(2b)

Notice that the output choice of the firm depends on the values of a, b and c, the demand and cost conditions – but not on F – the fixed costs. Maximising profit is about balancing changes in revenue with changes in cost and by definition fixed costs do not vary with output. From the point of view of choosing output “fixed costs don’t matter”. The monopolist’s choice of output fixes everything in our model. For example, you should now be able to confirm that P = (a + c)/2 and  = (a-c)2/4b– F. Note that profit does depend on fixed costs – it only worth being in business if (a-c)2/4b > F.

1.2

Graphical approach

There is another way to think about the monopolist’s problem, which involves the concepts of marginal cost and marginal revenue. We have already met revenue: price charged multiplied by the quantity sold at that price (determined by the demand curve). Marginal revenue is the extra revenue raised by the sale of an additional unit, or the derivative (slope) of the revenue function with respect to output. Now, suppose a monopolist lowers prices by just enough to sell an extra unit. When she sells another unit of output two things happen. First, she generates extra income on that extra new unit equal to the new price. But second, she has to take into account that selling an extra unit involves taking a price cut on all existing units sold (because the demand curve slopes downward). This means that marginal revenue must always lie below the demand curve – it is always less than the price at which the marginal unit can be sold. This is because there is a change to revenue from selling the marginal unit, but an additional change from the lowering of prices on all the inframarginal units.

Business Economics Lecture 4 – Page 2

When only a small number of units are sold, this effect is small, and marginal revenue is close to the demand curve. When the number of units sold is already large, then the sale of a marginal unit will involve a price cut on all those units and marginal revenue will be a long way below the demand curve. Eventually, marginal revenue can be negative, reflecting the idea that selling an extra unit actually diminishes total revenue due to the number of units across which prices have been cut. This is all illustrated in Figure 1 where the intercept on the top left axis is “a”. P

Demand P=a-bQ

curve,

0 Marginal revenue curve, MR=a-2bQ

Q

Figure 1: Demand and Marginal Revenue Given our assumptions about the demand curve we can also write total revenues (TR) as: TR = PQ = (a – bQ) Q Therefore marginal revenue (MR) is just the derivative of total revenue MR = d(TR)/dQ = a – 2bQ To confirm to yourself that relationship between the demand curve and marginal revenue is as shown in Figure 1 you could try to draw them on a diagram yourself: for example, assume a = b = 1 and then sketch the demand curve P = 1 – Q and the marginal revenue curve MR = 1 – 2Q. For a numerical example of the reasoning above on why MR lies below D, consider the following. Suppose I can 100 goods at £11 and 101 goods at £10. So why is not MR = £10 for the 100th to the 101st good? It is true that the 101st sale gets me £10. But, to make that sale, I have reduced the price from £11 to £10. So I have to sell all my previous goods, the inframarginal units, at £10 not £11. So I am losing £1 on each of them. So the MR from 100 to 101 must be less than the £10 since I have to take off the loss of revenue on all the other goods. So if the MR is less at that point, then MR must lie below D. In short, the MR on my Business Economics Lecture 4 – Page 3

marginal good is £10, but my total MR includes the MR on the inframarginal goods too. Since that is a loss in revenues, this pushes my total MR below £10. (Indeed in this example, MR is negative i.e. £10 minus the £1 loss on each of the 100 goods = -£90. So this is indeed why a portion of the MR curve is drawn negative. Since there’s a point where MR is positive, at “a” and where it’s negative, there must be a zero, in fact this is where elasticity of demand = 1).

1.3

Profit maximisation: marginal revenue and marginal cost

We can now say something about the relationship between marginal revenue (MR) and marginal cost (MC). Consider the diagram below, figure 2. If the monopolist chooses any quantity of output units it must be the case either that MR > MC, MR = MC or MR < MC. Suppose the MR > MC (i.e. on the left of the point Qm diagram). That means that the revenue from any extra unit of output is greater than the extra cost of production so the sale of this extra unit must add to profit: the monopolist should expand output. Now suppose MR < MC (to the right of Qm). If the monopolist were to cut back sales by one unit the reduction in cost would be greater than the loss of revenue it’s a profitable choice for the monopolist to reduce output. Only when MR = MC is the monopolist in a situation where neither expansion nor contraction will add to profit: in other words the profit maximising output level must be at the point where MR = MC. This can be shown on Figure 2:

P

PM

Demand

Marginal cost

QM

Q Marginal revenue

Figure 2: Profit maximisation when marginal revenue = marginal cost Business Economics Lecture 4 – Page 4

Finally, if QM is the profit-maximising quantity, then firms have to choose a corresponding price. That is shown by the demand curve, here PM, which is the price at which consumers will buy QM goods.

1.4

Why Monopoly is a Bad Thing

If you ask most people why monopoly is bad they will usually say something along the lines of “prices are too high” and “consumers are being exploited”. While this may be true, it is not very precise. The prices of lots of goods are high, even when they are produced in a competitive environment, and if one is to talk of “exploitation” it is necessary to explain exactly what this means. High prices may be bad for consumers but they can also create high profits for the firm. Is £1 more valuable if it is in the pocket of the consumer rather than the bank account of the firm? Choosing between these two groups in terms of “worthiness” is a difficult moral/political judgment. It is not for economists to make this decision on our behalf. Economists are neutral approach, treating £1 as equally valuable whether in the possession of the consumer or the firm. So, without a moral judgement, can we say anything? In fact, the output decision of the monopolist may still be “a bad thing”. To see this we need to consider again exactly what we mean by the demand curve. If we pick any quantity on the horizontal axis we can identify the price required to sell exactly that many units, a lower price would imply even greater demand and a higher price would imply that this total quantity would not be sold in full. What this means is that for a given quantity there are some consumers who would be “willing to pay” even more, i.e. those consumers that would purchase the product even if the price went up. However, there is also at least one buyer whose “willingness to pay” for a unit of the good exactly equals the price at which the good is sold – and this consumer would not purchase the product if the price rose even by only a small amount1. This is what we might call the “marginal consumer”. For every quantity you might try to sell, there is a marginal consumer whose willingness to pay exactly equals the price charged. However, for every other consumer who buys the product, they have a willingness to pay that exceeds the price at which the product sells. These are the “inframarginal consumers” and they obtain what we call “consumer surplus”. Consumer surplus is analogous to the profit of the firm. It is the excess of benefit over cost (price) that the consumer obtains from participating in the market. All consumers who buy the product, other than the marginal consumer, obtain consumer surplus.

1

I am assuming for simplicity that each consumer only ever buys one unit of the product. In reality, consumers may each buy many units- in which case they will have different willingness to pay for each unit they purchase. In this context you should recognise that “willingness to pay” is nothing more than the monetary equivalent of “marginal utility” discussed in lecture 1. Business Economics Lecture 4 – Page 5

P

Willingness to pay, consumer A A

WTP A

B C D E

P

5

Demand

1

2

3

4

Q*

Q

Figure 3: Price and Consumer Willingness to Pay At the top of the demand curve there is one consumer willing to pay as much as WTP(A) to obtain a single unit of the product. However, at a price P this consumer is in fact paying much less than his willingness to pay. He obtains a surplus equal to WTP(A) – P. The second consumer has a willingness to pay equal to WTP(A), so at price P obtains a surplus equal to WTP(A) – P. From the diagram you can see that the consumer of each of the first four units purchased obtains some surplus. The consumer of the fifth unit (the marginal consumer) pays a price that exactly equals his willingness to pay and so obtains no surplus at all. Although there exists a consumer willing to purchase a sixth unit, at price P this consumer would pay more than the consumer surplus she expected to obtain from purchasing this unit – an economic loss – and so in fact she will not buy the product at price P. Consumer surplus is an index of the well-being (utility) that consumers obtain from their participation in market activities and this is a widely used concept amongst economists. We can think of total consumer surplus on our diagram as being equal to the triangle defined between the demand curve, the vertical axis (that measures value) and the horizontal line that defines the price paid in the market (see Figure 4). Consumer surplus increases as prices fall and decreases as prices rise.

Business Economics Lecture 4 – Page 6

Price Consumer Surplus (P)

P Demand Curve Q(P)

Quantity

Figure 4: Consumer Surplus for a given price P Note that whilst economists use this idea, you don’t see it in any economic statistics. For example GDP tells you the value of goods produced in the economy and in this case is, without any other complications, just P×Q. That is not consumer surplus, even though consumer surplus exists in this economy. With this in mind we can now re-examine the profit maximising output choice of the monopolist (Figure 5 below). Given output QM the price in the market will be PM. Obviously consumer surplus could be increased by reducing the price. But profits would fall. So is it just one surplus evaluated against another? No. Look at consumer 6 with WTP 6. Before they were not in the market. But now suppose the monopolist could make a side deal with them and get them to pay, say WTP6 for the good, with all other prices the same. The consumer prefers this, since they are served. The monopolist prefers this since, by the diagram, the cost of the extra good for consumer 6, MC, is less thanWTP6. So the monopolist gains, no consumers lose. Hence everyone is better off. Now, this potential extra surplus could be divided between the producer and the consumer in many ways. We could have the monopolist sell at marginal costs, in which case all the extra surplus goes to consumer 6. This does not matter. What matters is that this surplus will not be realised because the monopoly price is in fact P M. In other words, the monopolist’s choice results in socially desirable transactions (i.e. desirable for the producer, the consumer, or both (and not harming anyone else)) not taking place. This is “inefficient”, and this is the primary criticism of monopoly by economists. By “inefficient” economists don’t mean productivity is too low or similar. Rather, there are some trades available that would be mutually advantageous for parties in the economy and so there is some lost surplus if they are not consummated. Business Economics Lecture 4 – Page 7

Deadweight loss Price

PM WTP(6) Lost surplus on unit i due to monopoly

Marginal cost

QM

qi

Q*

Quantity

Figure 5: The Deadweight Loss The precise damage due to the existence of monopoly can in fact be measured, and is indicated by the shaded triangle in Figure 5. This is the social surplus lost on transactions that could take place at prices below the monopoly price and above marginal cost. This triangle is called the “deadweight loss” due to monopoly and thus reflects the statement in lecture 1 that total surplus is not maximised when prices are not at supply and demand values. Another way of thinking of the deadweight loss due to monopoly is that it is equal to the value of consumer surplus lost as a result of charging the monopoly price PM rather than charging a price equal to marginal cost. Besides causing a deadweight loss there are some other economic reasons to suppose monopoly is a bad thing:

1.4.1 Rent seeking behaviour Sometimes monopoly is described as the absence of competition, but a close study of monopolistic activities usually shows that competition has not been abolished, simply directed into another activity, which might be described as “competition to become the monopolist”. For example, when government auctions the right to run the National Lottery it is creating competition to monopolise this industry. In many cases Business Economics Lecture 4 – Page 8

governments pass laws in order to ensure that a particular industry is a monopoly so that they can raise revenues from the auction of the right to be the monopolist. In many cases competitors for the right to be a monopolist expend considerable resources on that competition, and usually much more than is strictly necessary from society’s point of view. Investments made to compete for monopoly rights may be legitimate (e.g. tender documents and presentations) or sometimes illegal (bribery and corruption) but either way there is usually too much money wasted in this competitive activity. This is sometimes called “rent-seeking behaviour” (another term for the economic profit made the monopolist is “economic rent”). In the extreme, rent seeking behaviour can undermine the whole economic and political system if corruption takes a hold. Indeed, many have argued that one reason why oil-rich developing countries have done so badly is that resources have been diverted into corruption.

1.4.2 Innovation In the model above, costs are assumed. But in many markets companies try to lower costs by innovating and improving. What of monopolies? Nobel Laureate Sir John Hicks once wrote “The greatest of all monopoly profits is a quiet life”. What he meant was that a true monopolist does not need to worry about competition and so has limited incentive to make innovative products or provide a good service. It could be argued that this was the fundamental problem of the former centrally planned economies of the Soviet Union and its satellites. The central complaint of consumers was the undersupply of consumer goods at adequate quality levels, largely because all industry was organised on a monopolistic basis with no profit incentive.

2

Price Discrimination and Monopoly

We may get a lot of insights in pricing and welfare from thinking about consumer surplus, particularly if we highlight one crucial assumption that we have not made explicit until now, namely the monopolist is assumed to sell all units at the same price to all consumers. In many cases, this is a sensible assumption. Supermarkets for example have to sell at the same price to all (although more recently in the information age they offer personalized coupons to their shoppers depending on past shopping records suggesting that they would prefer to vary their prices if they could). But if it were not true by assumption, we can immediately observe that firms would like to charge different prices if they could: in figure 3, price A to consumer A, price B to consumer B etc. That would appropriate consumer surplus and be much more profitable than charging just one price. This practice is known as “price discrimination” (businesses practising this technique hate this terminology, since the word “discrimination” sounds bad, and they often use other term such as “market segmentation” or “differential pricing”).

Business Economics Lecture 4 – Page 9

Let us go through the different cases, but remembering the key point about pd: price discrimination has the potential to raise profits. There are two types of pd: 2 1. dire...