Economics 352: Intermediate Microeconomics Notes and Sample Questions Chapter 13: Models of Monopoly Monopoly literally means “one seller.” The discussion in this chapter would be appropriate to situations where there was literally one seller of a particular good, but these are fairly rare and depend on a very limited definition of the market. For example, there may be one seller of a particular brand of gasoline at a particular intersection, but that seller doesn’t have a monopoly on the sale of gasoline in the city. A more useful interpretation of the monopoly models we’ll study is that they apply in situations where a seller has some ability to raise or lower prices, with the understanding that raising the price will result in fewer units being sold and lowering them will result in more units being sold. This is because no other firm is selling a perfect substitute for the monopolist’s product or, perhaps, that the consumer is unaware of the existence of a perfect substitute. In fact, this describes most firms, making monopoly analysis a decent model of some aspects of firm behavior. A further consideration is that a monopolist is protected by some type of barrier to entry that keeps competitors from entering the market and can preserve positive economic profits in the long run. These barriers may take a variety of forms: 1. Economies of Scale: If one firm can produce enough output to satisfy the market more cheaply than two firm, then, in some sense, there is not room for two firms in the market. This situation is often referred to as a natural monopoly. The key here is that a natural monopolist often has very large fixed costs and low variable costs so that, as quantity rises, average costs decreases. 2. Patent: A firm that invents a product or process is given a legal monopoly over it for a period of time. 3. Ownership of a critical resource: If a firm or organization owns all of some resource, they effectively have a monopoly over it. The classic example of this is DeBeers, the diamond cartel, although they are much more creative than just this. 4. Government granted monopoly: This is what cable television companies have. This is also what a patent is. 5. Violence: Very handy in trash hauling on the east coast. Profit Maximization and Output Choice The monopolist’s profit maximizing output quantity is the quantity where marginal revenue is equal to marginal cost. The standard linear demand model has a marginal revenue curve that has the same vertical intercept and is twice as steep as the demand curve. Here’s why. Start with the linear demand function:

P = A – BQ The revenue function is then R = PQ = AQ – BQ2 Marginal revenue is the derivative of the revenue function: MR =

dR = A − 2BQ dQ

The marginal revenue function, then, has the same vertical intercept, A, and is twice as steep as the demand curve. In a graph, this looks like:

Now, the profit maximizing quantity is the quantity where marginal revenue equals marginal cost. The graph of this is:

If you know the position of the average cost curve, you can determine whether the monopolist is making positive, negative or zero profits.

Also, there is dead weight loss associated with a monopoly because at the monopolist’s profit maximizing quantity, marginal cost is not equal to demand (marginal value). The dead weight loss is shown as:

Here’s a standard mathematical example: Consider a monopolist with the cost function TC(q)=1200 + 3q2 facing the demand curve p=4200 - q/2. Solve for the profit maximizing level of output, the monopolist's profit at that level, the dead weight loss, the efficient level of output and the monopolist's profit at that level. How does the difference between the monopolist's profit at the profit maximizing and at the efficient quantities compare to the dead weight loss. That is, would it be possible to bribe the monopolist to produce q* rather than qm ? The monopolist's revenue function is equal to pq or TR(q)=4200q - q2/2 And marginal revenue is the derivative of this MR(q) =

dTR q = 4200 − 2 ⋅ = 4200 − q dq 2

Marginal cost is the derivative of total cost: MC(q) =

dTC = 2 ⋅ 3q = 6q dq

Equating marginal revenue and marginal cost gives us: 4200-q=6q qm=600, p=3900 TR=2,340,000

TC=1200+3(600)2=1,081,200 Profit=TR-TC=1,258,800 At this quantity, the marginal cost is 6(600)=3600 The efficient quantity is where price equals marginal cost: 4200 - q/2 = 6q q*=646.15 And the dead weight loss is the area of the triangle DWL= 1/2 * (3900-3600) * (646.15-600) = 6299.50. The monopolist's profit at the efficient quantity would be profit = TR − TC = p(646.15) ⋅ 646.15 − TC(646.15) 646.15   2 profit =  4200 −  ⋅ 646.15 − 1200 − 3(646.15) 2   profit = 3876.925 ⋅ 646.15 - 1200 - 1252529.4675 profit = 2505075 - 1253729 profit = 1251346

The difference in profits is 1,258,800-1,251,346=7,454 So, by moving from the profit maximizing quantity to the efficient quantity, the monopolist would lose 7,454. This loss is greater than the dead weight loss of 6299.50, so the dead weight loss isn't large enough to use to bribe the monopolist to increase the quantity.

Monopoly, Product Quality and Durability The textbook investigates the question of whether a monopolist would use her market power to produce a good that was somehow distorted in terms of its quality or durability from what would result in a competitive market. The results here are generally ambiguous. Imagine that demand is given in the form of an inverse demand function (where price is expressed as a function of quantity, Q, rather than the other way around) that includes quality, X, as an argument: P = P(Q,X) And that the demand curve is downward sloping and people are willing to pay more for higher quality goods, so that:

∂P ∂P >0 < 0 and ∂X ∂Q The cost of producing output is a function of the quantity produced and the quality of the product: C = C(Q,X) And it can be assumed that larger quantities and higher quality are more costly to produce: ∂C ∂C > 0 and >0 ∂Q ∂X Now, the monopolist’s profit function is:

π = P(Q, X) ⋅ Q − C(Q, X) and the partial derivatives with respect to Q and X are: ∂π = PQ (Q, X) ⋅ Q + P(Q, X) − C Q (Q, X) = 0 ∂Q ∂π = PX (Q, X) ⋅ Q − C X (Q, X) = 0 ∂X The first of these just says that marginal revenue should equal marginal cost. The second says that the marginal revenue that comes from an incremental addition to quality should be equal to the marginal cost of that addition. The book goes through and shows that the derivatives (also known as the first order conditions) from the monopolist’s decision about the profit maximizing quality level are different from the derivatives from calculating the socially optimal quality level, thus establishing that, in general, monopolists won’t give consumers the socially optimal level of quality or durability, but it is not generally clear whether the level of quality or durability that they will give customers will be too high or too low. Part of the issue is that the monopolist is maximizing profits and will be basing a quality decision on her profit maximizing quantity whereas the socially optimal quality level would be based on the socially optimal quantity. The potential ambiguity can be thought of in a couple of ways. A monopolist might choose to sell a low quality product if there is no competitor to whom dissatisfied

customers could turn. On the other hand, a monopolist might produce a very durable and high quality product so that any new entrant would have a difficult time winning customers. Attempts to resolve this question seem to quickly deteriorate into differences regarding assumptions about the product.

The Monopoly Price and Its Relationship to Elasticity of Demand An alternative model of monopoly behavior expresses the profit maximizing price a monopolist charges as a function of the monopolist's marginal cost and the price elasticity of demand for the product. The formula is P = MC * [n/(n+1)] where n is the price elasticity of demand for the product. EX: If PED=-2 and MC=$10, we have P = $10 * [-2/(-2+1)] = $20. If PED=-5 and MC=$10, we have P = $10 * [-5/(-5+1)] = $12.50. You may notice that this formula doesn't generate a reasonable answer when demand is inelastic. This is because inelastic demand is inconsistent with profit maximization for a monopolist. To figure out why this is so, consider what a profit maximizing monopolist would do if demand was inelastic.

Price Discrimination Price discrimination is when a monopolist charges different people different prices for different quantities of goods. The goal in price discrimination, or any pricing system where you don't simply charge every person the same price per unit, is to capture some of the consumer surplus. Sometimes this is necessary for the supplier to remain in business.

Necessary conditions for price discrimination Market power Distinguish between types of customers Prevent resale Three degrees of price discrimination 1. First degree or perfect price discrimination: Charge each customer their marginal value for each unit they consume Will extract all CS Will result in the efficient quantity being exchanged A lump sum tax could resolve any distributional issues It's not clear why a customer would choose to go to the store at all 2. Second degree: Price per unit depends on the quantity bought If all consumers are identical then this will result in the efficient quantity being bought and the extraction of all CS. Typically, this will not extract all CS or result in the efficient quantity because customers have different demand curves 3. Third Degree: Charge different types of consumers different per unit prices. This won't allow extraction of all the CS, but will typically increase profits EX:

Consider a monopolist with marginal costs of $20 with two types of customers. One has a price elasticity of demand of -3 and the other has price elasticity of demand of -10. Calculate the price each customer type will pay if the monopolist can price discriminate. The formula is P = MC * [n/(n+1)] where n is the price elasticity of demand for the product. If n=-3, P=$20 * [-3/-2]=$30 If n=-10, P=$20 * [-10/-9]=$22 So, the person with more elastic demand pays a lower price. Effect of price discrimination on DWL Because monopolists produce and sell more when they price discriminate, price discrimination actually reduces dead weight loss.

Price discrimination techniques we see every day Movies Airlines Universities and colleges offer “financial aid” after you’ve revealed your income and assets to them on a “financial aid form.” Senior citizens and kids discounts at movies At a jewelry store you're always asked, "How much were you hoping to spend?" The cost for cleaning and boxing a dress depends on whether or not it's a wedding dress

Florists may charge higher prices for the same flowers if they're for a wedding. In any case, the typical advice to people planning a wedding is not to tell any of the businesses with which you deal that the arrangements are for a wedding because they will typically charge more. Doctors and other health care professionals will sometimes offer a sliding fee scale depending on a patient or client's income. While they undoubtedly do this in order to help those less able to pay for their services, a side effect of this practice is that it will increase profits as long as the price that patients pay is greater than the marginal cost of the visit or treatment. Drug companies sell drugs at lower prices in poorer countries. When buying an automobile, the salesperson will typically engage you in a discussion of your job, where you live and what you like to do in order to make sure you purchase a car which will meet your needs and to try to determine your ability and willingness to pay. Further, if you have a low enough value of time to debate the sales price at length, you are probably a low demand type of consumer. In the absence of a sales person, all consumers will pay the highest price that a salesperson could have extracted. Theaters will offer discounts for some performances and some customers. Second run movie theaters may be seen as a method of price discriminating between customers who want to see a movie when it first comes out and those who are willing to wait. Coupons Mail-in rebates American Economic Association membership fees are on a sliding scale according to your income. My only question is, do they exclude anyone who claims to be a highincome member?

Natural Monopoly A natural monopoly is a firm which has very large fixed costs and low marginal costs so that their average cost curve is always decreasing. In this situation, it is less costly to have one firm supplying a market than to have two. The problem is in reducing the dead weight loss associated with the monopoly. Forcing a natural monopolist to charge the efficient (MC=MV) quantity will result in their losing money because a price equal to marginal cost will be less than the average cost. A good compromise is average cost pricing, but there are problems with that. What would you do if a regulatory board assured you that your price would be adjusted so that your costs were covered and you made an acceptable rate of return on your capital? You would have very nice office furniture, to say the very least. Also, there is dead weight loss from average cost pricing.