Chapter 12

MONOPOLY
Boiling Down Chapter 12
When there is only one producer in a market, a monopoly exists. Unlike competitive producers, monopolists can set price wherever they please, although they are still subject to demand conditions. They have acquired this pricing freedom because they operate with at least one of the following features. 1) They may have control over an input to production. 2) They may benefit from economies of scale, which are now even more pronounced in the information economy with its networked components than it was in the heavy manufacturing sector of the economy. 3) They may have acquired a patent. 4) They may be protected by a government law or license.
Although monopolists can likely sell some output at very high prices, they are limited by the market demand curve. A higher price will reduce sales and, eventually, total revenue. As price is increased, total cost drops because less output needs to be produced. When both revenue and cost drop, it is important to know which is dropping faster. As long as costs are falling faster than revenue, profit is increasing. At the point where both drop by the same amount, profits are maximized.
The relationship of cost to output was explored in Chapter 10. Revenues were related to market demand in Chapter 5, but they were discussed as consumer expenditures at that time. Now they are looked at from the producer's perspective. It is important for the monopolist to understand how revenue changes as price is altered. The perfect competitive producer has a linear total revenue function and a constant marginal revenue (MR) because the firm's demand curve is a horizontal line. However, when the firm faces the market demand curve, the revenue functions are different.
In Chapter 5 the relationship of total revenue to elasticity was explored. Consumer expenditure, or producer revenue, was shown to rise as price fell in the upper half of a straight-line demand curve. At the midpoint of the demand curve, total revenue peaked, after which it fell. Thus the total revenue of a monopolist will appear as a mountain that peaks where demand has unitary elasticity.
Drawing from the material in Chapter 10, the total cost curve for a monopolist has the same characteristics as total cost for any other producer, because the technological relationships of production and cost are not dependent upon market structure. The sketch on the following page illustrates these two curves and shows that a monopolist will maximize profit by producing where the gap between total cost and total revenue is greatest. The lower graph in Figure 12-1 sketches the marginal values, or slopes, of both total functions These slopes of the total cost and total revenue curves are called the marginal cost and marginal revenue functions, respectively.
It is now clear how far up the demand curve a wise monopolist will go in an effort to price where profits are maximized.

 

 

It is wise to thoroughly understand marginal revenue as a key piece of information in this pricing process. It can be derived several ways. First, it is the first derivative of the total revenue function. Second, when price is reduced, marginal revenue is the difference between the extra money gained from the new sales that occur and the revenue lost because previous items sold must be sold at a lower price. Third, the formula, MR = P(1- 1/e), derived from the elasticity and MR definitions, also adds to a fuller understanding of the concept. Geometrically and mathematically, it can be shown that the slope of the MR curve will be twice the slope of a linear demand curve.
With the details of cost and revenue mastered, it is not difficult to equate MR with MC graphically or algebraically to find the profit-maximizing solution for the monopolist. The addition of the average cost into the graph will show profit per unit (the vertical distance between price and ATC) and total profit (the rectangle whose profit per unit is the height and whose width is units sold). Of course, it is possible to have average cost above average revenue if a monopolist, even while doing its best, is experiencing rapid cost increases or a dying market. In this case the firm will stay open in the short run only if its revenue is sufficient to cover its variable costs. To verify your understanding of these concepts, sketch on scrap paper a profit-maximizing monopolist making profits, incurring losses but staying open, and incurring losses and shutting down.
In the long run the monopoly will pick the plant size where the long-run marginal cost equals MR, because this means that no other size plant can produce more profit.
Even though monopolies have pricing power, they are not able to capture the entire consumer surplus that is available in a market as long as they must charge the same price to all customers. Because some value a good more than others, yet pay the same price, they reap a benefit that the producer would like to appropriate to herself. In order to do this, a producer must have customers with differing elasticities of demand who cannot get together and sell the product to each other. If these conditions are met, the marginal revenue in each separate market is summed horizontally and related to the MC of producing. This will determine the level of MC that is relevant in the pricing decisions made in each market. Price in each market will be what that market will bear at the output level where the marginal revenue of that market equals the MC of producing. This price differentiation among buyers in separate markets is called third-degree price dis­crimination.
The producer who charges every buyer the maximum that he is willing to pay for a good is called a perfect price-discriminating monopolist. Although it is impossible to perfectly discriminate in practice, producers will estimate a consumer's total valuation of a product and attempt to charge a price that will capture as much of the consumer surplus as possible. If all surplus was captured, the MR curve would be identical to the demand curve, because no revenue would be lost on previous units when price is lowered to sell an additional unit. The result would be an output level that would be equal to the perfect competitive efficient ideal.
Another form of price discrimination is called second-degree dis­crimination, in which quantity discounts are made to those who buy larger quantities. This allows the producer to capture some of the consumer surplus that would be lost if all output were sold at one price.
The last form of price discrimination discussed here is the hurdle model. This model allows those who would not be willing to pay the higher money price for a product to pay in time and money. A hurdle, such as time spent filling out a rebate form or clipping coupons, will not attract those with a high cost of time, but will appeal to customers who have low time costs. The perfect hurdle will be one that will not be used by those willing to pay the higher price.
In the single-price monopoly, output is restricted so that all the con­sumer surplus from those who have left the market is lost to the system. This loss of welfare is referred to as a deadweight loss. Price discrimination enhances efficiency because output is expanded toward the perfect competi­tive output level. However, compared with the competitive model, income is transferred from the consumer to the producer in the process.
In areas like public utilities, high fixed costs lead to economies of scale, which results in natural monopolies. Single-price monopoly pricing in these areas is socially undesirable in many settings, so government policy frequent­ly intervenes to improve efficiency. Policy that provides state ownership or regulation of the natural monopoly fails to provide incentives to contain production costs, while exclusive contracting requires product specification details that are difficult to create and monitor. Because of all these problems and because antitrust action is not suited for natural monopolies, the best policy may be to promote relevant forms of price discrimination, to tax monopoly profits sufficiently, and to create social pressure that will lead to socially desirable outcomes.
Monopolists are sometimes accused of suppressing innovation. How­ever, a new invention will itself be another monopoly product that can be sold for monopoly profit. High prices rather than suppression is the likely outcome of innovation in concentrated markets.
Chapter Outline

• Monopoly is a market structure in which a single seller of a product with no close substitutes serves the entire market.
• Monopoly exists when a firm has control over key inputs, faces economies of scale, owns a patent, or secures a govern­ment license.
• Profit maximization is usually assumed in monopoly models.
• Total profit peaks where the gap between total cost and total revenue is the greatest or where marginal cost equals marginal revenue.
• Marginal revenue is always less than price because of the loss ab­sorbed when price is lowered for all output in order to sell more units.
• Marginal revenue is positive when demand is elastic and negative for inelastic portions of the demand curve.
• Marginal revenue has twice the slope of the demand curve.
• The graphical interpretation of short-run profit maximization shows the profits or losses realized by equating marginal cost and marginal revenue.
• Because marginal cost is always positive, the profit-maximization out­put always will be where demand is elastic.
• The profit-maximizing markup is the difference between price and marginal cost as a percentage of the price.
• Monopolists shut down if their price falls below average variable cost.
• Because monopolists are not price takers, they do not have a specific supply curve of output.
• In the long run a monopolist will produce where long-run marginal cost equals marginal revenue.
• There are four kinds of price discrimination.
• Third-degree price discrimination occurs when different prices are charged to buyers in totally separate markets.
• First-degree price discrimination occurs when each unit of output is sold at a different price so that all the consumer surplus goes to the seller.
• Second-degree price discrimination occurs when the seller prices the first block of output at a higher price than subsequent blocks of out­put.
• The hurdle method of price discrimination exists when the seller of­fers a lower price, coupled with an inconvenience that rich con­sumers prefer to avoid.
• There is deadweight loss to society when a single-price monopoly profit maximizes.
• When average cost continually falls, a natural monopoly exists, and at least five options should be considered.
• The government could own and operate the company.
• The government could regulate the private owners.
• Exclusive contracts could be awarded to foster competition.
• Antitrust laws could break up the monopoly.
• A laissez-faire policy could be adopted if the disease is less harmful than the cure.
• Monopolies do not have a great incentive to suppress innovation.

 

Important Terms

monopoly	arbitrage
The networked economy law of one price	hurdle model patents
natural monopoly	deadweight loss
total revenue curve	fairness objective
marginal revenue	efficiency objective
profit-maximizing markup	X-efficiency
local minimum profit point	rate-of-return regulation
local maximum profit point	cross-subsidy effect
global maximum profit point	gold-plated water cooler effect
price discrimination	exclusive contracting
first-degree price discrimination	antitrust laws
second-degree price discrimination	laissez-faire
third-degree price discrimination

A Case to Consider

• Back from his dream, Matt begins some strategic planning for starting another store in a small town that has no computer store and is not inclined to use mail order buying methods. He believes the annual demand in the town will be P = 1800 – 10Q. First, calculate Matt's marginal revenue curve, and then graph both the demand and MR curves.

 

 

 

• He estimates his marginal cost per computer to be constant at 600. Sketch on the graph the marginal cost curve. From this data, calculate how much he should sell to maximize profit and what price Matt should charge.

 

 

• If capital costs are fixed at $12,000 for the year what is Matt’s total cost function and his average cost per computer at the optimal output?

 

• From the average cost at profit maximum output, show the profit rectangle on your graph above. (See figures 12-9 and 12-10 in your text)

• If Matt were able to perfectly price discriminate, what would be his output and profit?

Multiple-Choice Questions

• What is the most likely reason that theater operators charge students and senior citizens less than everyone else for tickets, but charge everyone the same price for popcorn?
• They have compassion for lower-income people.
• They believe movies are more of a necessity than popcorn.
• They can more easily detect age than hunger, and the elasticity for movies varies more among the groups than does the elasticity for popcorn.
• They are required by antitrust law to give seniors lower prices.
• A monopolist in the United States can legally gain monopoly control of a market by all but which of the following methods?
• By gaining control over an important raw material of production
• By agreeing with competitors to charge monopoly prices
• By having high fixed costs and economies of scale
• By acquiring a patent
• Cell phones, AOL software, and email accounts are frequently given away in some fashion. This is because
• they all have low marginal costs and high fixed costs.
• they all represent part of the networked economy
• each item given away is linked together in some way with all the other items like it that are given away.
• all of the above are true.
• The law of one price for a monopolist implies that
• when price is lowered, the marginal revenue will be less than the price.
• the monopolist is not acting wisely in the market.
• every seller must charge the same price as all other sellers of the same product.
• all the above are true.
• With respect to price elasticity, it is true that
• monopoly market demand need not be less elastic than market demand in a competitive industry.
• monopoly firms face less elastic demand than do competitive firms.
• a monopolist should not produce where demand is inelastic.
• all the above are correct statements.
• A monopolist will maximize profit
• where total revenue is maximized.
• where the slope of the total revenue function equals the slope of the total cost function.
• where average cost is at a minimum.
• where all the above are true.
• somewhere other than the solutions listed because none of them are true.
• Marginal revenue for a single-price monopolist will
• have the same slope as the demand curve.
• be 0 when price is 0.
• be negative if the firm is incurring economic losses.
• always be positive if the firm is profit maximizing.

 

• A single-price monopoly that profit maximizes by reducing price from $61 to $60 must have a marginal cost of (remember MC = MR)
• $21.
• $60.
• $39.
• $0.
• If the monopolist facing the demand above is a perfectly discriminating monopolist and marginal cost is constant at $40, how much will the firm sell if it profit maximizes?
• 40
• 30
• 60
• Indeterminate with the information given
• If marginal costs are zero for the single-price profit-maximizing firm facing the demand curve above, what will profits be if fixed costs are $1000?
• $2500
• $0
• $9000
• $1500
• None of the above
• If the firm in question 10 above is a perfect price discriminator instead of a single-price monopolist, what will profits be if fixed costs are still $1000?
• $2500
• $0
• $9000
• $1500
• None of the above
• A single-price monopolist has a demand curve with a constant slope of -5 and an intercept of 50. If it drops its price by 5 units, we can be sure that
• sales will increase by 5 units.
• marginal revenue will decrease by 5 units.
• marginal revenue will be less than it was before.
• none of the above are true.

 

 

 

• In the figure on the right, for the demand curve shown, marginal revenue for the price reduction from a to b can be measured using areas x and y by
• If marginal revenue is shown by the equation MR = 100 - l0Q, what is the corresponding demand curve equation?
• P= 100-5Q
• P = 50- l0Q
• P = 100 - 20Q
• P = 50-5Q
• Which statement is true for the single-price monopoly that is operating on the demand curve P = 75 - 5Q at the point where price is $37.50?
• The firm should definitely not lower its price.
• The firm should definitely lower its price.
• If the marginal cost is 0, the firm should definitely raise its price.
• None of the above can be stated with assurance.
• A monopolist does not have a typical supply curve because
• numerous demand curves could have identical marginal revenue at a given point on a monopolist's marginal cost curve.
• a monopolist is not a price taker.
• there is no unique correspondence between price and revenue when the market demand curve shifts.
• of all the above.
• If the LMC curve is less than the MR curve at the point of output for a monopolist that is making profit, then the firm has
• too large a plant size.
• too small a plant size.
• insufficient knowledge about plant size until he knows his short-run marginal cost.
• insufficient knowledge about plant size until he knows his demand curve.
• Monopolists that vigorously seek to innovate
• are irrational since they are competing with themselves.
• could be profit maximizing because they expect to lower costs by innovation.
• do so out of a fear of future competition or they would not innovate.
• do not exist because they have the entire market to themselves already.
• Which statement is not true of monopolists?
• Compared to perfect competitive firms, monopolists reduce consumer surplus.
• Compared to perfect competitive firms, monopolists restrict output.
• When monopolists perfectly price discriminate they restrict output more than when they single price their product.
• Natural monopolies are characterized by falling ATC over a large range of output.

 

• A third-degree price discriminator will
• receive the same marginal revenue from each market.
• still maximize profit by equating marginal cost with marginal revenue.
• make more profits than an identical non-price discriminator.
• do all the above.
• A perfect price-discriminating monopolist will
• leave no consumer surplus for his customer.
• produce where MC = MR.
• produce the amount that is larger than a non-price discriminator.
• do all the above.
• Which would not be an example of the hurdle model of price discriminat­ing?
• An airline giving cheaper rates to those who stay over Saturday night
• A college giving lower tuition to a minority applicant
• A price reduction only if you have a coupon
• Lower-priced circus seats in the upper deck
• A single-price, profit-maximizing monopoly that has constant MC imposes a deadweight loss on society by
• under-producing and forcing potential consumer surplus to be wasted.
• overproducing and having the costs of the last units produced exceed their benefit to society.
• redistributing money from the consumer to the producer.
• pushing marginal revenue all the way to 0 to maximize revenue for itself, an act that costs society welfare.
• Natural monopoly is characterized typically by
• increasing average costs, which makes it hard for new entrants to enter the industry.
• low fixed costs but very high variable costs.
• highly elastic product demand curves.
• marginal costs that are lower than average cost for large quantities of output.
• none of the above.
• Which is not true of state owned and managed natural monopolies?
• The state is better able to price at MC because it can use its taxing power to cover the losses that result from marginal cost pricing.
• X-inefficiency is common because the incentives for profit are miss­ing.
• Bureaucrats frequently maximize the operating budgets of their departments rather than function with a profit-maximization objec­tive.
• The wise state government will set price equal to average total cost so that losses will not have to be borne by the taxpayer.
• Which of the following methods is likely to provide public services as close to the competitive price as possible?
• exclusive contracting
• state regulation
• state ownership
• laissez-faire free market activity

27.  Which industry is most likely to fall prey to the “gold-plated water cooler effect?
a.   Natural gas supply industry
b.   office appliance industry
c.   steel industry
d.   soft drink industry
Problems

• Authors receive royalties for their books, which are a percentage of the sales revenue of the book. For this reason, economists have pointed out that an author has an interest in a book's price being lower than the price that maximizes a publisher’s profits. Show why this is true graphically and explain your graph.

 

 

 

 

 

• A monopolist's demand curve is P = 100 - Q. The marginal cost of production is constant at 20. If the firm is a profit-maximizing enterprise, how much welfare is lost to society because of this monopoly's strategy?

 

 

• The following four questions relate to the monopolist in question 2 above. Assume fixed costs are $500 for each question.
• How much economic profit is being made at the profit-maximizing solution?

 

 

• If there is a profits tax of 25%, what will the price, output, and after tax profit be if the firm is profit maximizing? (The profit tax applies only to this question.)

 

• If the firm could perfectly price discriminate, what would its output be and how much profit would it make?

 

 

 

• If the firm is regulated as a natural monopoly by a public utility commission and is forced to price at MC, how big a subsidy will be needed from government for the utility to cover its opportunity cost?
• Sketch a monopoly firm at long-run equilibrium. Show LAC, ATC, demand, MR, SMC, per unit profit, and total profit.

 

 

 

 

 

• A monopoly company has a demand curve that can be shown as P = 3000 - 100Q. It has fixed costs of $1000 and additional cost per unit produced of $200.
• What is the total cost equation?

 

• What is the marginal cost equation?

 

• What is the total revenue equation?

 

• What is the marginal revenue equation?

 

• What is the profit-maximizing output?

 

• The following two equations are the demand equations for airplane trips for a business person and a vacationer. The airlines marginal cost is $20 per passenger. 
• P = 620 - 100Q 
• P = 180 - 40Q  

What price should the airlines charge each person if the firm’s objective is to maximize profit?

 

7.    Describe in words the difference between first degree and second degree price discrimination. Give an example of how one might go about using first degree price discrimination in practice.

 

 

Answers to Questions for Chapter 12
Case Questions

• Matt's MR = 1800 – 20Q.

• MC = MR at an output of 60, while price will be $1200.
• TC = 12,000 + 600Q.  ATC = TC/Q or ATC = 12,000/Q + 600

4.  See the arrow on the graph above. It equals 400 times 60 or 24,000.
5.  Matt would produce 120 and his profit would be all the consumer surplus minus the fixed costs of $12,000. Thus $72,000 – 12,000 equals profit of $60,000.
Multiple-Choice Questions

• c, Price discrimination requires that markets can be segregated. 
• b, Collusion in the USA is prohibited by law and there may be some limitations on the other ways suggested as well.
• d, a and c are aspects of the networked economy.
• a, This is true because the producer must lower the price on all previous units sold.
• d, Letter (a) is confusing unless one highlights the market, not the firm's, demand.
• b, This is where MR = MC, which is the rule of maximizing anywhere.
• d, No firm could have MC = MR at a negative MR because MC cannot be negative.
• a, The MR of a $1 price drop will be $21 so the MC must be that also.
• c, The MR will equal the demand and MR = MC where the demand curve is at 60.
• d, Take total revenue of $2500 and subtract out the fixed costs.
• e, Total revenue will be $5000 and profits will be $4000.
• c, Marginal revenue is always less than demand for a single-price monopolist.
• b, Take the revenue gained (y) and subtract the revenue lost (x) on earlier units sold.
• a, MR has twice the slope of a linear demand function. This reverses the logic.
• a, It is at unitary elasticity and would not want to go to the inelastic part of demand.
• d, A menu of  price-quantity supply coordinates does not exist for the monopolist.
• b, Whenever MC is below MR more output and a larger plant is profitable.
• b, If costs are lowered by innovation, profits will be increased.
• c, Perfect price discriminators increase output up to the perfect competitive output. 
• d, By splitting markets and following the MC = MR in each profits go up.
• d, Remember that the MR is now equal to the demand curve, so output goes up.
• b, All require some effort above normal except being a minority. 
• a, A distribution of income is not a deadweight loss although it may be undesirable.
• d, This means that ATC is falling over the entire range of production, due to high FC.
• d, The efficient policy sets price equal to MC, not ATC, unless a subsidy isn't feasible.
• a, The competitive bidding of potential monopolists dissipates the monopoly profits.
• a, Natural gas is a regulated public utility and so it gets a return on capital. A cooler can be part of the capital equipment for the company and so there is incentive to have an expensive one.

Problems

• Since profit maximization occurs at a lower total  revenue and higher price than does revenue maximization, authors prefer the lower price so that their royalties are highest. See the sketch labeled Problem 12‑1 below.

 

• The deadweight loss triangle is 40 x 40/2  =  800.
• a) Profit is TR _ TC or 2,400 _ 1,300 = 1,100.

3.   b) The output and price will not be changed, and the after-tax profit will be 825 (75% of the profit).
3.   c) If the firm were able to price discriminate per­fectly, its demand curve would become its MR, and MC = MR at an output of 80. Total revenue will be 4,800 and variable cost will be 1600. Since fixed costs are 500, the remaining profit is 2700.
3.   d) A 500 subsidy is needed, because only the variable cost is covered by the regulated price.
4.   Make sure you practice several times on your own so that the key locations are understood.

The key points to keep in mind here is that monopolists curb output to keep price elevated. They produce with the wrong sized plant and they use their plant at less than capacity. All this, of course assumes that the ATC declines over a wide range of output. If the LATC is L shaped, then production costs will not be higher than competitive costs, but the monopolist will still restrict production to keep prices elevated to the profit maximization point.
5.   a) TC = 1,000 + 200Q
5.   b) MC = 200
5.   c) TR = 3,000Q _ 100Q2 
5.   d) MR = 3,000 _ 200Q
5.   e)  MR = MC at Q = 14
6.   Since MC is constant, the airlines need only to equate the MR in each market with the $20 marginal cost. This leads to a price of $320 for the business person and $100 for the vacationer. The business person will fly 3 times, and the vacationer twice.

7.   First degree price discrimination seeks to capture all the consumer surplus the consumer gets from the product or service. Second degree discrimination charges different prices for the product or service depending on the quantity consumed. Because of diminishing marginal utility of consumption it is logical that the first units are valued higher than subsequent units so it pays to lower price as consumers increase usage. One of the ways to try to first degree discriminate is to make “all or nothing “ offers. If an accurate assessment of the consumers demand function is known, then the offer will be accepted if it is a penny less than the full consumer surplus. This, of course assumes the consumer is following strict rational choice behavior.

• A resort island 10 miles off the mainland has enough daily traffic to fill either one large ship or 15 small boats. Vacationers have the same preferences for time of travel, so having many small boats at differing times is no advantage. The ATC of the small boats is $35 when they run at capacity. Unfortunately, there is not enough business for both types of operation to succeed. The large shipping company estimates the demand to be P = 100 - 0.1Q and has a total cost function TC = 10,000 + 15Q. The island council has a petition before it to outlaw the large shipping operation. The petition says that the island citizens can not be held hostage to a monopoly. Analyze this petition by answering the following questions.
• What would the shipping company be inclined to do in order to secure its monopoly status if there were no governmental action?

 

 

• Once the monopoly was established, what would keep the small boats from coming back into the market if the shipping price went above $35?

 

• What would be the ship's profit-maximizing price?

 

 

 

• Is the petition the best solution? What options does the island have in addition to  passing the petition? (A numerical answer is not required.)

 

• What is the consumer surplus if the monopolist is a single price profit maximizer?

 

 

• This industry controlled by a single price monopolist will
• provide ____________ less total benefit to consumers than firms in a competitive industry.
• use ___________ less resources than firms in a competitive industry,
• cause a ____________ deadweight loss to society.

• A single price monopoly firm would need to go out of business in the long run if its ATC was as shown with the dotted line. However, a price discriminating monopolist might make a profit under certain circumstances. Describe with letters what would need to be true for the price discriminating firm to stay in business in the long run ________________.

 

• If the dotted ATC is eliminated and the variable costs are the only costs, how much profit will a single price monopolist make ___________?  Also with no fixed costs, how much profit will a perfect price discriminator make ___________? (Remember: the sum of all the marginal costs = the total variable cost.)

• If a 10% tax is put on all profit, a single price monopolist will do what to his price ________? (direction of change if any)  A perfect price discriminator will do what to his quantity produced if the same tax is imposed ________? (direction of change if any)

 

• Answer the following questions for the single priced monopolist sketched on the previous page if the demand curve shown above is P = 21 - .5Q and the marginal cost curve is MC = .5Q. Fixed costs are 20.
• What are the numerical values of: the single price monopolist’s profit             _____________?
• What is the deadweight loss imposed on society ____________?
• What is the value of the consumer surplus that is generated ____________?

   

• Given the same information as in (f) above except that the firm is now a perfect price discriminator.
• What is the profit of the firm _____________?
• What are its total cost of production ____________?
• How much output does it produce _____________?

3. If monopoly involves a deadweight loss to society so that consumers pay a higher price for the product and have less than an optimal amount of it available, why does our government give patents to some firms for products so that they can keep a monopoly over a product for many years?