Article review -Networks, Dynamics & Behavioral Economics

Monopoly

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Table of Contents

9.1

9.2

9.3

9.4

9.5

9.6

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Monopoly Profit Maximization

Market Power

Market Failure Due to Monopoly Pricing

Causes of Monopoly

Advertising

Networks, Dynamics & Behavioral Economics

Introduction

Managerial Problem

Drug firms have patents that expire after 20 years and Congress expects drug prices to fall after it. But, evidence shows that prices went up.

Why can a firm with a patent-based monopoly charge a high price? Why might a brand-name drugs’ price rise after its patent expires?

Solution Approach

We need to understand the decision-making process for a monopoly: the sole supplier of a good for which there is no close substitute.

Empirical Methods

The relevant market structure is monopoly, a single seller that sets price or output level to maximize profit where MC = MR.

A monopolist sets its price above its MC (market power) and creates a deadweight loss or market failure due to monopoly pricing.

A patent is one form of creating a monopoly, the other is cost.

To increase profits a monopoly can use advertising and charge an initial low price to create a long run network effect.

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9.1 Monopoly Profit Maximization

Marginal Revenue: MR = ΔR/Δq

A firm’s marginal revenue, MR, is the change in its revenue from selling one more unit.

Marginal Revenue and Price

The MR for a competitive firm

In Figure 9.1, panel a, a competitive firm that faces a horizontal demand and Δq=1. This competitive firm can sell more without reducing price.

So, MR = ΔR = B = p1

The MR for a monopoly firm

In Figure 9.1, panel b, a monopoly faces a downward-sloping market demand and Δq=1. This monopoly firm can sell more only if price goes down.

So, MR = ΔR = R2-R1 = B-C = p2 – C

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9.1 Monopoly Profit Maximization

Figure 9.1 Average and Marginal Revenue

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9.1 Monopoly Profit Maximization

The Marginal Revenue Curve

The monopoly’s MR curve lies below a downward-sloping D curve for every q, and MR depends on the shape of the D curve.

MR Curve for a Linear Demand

The MR curve is a straight line that starts at the same point on the vertical (price) axis as the D curve but has twice the slope. In Figure 9.2, the D and MR curves have slopes –1 and -2, respectively.

MR Function: MR = p + (Δq/ΔQ) Q

The monopolist MR function is lower than p because the last term is negative.

When inverse D is p = 24 – Q, then MR = 24 – 2Q

MR Function with Calculus: MR(Q)=dR(Q)/dQ

When inverse D is p = 24 – Q, R(Q) = (24 – Q)Q = 24Q – Q2. So, MR(Q)=24 – 2Q

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9.1 Monopoly Profit Maximization

Figure 9.2 Elasticity of Demand and Total, Average, and Marginal Revenue

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9.1 Monopoly Profit Maximization

Marginal Revenue and Price Elasticity of Demand

The MR at any given quantity depends on the demand curve’s height (the price) and shape.

The shape of the demand curve at a particular quantity is described by the price elasticity of demand, ε = (∆Q/Q)/(∆p/p) < 0 (percentage change in quantity demanded after a 1% change in price).

MR & Elasticity Relationship: MR = p (1 + 1/ε)

This key relationship says MR is closer to price as demand becomes more elastic. Table 9.1 shows this relationship.

Where the demand elasticity is unitary, ε = –1, MR is zero.

Where the demand curve is inelastic, –1 < ε ≤ 0, MR is negative.

Where the demand curve is perfectly elastic, ε = -∞, MR is p.

Figure 9.2 shows a linear D with all the elasticity values in Table 9.1.

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Table 9.1 Quantity, Price, Marginal Revenue, and Elasticity for the Linear Inverse Demand Function p = 24 – Q

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9.1 Monopoly Profit Maximization

Choosing Price or Quantity

Any firm maximizes profit where its MR and MC are equal.

Rule for monopoly maximization: MR(Q)=MC(Q)

A monopoly can adjust its price or its quantity to maximize profit.

Monopolist Sets One, Market Decides the Other

Whether the monopoly sets its price or its quantity, the other variable is determined by the downward sloping market demand curve.

The monopoly faces a trade-off between a higher price and a lower quantity or a lower price and a higher quantity.

Either Maximize Profit

Setting price or quantity are equivalent for a monopoly. We will assume it sets quantity.

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9.1 Monopoly Profit Maximization

Two Steps to Maximizing Profit

All profit-maximizing firms use a 2-step analysis:

1st, they determine the output Q* that maximizes profit.

2nd, they decide whether to produce Q* or shut down.

Profit-Maximizing Output (1st step)

Profit is maximized where marginal profit equals zero, or MR(Q)=MC(Q)

In panel a of Figure 9.3, this occurs at point e, Q=6, p=18, π=60. This is the maximum profit in panel b.

At quantities smaller than 6 units, the monopoly’s MR > MC, so its marginal profit is positive. By increasing its output, it raises its profit.

At quantities greater than 6 units, the monopoly’s MC > MR, so its marginal profit is negative. By reducing its output, it raises its profit.

A monopoly’s profit is maximized in the elastic portion of the demand curve. In panel a, Figure 9.3, the elasticity of demand at point e is –3.

A profit-maximizing monopoly never operates in the inelastic portion of its demand curve.

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9.1 Monopoly Profit Maximization

Figure 9.3 Maximizing Profit

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9.1 Monopoly Profit Maximization

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9.1 Monopoly Profit Maximization

Using Calculus, Output Decision: dπ(Q) / dQ = 0

By setting the derivative of the profit function with respect to Q equal to zero, we have an equation that determines the profit-maximizing output.

dπ(Q)/dQ = dR(Q)/dQ – dC(Q)/dQ = MR – MC = 0

In Figure 9.3, , MR = 24 – 2Q = 2Q = MC. So, Q=6. Substituting Q = 6 into the inverse demand function (Equation 9.2), p = 24 – Q = 24 – 6 = 18.

Using Calculus, Shutdown Decision

At Q = 6, AVC = Q2/Q = 6, which is less than the price. So, the monopoly does not shut down.

At Q = 6, AC = (6 + 12/6) = 8, which is less than the price. So, the monopoly makes a profit.

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9.1 Monopoly Profit Maximization

Effects of a Shift of the Demand Curve

Competitive Market Case

The effect of a shift in demand on a competitive firm’s output depends only on the shape of the marginal cost curve.

The new equilibrium (P = MC) occurs along the marginal cost curve, and for every equilibrium quantity, there is a single corresponding equilibrium price, as illustrated in Figure 9.4, panel a.

Monopoly Case

The effect of a shift in demand on a monopoly’s output depends on the shapes of both the marginal cost curve and the demand curve.

The new equilibrium (MR = MC) may occur at new levels of prices and quantities, or two different prices for the same quantity, or the same price for two different quantities.

In Figure 9.4, panel b, the shift of demand from D1 to D2 causes the optimum to change from E1 to E2. The monopoly quantity stays the same, but the monopoly prices rises (one q associated with 2 prices).

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9.1 Monopoly Profit Maximization

Figure 9.4 Effects of a Shift of the Demand Curve

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9.2 Market Power

Market Power and the Shape of the Demand Curve

If the monopoly faces a very inelastic demand curve (steep) at the profit-maximizing quantity, it would lose few sales if it raises its price.

However, if the demand curve is very elastic (flat) at that quantity, the monopoly would lose substantial sales from raising its price by the same amount.

Profit-Maximizing Price: p = [1/(1+1/ε)] MC

The monopoly’s profit-maximizing price is a ratio times the marginal cost and the ratio depends on the elasticity. In Table 9.2:

If ε = -1.01, only slightly elastic, the ratio is 101 and p = 101 MC

If ε = -3, more elastic, the ratio is only 1.5 and p = 1.5 MC

If ε = – ∞, perfectly elastic, the ratio shrinks to 1 and p = MC

Thus, even in the absence of rivals, the shape of the demand curve constrains the monopoly’s ability to exercise market power.

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9.2 Market Power

Table 9.2 Elasticity of Demand, Price, and Marginal Cost

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9.2 Market Power

The Lerner Index or Price Markup: (p – MC)/p

The Lerner Index measures a firm’s market power: the larger the difference between price and marginal cost, the larger the Lerner Index.

This index can be calculated for any firm, whether or not the firm is a monopoly.

Lerner Index and Elasticity: (p – MC)/p = – 1/ε

The Lerner Index or price markup for a monopoly ranges between 0 and 1.

As Table 9.2 illustrates, the Lerner index for a monopoly increases as the demand becomes less elastic:

If ε = -1.01, only slightly elastic, the monopoly markup is 0.99 (99%)

If ε = -3, more elastic, the monopoly markup is 0.33 (33%)

If ε = – ∞, perfectly elastic, the monopoly markup is zero

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9.2 Market Power

Sources of Market Power

Availability of substitutes, number of firms and proximity of competitors determine market power.

Less Power with …

Less power with better substitutes: When better substitutes are introduced into the market, the demand becomes more elastic (Xerox pioneered plain-paper copy machines until …)

Less power with more firms: When more firms enter the market, people have more choices, the demand becomes more elastic (USPS after FedEx and UPS entered the market).

Less power with closer competitors: When firms that provide the same service locate closer to this firm, the demand becomes more elastic (Wendy’s, Burger King, and McDonald’s close to each other).

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9.3 Market Failure Due to Monopoly Pricing

A perfect competitive firm achieves economic efficiency (maximizes total surplus, TS = CS + PS).

However, unlike perfect competition, a monopoly is economically inefficient because it wastes potential surplus, resulting in a deadweight loss.

The inefficiency of monopoly pricing is an example of market failure.

Market failure: non-optimal allocation of goods & services with economic inefficiencies (price is not marginal cost).

A monopoly sets p > MC causing consumers to buy less than the competitive level of the good. It destroys some of the potential gains from trade. So society suffers a deadweight loss.

In Figure 9.5, the monopolist’s maximizing q and p are 6 and $18. The competitive values would be 8 and $16.

The deadweight loss of monopoly is –C – E. Potential surplus that is wasted because less than the competitive output is produced.

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9.3 Market Failure Due to Monopoly Pricing

Figure 9.5 Deadweight Loss of Monopoly

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9.4 Causes of Monopoly

Monopoly markets exist mainly because of cost considerations and government policy.

Cost-Based Monopoly

Cost advantages: A firm with substantial lower costs than potential rivals.

A low-cost firm is a monopoly if it sells at a price so low that other potential competitors with higher costs would lose money. No other firm enters the market.

The sources of it are superior technology, better production methods, control of either an essential facility or a scarce resource.

Natural monopoly: A firm may produce the total output of the market at lower cost than two or more firms could.

C(Q) < C(q1) + C(q2) +  + C(qn), where Q = q1 + q2 + … + qn is the sum of the output of any n firms where n ≥ 2 firms.

The reason is economies of scale: a natural monopoly has an strictly declining average cost curve (Figure 9.6)

When just one firm is the cheapest way to produce any given output level, governments often grant monopoly rights to public utilities of water, gas, electric power, or mail delivery.

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9.4 Causes of Monopoly

Figure 9.6 Natural Monopoly

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9.4 Causes of Monopoly

Government Creation of Monopoly

Governments grant a license, monopoly rights, or patents

Barriers to Entry

Governments create monopolies either by making it difficult for new firms to obtain a license to operate or by explicitly granting a monopoly right to one firm, thereby excluding other firms.

By auctioning a monopoly to a private firm, a government can capture the future value of monopoly earnings. However, for political or other reasons, governments frequently do not capture all future profits.

Patents

A patent is an exclusive right granted to the inventor of a new and useful product, process, substance, or design for a specified length of time.

The length of a patent varies across countries, although it is now 20 years in the United States.

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9.5 Advertising

Advertising and Net Profit

A successful advertising campaign shifts the monopolist market demand curve outward and makes it less elastic. This allows the monopolist to sell more units at a higher price.

In Figure 9.7, after successful advertising D2 is to the right and it is less elastic than D1.

Deciding Whether to Advertise

Do it only if firm expects net profit (gross profit minus the cost of advertising) to increase.

In Figure 9.7, gross profit is B. Only if its cost of advertising is less than B, its net profit rises and advertising should be done.

How Much to Advertise

Do it until its marginal benefit (gross profit from one more unit of advertising or marginal revenue from one more unit of output) equals its marginal cost.

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9.5 Advertising

Figure 9.7 Advertising

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9.5 Advertising

Using Calculus: π (Q,A) = R (Q,A) – C (Q) – A

Profit equals revenue minus cost. Advertising, A, is a fixed cost and affects revenue, R. R(Q, A) = p(Q, A)Q. The monopoly maximizes its profit by choosing Q and A.

First Order Condition: ∂π (Q,A) / ∂Q = 0

∂R (Q,A) /∂Q – ∂C (Q) /∂Q = 0

The monopoly should set its output so that MR = MC

First Order Condition: ∂π (Q,A) / ∂A = 0

∂R (Q,A) /∂A – 1 = 0

The monopoly should advertise to the point where its marginal revenue or marginal benefit from the last unit of advertising, R/A, equals the marginal cost of the last unit of advertising, $1.

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9.6 Networks, Dynamics and Behavioral Economics

Network Externalities

A good has a network externality if one person’s demand depends on the consumption of a good by others.

If a good has a positive network externality, its value to a consumer grows as the number of units sold increases (smart phones).

Firms can benefit from direct size effects if a customer can get a direct benefit from a larger network

Firms can also benefit from indirect effects when users benefit from complementary goods that are offered when a product has a critical mass of users (enough adopters that others wanted to join).

Network Externalities and Behavioral Economics

The direct effect of network externalities depends on the size of the network because customers want to interact with each other. Why?

Bandwagon effect: A person places greater value on a good as more and more other people possess it

Snob effect: A person places greater value on a good as fewer and fewer other people possess it

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9.6 Networks, Dynamics and Behavioral Economics

Network Externalities as an Explanation for Monopolies

Because of the need for a critical mass of customers in a market with a positive network externality, we sometimes see only one large firm surviving.

The Windows operating system largely dominates the market—not because it is technically superior to Apple’s operating system or Linux—but because it has a critical mass of users.

But having obtained a monopoly, a firm does not necessarily keep it.

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Managerial Solution

Managerial Problem

Drug firms have patents that expire after 20 years and Congress expects drug prices to fall after it. But, evidence shows that prices went up.

Why can a firm with a patent-based monopoly charge a high price? Why might a brand-name drugs’ price rise after its patent expires?

Solution

When generic drugs enter the market after the patent expires, the demand curve facing the brand-name firm shifts to the left, and rotates to become less elastic at the original price.

Price sensitive consumers switch to the generic, but loyal customers prefer the brand-name drug (familiar and secure product for them).

Elderly and patients with generous insurance plans fit this group.

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