The Dominant Firm Model

Evolution of a Dominant Firm

• The typical cost structure for digital products is necessary, but not sufficient, for the emergence of a dominant firm.– Declining average cost (together with the absence of capacity

constraints) will permit a single firm to supply the whole market.

– This cost structure does not preclude many firms from serving the market however, as long as each individual firm can cover the interest costs (or opportunity costs) associated with the sunk fixed cost of its product.

Evolution of a Dominant Firm

• What additional conditions must be satisfied for a firm to become dominant?

– Barriers to entry• Technical barriers

– Large fixed costs ( large opportunity cost to entry)

– Network externalities and lock-in

• Legal barriers – Patents on technology ( control of standards)

– Trademarks and copyright

• Artificial barries– Advertising and marketing costs

Evolution of a Dominant Firm

• Network Externalities– The value of the network to any individual connected to

it increases as the total number of connections increase.

– Effect is an externality because the benefit occurs to a connected individual independently of that individual’s actions.

– Presence of externalities implies that many basic economics results don’t hold:

• Generally can’t have a perfectly competitive equilibrium

• Competitive equilibrium will generally not be efficient

Evolution of a Dominant Firm

• Market Tipping– Markets with network externalities generate positive feedback in

the sense that as the network grows, so does the incentive to join the network.

– Markets with positive feedback network externalities are competitively unstable, in the sense that regardless of how competitive the markets starts out, if one firm starts to gain market share, customers will face strong incentives to switch to the large network, leading to an upward cycle of growth by this firm which culminates in market dominance.

– Classic example: Microsoft’s growth from garage-based upstart to dominance of the PC market.

Evolution of a Dominant Firm

• Lock-In– Lock-in is the flip-side of positive feedback network

externalities.• Just as positive feedback makes joining the dominant network

valuable, it also makes leaving it costly.

• Network members can face significant switching costs should they wish to opt out of the network, and these costs give the dominant firm leverage to maintain market share.

Monopoly Pricing

• Dominant firms are price setters– Unlike competitive firms, a monopolist needs to be concerned

with the fact that reducing prices to sell more also reduces revenues on all previous units sold.

• Single firm, homogeneous product model– Profit maximization: =pq-C(q)

– Prices are determined by inverse demand function p=p(q).

– First-order conditions are standard: Choose output so that marginal revenue from selling an additional unit is equal to the marginal cost of producing the additional unit.

Monopoly Pricing

• Mathematics of monopoly pricing

qCqp

qCp

q

dq

dpqp

qCqpqqp

qMCqMRq

qp

11

1

0

Monopoly Pricing

• Interpretation qp is the elasticity of demand with respect to price and measures

the %-change in quantity demanded given a 1% increase in price. - If we make our standard assumption that marginal cost is zero, the

first-order condition states that we should produce and sell to the

point where demand just becomes inelastic (i.e. where qp=1).

- Note: With MC=0, the monopoly price need not be large. Indeed, if demand is given by then the elasticity is just ; clearly, if this is greater than one, the firm will produce (and price to sell) a large amount of its product. ppq

Monopoly Pricing

• Heterogeneous Product Monopoly– More realistic case

– Example: Microsoft Windows and Office Suite

– Profit maximization problem (assuming zero marginal cost) now becomes

– Here is the vector of prices for each of the firm’s products. Note that the demand for each product will generally depend on all prices.

Cpqpi

ii

nppp ,...,1

Monopoly Pricing

• First-order conditions for profit maximization

0

ij i

jj

i

iii p

qp

p

qpq

Monopoly Pricing

• With some algebraic manipulation, this can be put in the

form

• Here ii is good i’s own price elasticity of demand, and ij is good j’s demand elasticity respect to a change in the price of good i.

ij

ijii

jjii qp

qp1

Monopoly Pricing

• Application to Microsoft: Windows and Office

• First-Order Conditions become

owoo

wwoo

woww

ooww

qp

qp

qp

qp

1

and

1

Durable Goods Monopoly• A second application of multi-product monopoly

– Indestructibility and durability of digital products mean that a firm like Microsoft will find itself competing with its own earlier products.– Durable goods are, therefore, substitutes, though not perfect substitutes, since they are available at different points of time.– Example: Books -- Hardcover or Paperback?

• Difference in production costs is small• Price differences are large• Form of price discrimination, separating patient from impatient.• Why does this occur?

Durable Goods Monopoly

• Durable goods monopolist faces the question of whether to lease the good or sell it.

• A simple model of the lease-or-sell decision.– Two periods t=1,2 (good is obsolete after second period of use, replaced

by a new product).

– MC=0 in both periods (without loss of generality, let C=0 in both periods).

– Demand in each period given by q(p)=1-p.

– Both firm and customers discount future value by the discount factor (with r = interest rate)

r

1

1

Durable Goods Monopoly

• Leasing– Monopolist chooses outputs q1 and q2 to maximize ptq(pt) in each

period (i.e. the monopoly price in each period). From our specification of demand, this yields p1=p2=1/2.

– Since demand at these prices is q=1/2, and the good is durable, it follows that the monopolist’s optimal output sequence is q1=1/2 and q2=0.

– The present discounted value of the firm’s profit is then

14

1

4

1

4

1l

Durable Goods Monopoly

• SellingBackward Induction: Period 2– When the monopolist produces and sells q1 in the first period, we

assume that this amount is “re-offered” on the market in the second period.

– Monopolist chooses q2 to maximize second-period profit. Given q2, the price the monopolist gets in period 2 is determined by market-clearing: p2=1-q1-q2. Hence, the monopolist will choose q2 to maximize q2(1-q1-q2). This maximization has solution q2=½ (1-q1). The second period profit is then 2=¼(1-q1)2.

Durable Goods Monopoly

Period 1– The rental cost in period 1 for using q1 units of the good is (from

the demand function for period1) (1-q1). The purchase price of the good, however, depends on both the rental cost, and on the anticipated future price p2

a. Given the anticipated second period price, the period one price will be p1=(1-q1)+p2

a.

– To close the model, we assume that agents correctly anticipate the future price, so that p2

a=p2. From the calculation for period 2, agents know the monopolist’s output in terms of q1, and hence the second period price in terms of q1: p2=½(1-q1).

Durable Goods Monopoly

Period 1, continued.– Given this, the price in period 1 is

• p1=(1-q1)+½(1-q1) or

• p1=(1-q1)(1+ ½)

– Note that the quantity demanded in period one at any price p1 is lower than it would have been if the monopolist could commit not to produce in period 2

• In particular, if monopolist can commit to q2=0, then p1=(1-q1)(1+ )

• Question: Why can’t the monopolist commit not produce?

– The implied shift in demand in period one means that the monopolist will not be able to sell as much in period 1 as he would if he could commit to q2=0.

Durable Goods Monopoly

Period one, continued

– The monopolist’s profit function is then given by s=q1(1-q1)(1+/2)+ ¼(1+q1)2.

– Maximizing profit with respect to q1 yields

– In particular, it is easy to verify that s< l and the monopolist would prefer to lease.

.

2

1

42

2

2

1

4

2

2

1

1

p

q

and

Durable Goods Monopoly

• Conclusion– Coase conjecture: The durability of a good erodes a monopolist’s market

power since the monopolist cannot credibly commit not to compete with himself for future sales.

– Mechanism: When the monopolist sells, there will be some residual demand for the good in period 2 which can be supplied by the monopolist or by individuals who purchase the good in period 1. The monopolist therefore has an incentive to supply the market in period 2 at a lower price than he charged for the same good in period 1. Consumers with marginal valuations will benefit, in this case, from waiting and purchasing in period 2. This reduces demand in period 1, forcing the monopolist to reduce prices in period.

Durable Goods Monopoly

• Conclusion, cont.– Intertemporal Price Discrimination: Note the price discrimination

implicit in this result. The monopolist who cannot lease his product will sell first to high-valuation buyers at a higher price than he subsequently sells to lower-valuation buyers, who wait to make their purchases.

– Limit Results: Economists who have studied the Coase conjecture have been able to show that as the length of the period over which the monopolist can credibly commit not to change his prices gets shorter, the profit maximizing price gets closer to the competitive price (i.e. to marginal cost).