Entry, Accommodation and Exit.

Why do supernormal profits persist in industries?

Why doesn’t entry of new firms wipe out such profits?

Harvard school of IO economists (Joe Bain): barriers toentry.

Bain: a barrier to entry is anything that allows incumbentsto enjoy strictly positive economic profits without threatof entry.

These may include government regulation-permits, licenses,patents etc. - but we shall abstract from these.

Bain argued there are four major types of entry barriers:

1. Economies of Scale (fixed cost): If minimum efficientscale is large relative to market demand, there can only befew firms in the market (e.g., natural monopoly) & theymay earn strictly positive profit without inviting entry.

2. Absolute Cost Advantages: of incumbents

(superior technology, previous capital accumulation, firmspecific learning etc.)

3. Product Differentiation Advantages:

Incumbents may have patented product innovations &cornered important niches in the product space,

dynamic investment in forming consumer loyalty....

4. Capital requirement:

imperfect capital market, entrants may find it more diffi-cult or costly to raise capital.

The Chicago school led by George Stigler approached en-try barriers as simply being cost asymmetries betweenincumbent firms and outsiders (incumbents could chargeprice above average cost because outside firms had higheraverage cost curves) .

Traditional model of entry barrier by incumbent firms:

Limit pricing model by Sylos-Labini, Modigliani etc.:

Incumbent prices low enough so that outside firms cannotenter.

This theory suffers from a credibility problem.

Why would potential entrants believe that incumbentswould hold on to those low prices if entry occurred?

Not subgame perfect.

Modern version:

Spence (1977) - Dixit (1979,1980)

Model: Capacity choice used as a credible precommit-ment to flooding market & low prices.

Milgrom - Roberts (1982): asymmetric information be-tween incumbents and potential entrants,

- low prices signal private information about low prof-itability of potential entrants after entry.

Scale Economies as Entry Barrier: Contestability.

The idea that scale economies act as entry barriers isbest exemplified by the case of increasing returns to scaleleading to a natural monopoly.

If the average cost continually declines with output, nomore than one firm can produce profitably in the industry

(in a homogenous good market, if two firms sell out-put q1, q2 > 0 at price p that allows them to earn non-negative profit, then one of the two firms can sell q1+q2at a price slightly lower than p

and since average cost will be significantly lowered,

earn higher profit).

Even if the AC curve is U-shaped and the minimum effi-cient scale is large, the number of firms that can produceprofitably in the industry is small (natural oligopoly).

Baumol, Panzar and Willig (1982) argued that even thoughscale economies create entry barriers,

- the threat of being replaced by potential entrants mayact as a disciplining device on current incumbents

and restrict the degree of market power.

They developed the concept of contestable markets tocapture this idea.

Consider a homogenous good industry with n symmetricfirms each with cost function C(q), C(0) = 0.

Note that this allows for fixed cost (that is not sunk) aslong as limq↓0C(q) > 0.

Of these n firms, i = 1, ...m are incumbents and i =

m+ 1, ..., n are potential entrants, n > m.

Market demand is given by D(p).

A sustainable industry configuration is a set of output{q1, ..., qm} and a price p charged by all firms such that:

(i) market clears (demand = supply)

(ii) incumbent firms make non-negative profits

(iii) there does not exist any price pc ≤ p and outputqc ≤ D(pc) such that pcqc > C(qc)

(i.e., it is not possible for a potential entrant to makestrictly positive profit by charging a lower price and sellingsome quantity).

A perfectly contestable market is one where every "equi-librium" generates a sustainable industry configuration.

Consider the case of natural monopoly with increasingreturns to scale:

C(q) = cq + f, c > 0, f > 0 for q > 0

= 0, for q = 0.

Let πm = maxq[(P (q)−c)q] denote the gross monopolyprofit and assume

πm > f.

One can check that there is a unique sustainable indus-try configuration here where m = 1 and the incumbentcharges the price ep = P (eq) where

ep = c+feq .

This is identical to the solution obtained by average costpricing regulation and is the constrained socially optimalsolution when subsidies are not allowed.

It is remarkable that this solution can emerge throughmarket forces and threat of entry.

Thus, regulation of industries with high scale economiesmay not be warranted.

The trouble is that for other demand and cost functions,there may not be a sustainable industry configuration in anatural monopoly so that a constrained efficient industrystructure may not be sustainable against entry.

For example: U-shaped average cost curve where the de-mand curve intersects the AC curve slightly to the rightof minimum efficient scale.

How to think of the strategic foundation of the con-testable outcome?

Easy to see that the outcome in the natural monopolycase requires that incumbent does not alter price after helearns about the output decision of potential entrant.

One game: firms choose prices first and then choose out-put/entry.

Problem: Prices usually adjust faster than output or entrydecisions.

Sunk Cost/Capacity as Barrier to Entry: Stackelberg-Spence-Dixit Model.

Firms enter market at different points of time - someenter early because of technological leadership - and canbe thought of as incumbents.

Others enter later.

Early incumbents accumulate capacity and other formsof capital (including knowledge) over time that is "sunk"at any point of time.

This allows firms to compete aggressively

(for example, because marginal costs are low or produc-tion capacity is bigger).

So, when capacity or capital accumulation is observed bypotential entrants, the latter take this into account intheir calculation of post-entry profitability.

Early entrants can prevent entry by using their first moveradvantage and engaging in significant capital accumula-tion.

Model:

Homogenous good market with demand D(p) = 1− p.

Production cost =0.

2 firms.

Firm 1: Incumbent

Firm 2: (Potential ) entrant.

Entrant incurs fixed entry cost f > 0 if it enters themarket.

For the incumbent, the entry cost is sunk, does not affectthe calculations and hence assumed to be zero.

Two stage game:

Stage 1: Firm 1 sets its capacity K1.

Stage 2: Firm 2 (after observing firm 1’s choice) sets itsown capacity K2 (no entry equivalent to K2 = 0)

After this both firms set a price that clears the marketwhen they produce at full capacity viz., p = 1−K1−K2(p = 0, if K1 +K2 ≥ 1).

Profits:

π1(K1,K2) = K1(1−K1 −K2), if K1 +K2 ≤ 1= 0, if K1 +K2 ≥ 1

π2(K1,K2) = K2(1−K1 −K2)− f, if K2 > 0 and K1 +

= −f, if K2 > 0 and K1 +K2 ≥ 1= 0, if K2 = 0.

Definition: Entry is said to be blockaded if the entrantdoes not enter even though the incumbent’s action isidentical to what would be optimal (for the incumbent)if there was no threat of entry.

Entry is said to be deterred if the entrant does not entereven because the incumbent chooses an action that wouldbe suboptimal (for the incumbent) if there was no threatof entry.

Entry is said to be accommodated if entry occurs and theincumbent adjusts his behavior reconciling to entry.

Blockaded entry:

If there was no threat of entry, incumbent would chooseK1 at the monopoly output level i.e., solving

maxK1

K1(1−K1)

which yields Km1 = 1

2.

Given this capacity of firm 1, the maximum profit thatfirm 2 can make by entering is given by:

maxK2

K2(1

2−K2)− f

=1

16− f.

Thus: entry is blockaded if f ≥ 116.

Entry Deterrence:

If f < 116, entry will occur if the incumbent ignores the

possibility of entry and sticks to monopoly capacity level.

However, if it sets capacity at a sufficiently higher level,the entrant will find it unprofitable to enter.

What is the critical level of incumbent’s capacityKb1 such

that entrant is indifferent between entering and not en-tering:

maxK2

K2(1−Kb1 −K2) = f

and this implies:

Kb1 = 1− 2

qf.

Note f < 116 implies K

b1 = 1 − 2√f > 1

2.. Obviously,Kb1 < 1.

Consider stage 2 subgame for f < 116.

If the capacity set in stage 1 is K1 ≥ Kb1, then no entry

occurs (i.e., K2 = 0) .

If, on the other hand, K1 < Kb1, then entry occurs and

firm 2 sets K2 so as to:

maxK2

K2(1−K1 −K2)− f

which yields reaction function:

K2(K1) =1−K12

which yields the following profit for firm 1:

K1(1−K12

).

Now, consider the reduced form game in stage 1.

Firm 1’s reduced form payoff:

π1(K1) = K1(1−K12

),K1 < Kb1

= K1(1−K1),K1 ≥ Kb1.

Observe that firm 1 will never set K1 > Kb1 because

Kb1 >

12. and

∂π1

∂K1|K1>K

b1= 1− 2K1 < 0.

Therefore, the optimal capacity choice for firm 1 on [Kb1, 1]

is Kb1 yielding profit:

Kb1(1−Kb

1) = 2qf(1− 2

qf) (1)

This is the profit from deterring entry.

On [0,Kb1), the profit maximizing capacity of firm 1 is

given by setting:

∂π1

∂K1|K1<K

b1= 0

which yields:

K1 =1

2

and profit:

1

8. (2)

This is the profit from accommodating entry.

Entry deterring profit in (1) ≥ entry accommodatingprofit in (2) iff

2qf(1− 2

qf) ≥ 1

8.

Let f∗ be defined by

2qf(1− 2

qf) =

1

8.

It can be checked that f∗ ∈ (0, 116.).

Thus: for f ≤ f∗, entry is accommodated.

For f ∈ (f∗, 116.), entry is deterred (and the incumbentholds large capacity equal to 1− 2√f).

Note that when entry is deterred, the market appearsto be a monopoly but market power is lower than in amonopoly.

Potential entry restrains the exercise of market power.

Also, verify that when entry is accommodated, the sub-game perfect equilibrium is K1 =

12,K2 =

14 leading to

profits π1 = 18, π

2 = 116 − f.

Even if f = 0,firm1 has a first mover’s advantage.

The version of the above sequential game where f = 0

is called the Stackelberg game.

Stackelberg- Spence-Dixit sequential capacity choice byincumbent-entrant.

Original Stackelberg game: sequential choice of quanti-ties.

Interpretation of payoff function?

Why incumbent’s first mover advantage in quantity?

Why quantity has commitment value?

Spence-Dixit: interpret quantity as capacity.

- the profit function after both choose capacity inter-preted as reduced form payoff from short run productmarket competition (for example, price competition) givencapacity levels

- first mover advantage may arise as one firm (jncumbent)has earlier access to technology or quicker to act

- capacities are sunk, difficult to change in the short run,and hence have commitment value.

The actual models of Spence and Dixit - short run compe-tition after capacity choice is simultaneous quantity com-petition.

This last stage may itself be interpreted as the reducedform of a two stage game where firms first set "selling ca-pacities" (given production capacities) and then competein prices.

Also, they allow firms to add (but not reduce!) capacityin the product market competition stage.

Dixit (1980):

Stage 1: Firm 1 sets capacity K1 ≥ 0

Stage 2: Firms 1 and 2 set capacities fK1 ≥ K1,K2 ≥ 0as well outputs q1 ∈ [0, fK1], q2 ∈ [0,K2] simultane-ously.

Cost of acquiring each unit of capacity: c0

Unit cost of production: c

For the time being, ignore fixed cost of entry for firm 2.

Consider stage 2.

Firm 2 sets equal capacity and output (K2 = q2)

- his decision problem is equivalent to that of determiningquantity of output at constant marginal cost c0 + c.

His reaction function (on the quantity space) is the stan-dard Cournot reaction function of a firm that producesat marginal cost c0 + c.

Firm 1’s problem in stage 2 is different.

Ignoring previous sunk cost of acquiring capacity, he canproduce any output up to K1 at marginal cost c

and output greater than K1 at effective marginal costc0 + c.

His reaction function is the Cournot reaction functionof a firm that produces at unit cost c as long as thatreaction output is below K1 and then it jumps below tothe reaction function of a firm that produces at unit costc0 + c.

A jump discontinuity at K1.

Firm 1 much more aggressive than firm 2 (higher reactionfunction) till K1.

If K1 = 0, the second stage game is just a simultaneousmove game with a symmetric Nash equilibrium.

By setting a high K1 in stage 1, firm 1 pushes up hisown reaction function in the second stage (by reducingcurrent marginal cost) for a whole range of output so thatthe new Nash equilibrium is more favorable to firm 1.

With fixed cost of entry, can be deterred.

One feature of the equilibrium in a linear demand model:no excess capacity - all capacity is used.

This is generally true as long as demand is concave (down-ward sloping reaction functions in the quantity space).

But if demand is convex and reaction functions are up-ward sloping - there may be excess capacity.

Maskin (1986): uncertainty about demand or cost canlead to incumbent acquiring too much of capacity to deterentry and thus lead to excess capacity in certain statesof nature.

Remark: Welfare analysis of entry deterrence is ambigu-ous.

Incumbent’s increase in capacity and output to deter en-try - is welfare improving (as long as all capacity is used).

If entry occurs (not deterred) after observing incumbent’scapacity, then entrant’s output and capacity is welfareimproving.

Fixed costs complicate.

Multiple incumbents:

Public good problem in entry deterrence?

If one incumbent deters entry by making a large invest-ment, other incumbents benefit.

Incentive to free ride ⇒ underinvestment in the aggre-gate.

Gilbert and Vives (1986) - contributing to entry deter-rence is not quite like contributing to a pure public good.

The benefit from entry deterrence also depends on eachfirm’s own "contribution".

Profit of an incumbent firm from entry deterrence de-pends on its own market share after entry is deterredwhich, in turn, creates competitive pressure to increaseinvestment in capacity.

⇒overinvestment in entry deterrence.

Possibility of post-entry merger

⇒ in bargaining for the buy-out of entrant by incumbent,entrant can certainly get whatever it would make if therewas no merger after entry

+ part of the increase in industry profit associated withmerger (monopolization).

Thus, prospect of buy-out encourages entry.

Of course, it also increases market concentration.

Note: entrant may acquire lot of capacity to increasebargaining strength (threat point) in the buyout phase.

After buyout, incumbent may not use all of entrant’s ca-pacity (hold excess capacity).

Other forms of capital accumulation to deter entry:

* Cost reduction (Process R&D) ⇒ makes incumbentmore aggressive competitor post entry.

* Learning by doing.

* Developing clientele : More imperfect the consumers’information and more important the costs of switchingsuppliers, the greater the clientele effect.

Sometimes, overinvestment in clientele may not be anoptimal way to prevent entry as the incumbent then hasa large captive segment and is therefore less aggressivein price competition making entry more lucrative for en-trant.

* Network effect among consumers: increases incentiveto expand size of installed network base by incumbentfirm.

* Exclusive franchises with retailers⇒ increases distribu-tion costs for entrants

* Development of new product - specially when patented.

Strategic effect of pre-commitment on rival’s actions:

overinvestment vs. underinvestment.

A simple reduced form three-stage model.

Stage 1: Firm 1 (incumbent) commits to a variable K1(call it "investment")

Observed by firm 2.

Stage 2: Firm 2 decides whether or not to enter.

Stage 3: Firms in the industry engage in short run productmarket competition and each firm i in the market decideson variable xi.

If entry does not occur, firm 2 receives zero payoff andfirm 1’s payoff is

π1m(K1, xm1 (K1))

where xm1 (K1) is the monopoly level of variable x1 (giveninvestment K1) that is set by firm 1 in stage 3.

If entry occurs, the profits for any choice of x1, x2 instage 3 are π1(K1, x1, x2) and π2(K1, x1, x2) whereπ2 is net of entry cost.

Assume: π1(K1, x1, x2), π2(K1, x1, x2) are differentiable.

Let {x∗1(K1), x∗2(K1)} be the Nash equilibrium of thestage 3 product market competition game, given K1.

It can be shown that x∗1(K1), x∗2(K1) are continuous inK1.

Assume: Given K1,NE is unique, interior and "stable".

If K1 is chosen such that

π2(K1, x∗1(K1), x

∗2(K1)) ≤ 0

then entry does not occur.

Indeed, if in equilibrium, firm 1 chooses K1 so that

π2(K1, x∗1(K1), x

∗2(K1)) < 0,

prevention of entry is not a binding constraint of firm 1’schoice of investment

⇒entry is blockaded.

Entry deterred:

π2(K1, x∗1(K1), x

∗2(K1)) = 0

Entry accommodated:

π2(K1, x∗1(K1), x

∗2(K1)) > 0.

Assume: π1m(K1, xm1 (K1)), π

2(K1, x∗1(K1), x

∗2(K1))

are strictly concave in K1 and that x∗1(K1), x∗2(K1) aredifferentiable.

Consider situation of entry deterrence:

π2(K1, x∗1(K1), x

∗2(K1)) = 0 (3)

As x∗2(K1) is the best response of firm 2 in stage 3 tox∗1(K1), FOC implies:

∂π2(K1, x∗1(K1), x

∗2(K1))

∂x2= 0.

Taking total derivative with respect to K1 of

π2(K1, x∗1(K1), x

∗2(K1))

we have

dπ2

dK1=

∂π2

∂K1+∂π2

∂x1

∂x∗1∂K1

+∂π2

∂x2

∂x∗2∂K1

=∂π2

∂K1+∂π2

∂x1

∂x∗1∂K1

= Direct Effect + Strategic Effect

Direct Effect : Change in K1 may directly change rival’sprofitability by changing demand for the latter’s productor its cost of production (through spillovers) etc

If K1 is investment that affects only firm 1’s own cost ortechnology, then direct effect is zero.

Strategic effect: change in K1 changes firm 1’s ex postbehavior and his choice in the product market which inturn affects firm 2’s profit.

These effects may run in opposite directions.

Taxonomy of business strategies:

Top dog: be big or strong to look tough or aggressive

Puppy dog: Be weak or small to look soft or inoffensive

Lean and hungry look: Be weak or small to look toughor aggressive

Fat cat: be big or strong to look soft or inoffensive

To deter entry, firm 1 wants to look tough.

Investment makes firm 1 TOUGH if dπ2

dK1< 0 and in that

case firm 1 should overinvest

("top dog" strategy).

Investment makes firm 1 SOFT if dπ2

dK1> 0 and in that

case firm 1 should underinvest

("stay lean and hungry" strategy).

In Spence-Dixit kind of investment games, overinvest-ment (top dog) strategy to deter entry is optimal.

But in investment in forming loyal clientele, underinvest-ment (stay lean and hungry) may be better to deter entry.

If entry deterrence is too costly, it is better for firm 1 toaccommodate entry.

Under accommodation, the incentive to invest is deter-mined by the effect of K1 on

π1(K1, x∗1(K1), x

∗2(K1)).

Observe:

dπ1

dK1=

∂π1

∂K1+∂π1

∂x1

dx∗1dK1

+∂π1

∂x2

dx∗2dK1

=∂π1

∂K1+∂π1

∂x2

dx∗2dK1

= Direct Effect + Strategic Effect

The direct effect exists even if firm 1’s investment is notobserved by firm 2.

The strategic effect is the effect of observing this invest-ment on firm 2’s behavior in the product market.

For the time being, let us focus on the strategic effect.

Assume: ∂π1

∂x2and ∂π2

∂x1have the same sign

(product market variables of both firms have the samenature).

Now,

dx∗2dK1

=dx∗2dx1

dx∗1dK1

= R02(x∗1)dx∗1dK1

so that sign of the strategic effect:

sign(∂π1

∂x2

dx∗2dK1

)

= sign(∂π1

∂x2)sign(R02(x∗1)

dx∗1dK1

)

= sign(∂π2

∂x1)sign(R02(x∗1)

dx∗1dK1

)

= sign(∂π2

∂x1

dx∗1dK1

)sign(R02)

Note ∂π2

∂x1

dx∗1dK1

= strategic effect under entry deterrence.

IfR02 > 0 (x1 and x2 are strategic complements), whetheroverinvestment or underinvestment is optimal under en-try accommodation (focusing on strategic effect) followsthe same prescription as under entry deterrence.

If R02 < 0 (x1 and x2 are strategic substitutes), over-investment is optimal under entry accommodation if un-derinvestment is optimal under entry deterrence and vice-versa.

Assume: ∂π2

∂K1= 0 so that dπ2

dK1in the entry deterrence

case depends only on the strategic effect.

The latter implies that in the entry deterrence case we

only have two kinds of situation:

(a) where the strategic effect is such that investmentmakes firm 1 look tough.

(b) where the strategic effect is such that investmentmakes firm 1 look soft.

(a) (b)strategic

complementsA : Puppy DogD : Top Dog

A : Fat CatD : Lean and Hungry

strategicsubstitutes

A : Top DogD : Top Dog

A : Lean and HungryD : Lean and Hungry

In all cases, firm 1 tries to make firm 2 behave softly.

Inducement of Exit:

Very similar to entry deterrence.

Suppose there are two firms in the market.

Fixed cost of staying on in the market.

Suppose firm 1 has a first mover advantage

Can pre-emptively commit to an investment (a long runvariable) K1 which is observed by firm 2

Then, firm 2 decides whether or not to exit the market.

If it does not exit, firms engage in short run productmarket competition setting x1, x2.

Exit occurs as long as

π2(K1, x∗1(K1), x

∗2(K1)) ≤ 0

The analysis of entry prevention can be easily re-writtenas exit inducement.

Applications of the taxonomy of business strategies forentry deterrence & accommodation.

In general, K1 can be interpreted as any stage 1 (or,long run) variable (whether or not set by a firm) that isobservable prior to product market competition betweenfirms in the industry and taken as given, at that stage.

* Voluntary limitation of capacity: Puppy dog ploy.

.

A firm may choose to commit to small capacity in orderto reduce price competition in the product market.

Price competition : strategic complementarity.

For example, entrant may commit to small capacity soas not to trigger aggressive price competition from largecapacity incumbent.

* Product Differentiation: Puppy Dog ploy.

Here, a firm commits to closeness to rival’s product typeor location, prior to price competition.

Closer = more aggressive price competition (think of thisas higher capital).

* Learning by Doing:

Two periods.

One firm in period 1.

Investment in capital = higher production in initial timeperiod.

Reduces marginal cost in the next period.

If second period market competition (if entry occurs) is inquantities (strategic substitutes), overinvestment is opti-mal i.e., top dog strategy.

It reduces firm 2’s market share in period 2 (if it enters).

This is independent of whether entry is deterred or ac-commodated.

What if product market competition is in prices?

Top dog is still good for entry deterrence.

But for accommodation, experience accumulation andlower marginal cost triggers lower price from rival.

Makes overinvestment less worthwhile - underinvestmentoften optimal. Puppy Dog.

Spillovers: learning reduces marginal cost of rival too.

This effect reduces the appeal of top dog strategy.

* Most favored customer clause (price protection).

Guarantees current customers that they will be reim-bursed any difference between current price and the low-est price upto a date in the future.

Helps to commit to not reduce price and sustain currentlevel of price in future.

Interesting effect: Reduces price competition in the futureand creates price-leadership!

Consider a two period differentiated good price duopoly.

Demand in each period Di(pi, pj).

For simplicity, set cost =0.

Firms set prices simultaneously each period.

Upward sloping reaction function.

No discounting.

If no price protection: Static NE (p∗1, p∗2) outcome ineach period.

Suppose firm 1 unilaterally introduces price protection inperiod 1 and sets price ep1 = p∗1 + in period 1.

Also, suppose consumers expect firm 1 not to reduce pricein future (so no one buys just to get a "reimbursement"):this will be self-fulfilling in equilibrium.

Quantity sold by firm 1 in period 1: eq1 = D1(ep1, p∗2).

Consider price competition in period 2.

Firm 1’s second period profit at any pair of prices (p1, p2)charged by the firms in period 2:

eπ1(p1, p2) = p1D1(p1, p2), if p1 ≥ ep1= p1D1(p1, p2)− eq1(ep1 − p1), if p1 < ep1.

Observe that price protection has led to a downward shiftof firm 1’s profit function - becomes weak to look inof-fensive.

Indeed, for p1 < ep1,eπ1(p1, p2) = p1(D1(p1, p2) + eq1)− eq1ep1

and maximizing this is equivalent to maximizing

p1(D1(p1, p2) + eq1)which is as if firm 1 faced higher demand curveD1(p1, p2)+eq1.Higher demand : price reaction higher.

So, firm 1’s reaction function in the modified price gamein period 2 is the standard static reaction function (whenfirm 1’s payoff is p1D1(p1, p2)) as long as his reactionprice is ≥ ep1.Let ep2 be such that ep1 = R1(ep2).For p2 < ep2, firm 1’s reaction jumps outward to the re-action function when this firm faces higher demand givenby D1(p1, p2) + eq1.Jump discontinuity.

NE: p1 = ep1, p2 = R2(ep1).(As long as ep1 is not too high relative to p∗1).Stackelberg price leadership outcome.

Both firms charge higher prices than in the static out-come.

Firm 1 loses some profit in period 1 as it is not chargingits best response to p∗2.

If ep1 is close to p∗1, the loss in firm 1’s profit is of "secondorder" (as marginal profit of firm 1 at p∗1 is zero).

But firm 1’s gain by getting the leadership profit in period2 is of first order.

So, firm 1 gains in total profit by unilaterally deviating toprice protection in period 1.

Puppy dog strategy

* Multimarket oligopoly.

Two separate markets.

Market 1 is a duopoly.

Firm 1 is a monopolist in market 2.

Firm 1’s production cost depends on sum of output soldin both markets.

(Diseconomy of scope or decreasing returns to scale...).

All quantities determined simultaneously.

If demand increases in market 2, firm 1 has incentive tosell more in market 2

- this raises its marginal cost of selling in market 1

- its reaction function in market 1 falls - yields marketshare to firm 2 in equilibrium.

Bulow et al (1985): total profit of firm 1 may fall.

Price competition + increasing returns to scale (economiesof scope): similar outcome.

Strategic disadvantage caused by puppy dog effect of in-crease in market demand.

* Quotas and Tariffs.

Changes strategic positions of domestic and foreign firm.

Export subsidy: makes domestic firm a top dog if quantitycompetition in foreign market.

Quota, tariff: lowers reaction function of foreign firm inthe domestic market.

* Vertical contracts.

Between manufacturers and retailers influence competi-tion between downstream units.

* Tying.

Whinston (1987).

Two firms and two completely unrelated markets.

Market A is monopolized by firm 1.

Unit mass of identical consumers with unit demand andvaluation v.

Unit cost c.

Market B: differentiated good price duopoly with firms 1and 2.

Same consumers in both markets.

Demand for firm i in market B: Di(pi, pj) ∈ [0, 1].

Unit cost (of both firms) in market B: c1

Question: Does firm 1 have an incentive to tie (or bundle)products A & B?

First, consider the following game:

Firms simultaneously decide on their prices and at thesame time, firm 1 decides whether to bundle the twoproducts or two sell them separately.

Given any p2, firm 1 can never gain strictly by tying thegoods.

To see this, suppose firm 1 ties the goods and sells thebundle at some price P1.

For a consumer who buys this bundle, the marginal pricepaid for good B is P1 − v.

So, quantity sold by firm 1 is D1(P1 − v, p2).

The profit is

(P1 − c− c1)D1(P1 − v, p2)

If firm 1 sells the good separately and prices good A atv and good B at P1 − v, his profit is

(v − c) + (P1 − v − c1)D1(P1 − v, p2)

≥ (v − c)D1(P1 − v, p2) + (P1 − v − c1)D1(P1 − v, p2)

= (P1 − c− c1)D1(P1 − v, p2)

with strict inequality unless D1(P1 − v, p2) = 1.

So, tying hurts firm 1 as it reduces its degrees of freedomin pricing.

Under bundling, if we set ep1 = P1 − v (the effectivemarginal price of buying good B for consumers), thenfirm 1 maximizes

(ep1 − (c1 − (v − c)))D1(ep1, p2)with respect to ep1.When selling separately and setting its price in market B,firm 1 sets price p1 for good B so as to maximize:

(p1 − c1)D1(p1, p2)

Under bundling the firm is effectively selling good B atlower marginal cost under bundling

- a unit of loss of sales in market B costs v− c to firm 1in Market A in terms of lost profit

- so its reaction is more aggressive in market B underbundling, then when selling separately.

Reaction function of firm 1 more aggressive (like a costreduction).

Next, consider the following two stage game:

Firm 1 first decides whether to bundle or sell separately.

Then, firms set prices in both markets simultaneously.

[If goods are complements, bundling may be equivalentto making firm 1’s product in market A incompatible withfirm 2’s product in market B: a technological decision.]

Here bundling intensifies price competition in stage 2 andhurts both firms.

Better to follow puppy dog strategy of no bundling.

But it still may be optimal to bundle for deterring entry.

* Systems of Complementary Products and Choice ofCompatibility

Ex. computer hardware and software; cameras, lensesand films; music systems...

Products in each system can be purchased individuallybut they cannot be consumed as a system ("mix andmatch") unless they are compatible.

A manufacturer that makes its system incompatible withother systems effectively bundles the components in hissystem.

Simple model:

Two firms.

Each firm produces two complementary products: X andY.

A unit each of X and Y together constitute a system.

Product differentiation:

Consumers are uniformly located on a unit-square on thex-y space.

Firms’ products are located at the two diametric ends ofthe square:

Firm 1 at (0,0) and Firm 2 at (1,1).

A consumer located at (x, y) incurs psychological costtx+ ty when buying both components from firm 1 andt(1−x)+ t(1− y) when buying both components fromfirm 2.

If she buys component X from firm 1 and Y from firm 2,her psychological cost is tx+ t(1− y) etc...

Suppose unit cost is same for both firms and both prod-ucts.

Under incompatibility: each firm offers a bundle of X andY and the consumer located at (x, y) compares

P1 + tx+ ty

with

P2 + t(1− x) + t(1− y)

If both systems are sold and market is fully covered, usingthe standard indifference condition, we can figure out thedemand for each firm’s system and the symmetric NE.

In this NE, the square is split along the diagonal betweenthe systems sold by the two firms.

Under compatibility, components are sold separately atprices (pX1 , p

Y1 , p

X2 , p

Y2 ) and consumer can mix and match.

There are four potential systems that the consumer canchoose from - product variety increases.

If she buys system with compenent X from firm 1 and Yfrom firm 2, her total cost is:

pX1 + pY2 + tx+ t(1− y)

and so on.

Consumer chooses one with minimum total cost.

If all four systems are sold and market is fully covered,then from indifference condition, we can get the linear de-mand function for each component of each firm as func-tion of all four prices.

Solve for symmetric NE.

In this NE, the square is split into four square quadrants,the southwest quadrant buys both components from firm1, southeast buys X from firm 2 and Y from firm 1 etc

Consumers in the NW and SE quadrants buy systemsby using mix-n-match that are closer to their taste thanunder incompatibility.

Compatibility:

** Raises demand - products better suited to taste⇒incentive to charge higher prices.

** Softens price competition (unbundled products).

When firm 1 cuts price of component X1:

- under incompatibility, it increases only the demand forits own bundled system (X1Y1) as that is the only systemthat includes component X1

- under compatibility, it also increases the demand for thesystem X1Y2 whose benefit accrues to firm 2.

This externality reduces the incentive of firm to cut price.

Price competition less aggressive.

So both firms gain under compatibility.