Chapter 8: Entry, Accommodation, and Exit • Barrier to entry (no government intervention) • 4 elements of market structure (Bain, 1956) – Economies of scale - Natural Monopoly – Absolute cost advantages - Superior technology – Product Differentiation advantage - Niche – Capital requirement - dif fi culty to fi nd fi nancing 3 kinds of behavior by incumbent: 1. Blockaded entry - market is not attractive to competitor 2. Deterred entry - strategic behavior from the incum- bent 3. Accommodated entry - let it be.... Limit pricing model • price is so low that it prevents entry (Bain, 1956) • Incumbent acquires a large capacity to deter entry (Spence (1977, 1979) Dixit (1979, 1980)) 1
• Asymmetric information - signalling aspect (Mil- grom Roberts (1982)) 2
1 Fixed costs: natural monopoly and contestability Fixed cost as a barrier to entry. 1.1 Fixed costs vs sunk costs Fixed costs are • independent from the produced quantity • and are sunk costs in the short run. ( f + cq if q > 0 C ( q ) = 0 if q = 0 1.2 Contestability • First approach to natural monopoly • homogeneous good industry • n fi rms • same technology, costs c ( q ) with c (0) = 0 • 2 groups of fi rms: m incumbents ( i = 1 , ...., m ), m − n ≥ 0 potential entrants. • industry con fi guration: { q 1 , q 2 , ..., q m } for incum- 3
bents • p price charged by incumbents De fi nition 1. Industry con fi guration is feasible if the market clears. De fi nition 2. Industry con fi guration is sustainable if no entrant can make a pro fi t taking the incumbent’s price as given. There exists no price p e ≤ p c and no quantity q e ≤ D ( p e ) such that p e q e > c ( q e ) . De fi nition 3. A perfectly contestable market is one in which any equilibrium industry con fi guration must be sustainable. • See graph to illustrate the concept Theory of contestability predicts: 1. There exists a unique operating fi rm in the industry, 2. the fi rm makes zero pro fi t, 3. average cost pricing prevails. 4
But with different demands, or cost functions, natural monopolies may not be sustainable. • The theory of perfectly contestable markets can be seen as a generalization of Bertrand competition with increasing returns-to-scale (Baumol et al., 1982) • But prices seem to adjust more rapidly than decisions about quantities or entry. • Short run capacity commitments. 1.3 War of attrition • Another approach to natural monopoly • Maynard Smith (1974) in theoretical biology, to explain animal fi ghts for prey. • 2 fi rms in a fi ght for a monopoly position. • Time is continuous from 0 to in fi nity • r rate of interest 5
• Same cost of production ( f + cq if q > 0 C ( q ) = 0 if q = 0 • price adjustments are instantaneous • If the 2 fi rms are in the market at time t , p = c (Bertrand). Each fi rm loses f per unit of time. • If one fi rm, price is p m and pro fi t is Π m − f > 0 for this fi rm and 0 for the other. • Both fi rms are in the market at date 0. • At each instant each fi rm decides whether to exit. Exit is costless. A fi rm that drops out never returns; the remaining fi rm stays forever. • Symmetric equilibrium in which at any instant each fi rm is indifferent between dropping or staying. – if one fi rm drops out: 0 forever; – if both fi rms are still in the market at date t , each fi rm drops out with probability xdt between t and t + dt . – Pro fi t of one fi rm from staying is ∗ − fdt is the other is still in, 6
e Π m − f if the other has dropped (which arises ∗ r with probability xdt ) – Thus Π m − f e 0 = − fdt + xdt + 0 r – and the probability of dropping is rf x = e Π m − f War of attrition: 1. there are 2 fi rms in the industry for a (random) length of time; then one exists 2. fi rms earn no ex ante pro fi t, but may have ex post pro fi t, 3. the price is fi rst competitive and then price is the monopoly price. 7
2 Sunk costs and Barrier to entry • The Stackelberg-Spence-Dixit model • Sunk costs have a commitment value • Dynamic game - Stackelberg (1934) • 2 fi rms – fi rm 1, incumbent – fi rm 2: potential entrant • Timing: – Firm 1 chooses K 1 ; – Firm 2 observes K 1 and chooses K 2 . • Pro fi ts Π i ( K i , K j ) = K i (1 − K i − K j ) i, j = 1 , 2 for i 6 = j • Properties: – ∂ Π i ∂K j < 0 - each fi rm dislikes capital accumulation by the other, ∂ 2 Π i – ∂K j ∂K i < 0 - capital levels are strategic substi- tutes. 8
No fi xed costs of entry • Firm 2 maximizes Π 2 = K 2 (1 − K 1 − K 2 ) and thus K 2 ( K 1 ) = 1 − K 1 2 • Firm 1 maximizes Π 1 = K 1 (1 − K 1 − K 2 ( K 1 )) and thus 1 = 1 2 = 1 4 , Π 1 = 1 8 > Π 2 = 1 K s 2 > K s 16 • First mover advantage. • If simultaneous game 2 = 1 K n 1 = K n 3 Π 1 = Π 2 = 1 9 • Firm 1 accumulates more capital than in simultane- ous game, fi rm 2 less. • Firm 1 accommodates entry . • Graph • Commitment value: “burning one’s bridge”. 9
Fixed cost f • Pro fi t of 2 is ( K 2 (1 − K 1 − K 2 ) − f if K 2 > 0 Π 2 ( K 1 , K 2 ) = if K 2 = 0 0 • If f > 1 16 ⇒ no entry 1 = 1 2 = 1 • If fi rm 1 chooses K s 2 , 2 will choose K s 4 and make a pro fi t of 1 16 − f > 0 . • Firm 1 may decide to choose K 1 to deter entry . 1 the level of capital such that fi rm 1 deters entry • K b Max { K 2 (1 − K 1 − K 2 ) − f } = 0 • K b 1 = 1 − 2 f 0 . 5 . • If f tends toward 1 16 , equilibrium of deterred entry, • If f = 0 (or small), equilibrium of accommodated entry, • If f > 1 16 , fi rm 1 blocked entry simply by choosing its monopoly capital level, K m 1 = 1 2 . 10
2.1 Welfare implication • p = 1 − K demand function, where K = K 1 + K 2 is the industry capacity and output. • p is the market price. • Welfare loss from monopoly or duopoly pricing is WL = p 2 2 . • If entrant enters, and entry cost, the welfare loss is p 2 2 + f . No entry cost • simultaneously choice p n = 1 3 • Sequentially p s = 1 4 • Thus, p n > p s and WL n > WL s 11
Entry costs f The losses are • if simultaneous decisions WL n = p 2 2 + f = 1 18 + f • and if sequential decisions and entry deterrence WL s = (2 √ f ) 2 = 2 f 2 • Thus WL n < WL s if f > 1 18 • The welfare analysis of entry deterrence is am- biguous because entry can result in biases in either direction. 12
3 A Taxonomy of Business Strategies • In Stackelberg model: commitment. • The incumbent over-invests to force the entrant to restrict its own capacity. • Here: over-investment and under-investment. • 2 periods • 2 fi rms: – incumbent ( fi rm 1), – potential entrant ( fi rm 2). Timing: • In period 1 , – fi rm 1 chooses K 1 (investment, capacity...); – Firm 2 observes K 1 and decides whether to enter. • In period 2 , if entry, both fi rms simultaneously choose ( x 1 , x 2 ) (quantities, prices...) 13
In period 2 • If no entry, fi rm 1 chooses x m 1 ( K 1 ) that maximizes Π 1 m ( K 1 , x m 1 ( K 1 )) . • If entry, the NE is ( x ∗ 2 ( K 1 ) ) that solves the 1 ( K 1 ) , x ∗ maximization program of each fi rm Π i ( K 1 , x i , x ∗ j ) for i, j = 1 , 2 and i 6 = j . In period 1 • What is the incumbent’s fi rst period choice, K 1 ? • Entry is deterred (and blockaded) if K 1 is chosen such that Π 2 ( K 1 , x ∗ 1 ( K 1 ) , x ∗ 2 ( K 1 )) ≤ 0 • Entry is accommodated if Π 2 ( K 1 , x ∗ 1 ( K 1 ) , x ∗ 2 ( K 1 )) > 0 • Assume that Π 1 m ( . ) and Π 1 ( . ) are strictly concave in K 1 and x ∗ 1 ( . ) are differentiable. 14
3.1 Deterrence of entry • The incumbent chooses K 1 so as to just deter entry Π 2 ( K 1 , x ∗ 1 ( K 1 ) , x ∗ 2 ( K 1 )) = 0 • Total derivative of Π 2 with respect to K 1 d Π 2 = ∂ Π 2 + ∂ Π 2 ∂x ∗ + ∂ Π 2 ∂x ∗ 1 2 dK 1 ∂K 1 ∂x 1 ∂K 1 ∂x 2 ∂K 1 • where ∂ Π 2 ∂K 1 is the direct effect ( DE d ) ∂x ∗ ∂ Π 2 ∂K 1 is the strategic effect ( SE d ) 1 ∂x 1 ∂x ∗ ∂ Π 2 ∂K 1 = 0 (envelope theorem) 2 ∂x 2 • DE d : – ∂ Π 2 ∂K 1 < 0 if K 1 is clientele accumulated, – ∂ Π 2 ∂K 1 = 0 if K 1 is an investment that affects fi rm 1’s technology. • SE d : K 1 changes fi rm 1’s ex post behavior ( ∂x ∗ ∂K 1 ), 1 and thus affect 2’s pro fi t ( ∂ Π 2 ∂x 1 ). 15
• Terminology: – The investment makes fi rm 1 tough if d Π 2 dK 1 < 0 – the investment makes fi rm 1 soft if d Π 2 dK 1 > 0 • To deter entry fi rm 1 wants to look tough. Taxonomy of business strategies: ¦ top dog - be big or strong to look tough or aggressive, ¦ puppy dog - be small or weak to look soft or inoffensive, ¦ lean and hungry look - be small or weak to look aggressive or tough, ¦ fat cat - be big or strong to look soft or inoffensive. • If investment makes fi rm 1 tough ( d Π 2 dK 1 < 0 ), the fi rm 1 should overinvest to deter entry - top dog strategy ; • If investment makes fi rm 1 soft ( d Π 2 dK 1 > 0 ) the fi rm should underinvest to deter entry; lean and hungry look . 16
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