Econ 8601: Industrial Organization (Thomas J. Holmes) Lecture 1. Part 1: The Cost of Monopoly in General Equilibrium. μ 1

Transcription

1 Econ 8601: Industrial Organization (Thomas J. Holmes) Lecture 1 Part 1: The Cost of Monopoly in General Equilibrium Set of goods [0, 1], x [0, 1] aparticulargood. Utility function of representative consumer U = σ = for μ>1. Ã Z 1 q(x) μdx 1 0 μ μ 1! μ Unit time endowment.

2 Technology: one unit of labor per unit of good. Let labor be numeraire, w =1 Goods x [0,λ] are controlled by a monopolist Goods x (λ, 1] are perfectly competitive. Therepresentativeconsumerownssharesinallthefirms.

3 Solution Let π M be the equilibrium monopoly profit of a representative monopolist. Income of the representative consumer I =1+λπ M. p C =1. Constant elasticity of demand the price in monopoly industries is p M = μ. Let q M and q C be quantities in the equilibrium of this economy.

4 Consumer MRS implies: q M q C = But p C =1and p M = μ, so Ã! σ pm p C q M = q C μ σ Resource constraint for labor, λq M +(1 λ)q C = 1 λq C μ σ +(1 λ)q C = q C = 1 (1 λ + λμ σ )

5 Welfare gains from antitrust v be the compensating variation (the change in income at the new prices so the representative consumer is indifferent to old system). New prices, p =1everywhere. Y =1 v be income.

6 U = Y and or 1 v = = Ã Ã 1 μ 1 λqm +(1 λ) q μ C! μ λ ³ q C μ σ 1μ +(1 λ) q μ = q C µλμ σ μ +1 λ µ μ λμ σ μ +1 λ = (1 λ + λμ σ ) v =1 µ1 λ + λμ μ 1 1 μ µ1 λ + λμ μ μ 1 1 μ C! μ

7 v =1 µ1 λ + λμ μ 1 1 μ µ1 λ + λμ μ μ 1 Observe that So Other parameters: lim 1 μ 1 μ μ 1 = lim μ μ μ 1 =.3679 μ 1 lim μ 1 v =0

8 μ λ

9 Discussion Harberger.1 percent of GDP. Credible? Not the fashion in IO today to produce aggegate estimates Much work today produces analytical tools to give to the Justice Dept

10 Other costs of monopoly Rent Seeking (could dissipate the profit) Posner, Hsieh and Moretti example of real estate agents. Effect of competition on productivity x-inefficiency? Leibenstein (1966). an ugly term. Not much there besides an Recent treatments: Parente and Prescott, Holmes and Schmitz

11 Lec 1B Dixit Stiglitz Unbounded set of possible goods, x [0, ] Utility function of representative consumer U = σ = for μ>1. µz 0 μ μ 1 q(x) 1 μdx μ L time endowment for economy Constant mar- Technology: φ fixed cost (labor) to setup a product. ginal cost of β (labor)

12 Let labor be numeraire, w =1 Let [0,N] be interval of goods produced in the market. price of good x. Let p(x) be

13 Definition of Equilibrium {N, p(x), q(x), x [0,N]} such that 1. Consumer demands q(x) maximize utility given the budget constraint 2. p(x) is the profit maximizing price of firm x, taking as given the prices of all other firms 3. Firms that enter make nonnegative profit 4. No incentive for further entry (Note (3+4) zero profit).

14 Problem of Consumer: subject to max q( ) Z N 0 NZ 0 q(x) 1 μdx μ p(x)q(x)dx = L (1) MRS condition: goods x 1 and x 0.

15 μ [] μ 1 ³ 1 1 μ q μ 1 μ [] μ 1 ³ 1 μ q 1 1 μ 1 0 = p 1 p 0 Ã q1! 1 σ = p 1 q 0 p 0 q 1 = p σ 1 (p σ 0 q 0) = p σ 1 k

16 The FONC of firm 1 p σ 1 k σ (p 1 β) p1 σ 1 k = 0 p 1 = σ (p 1 β) p 1 β Constant markup over cost. p 1 = 1 σ p 1 = μβ

17 Zero-profit condition μβq βq φ =0, (2) β (μ 1) q = φ So q = φ β(μ 1)

18 Use resource constraint to determine number of products: N (βq + φ) = L N = L βq + φ = = L Ã μ 1! 1 φ L (μ 1) + φ μ φ = L σφ

19 Consumer Welfare (per capita) µ R 0 q(x) 1 μdx μ utility per capita = µ L Nq 1 μ μ = L = Nμ q L = L = φ1 μ σ μ β(μ 1) Lμ 1 Increasing in L(love of variety). ³ Lσφ μ q

20 Lec 1C Basic Address Model of Product Differentiation (Hotelling, Salop) Geographic space is the real line. Consumers are uniformly distributed on the line with density of L per unit distance φ is fixed cost of opening a store at a particular location β is constant marginal cost t is transportation cost per mile. D is distance between stores

21 Social Planner s Problem Choose D to minimize average total cost (ATC) S = DL is store size given D Average Production Cost AP C = βs + φ S = β + φ S Average Transportation Cost (see figure!) AT rc = Dt 4

22 ATC AT C = AP C + AT rc = β + φ S + Dt 4 = β + φ DL + Dt 4 Minimize ATC. First order necessary condition (differentiate w.r.t. D) 0= φ LD 2 + t 4 Note sufficient second order condition holds

23 Solving for D... φ LD 2 = t 4 D 2 = 4φ Lt µ D 4φ = Lt 1 2 Store Size S = LD µ 4Lφ = t 1 2 Important comparative statics D increases in φ, decreases in L and t

24 S increases in φ and L, decreases in t

25 Market Equilibrium Problem (Hotelling/Salop Monopolistic Competition model) Note: model has issues that we will discuss at the end Each store a separate firm Firms set price taking as given prices of neighboring firms (Bertrand competition) An equilibrium is a (p e,d e ) so that (1) p e is profit maximizing given other firms set p e and distance is D e (2) firms make zero profit

26 Problem of the Firm Consider firm located at point 0 on the line Suppose firm sets price p and neighbors set p. Let x be location of consumer on the right indifferent between firm at 0 and next firm on the right p + tx = p +(D x)t 2tx = p p + Dt x = p p + D 2t 2

27 Demandoffirmat0is(addingupdemandonbothsides) Q d = 2Lx " p p = 2L 2t + D 2 # Profit is π = (p β) Q d φ " p p # = 2L (p β) 2t + D 2 φ FONC " p p 2L 2t + D 2 # +2L (p β) 1 2t =0

28 In a symmetric equilibrium, p p =0. or (p β) LD L t So we get =0 p β = td p = β + td Profit Setting equal to zero yields π = (p β) S φ = (p β) DL φ = td 2 L φ D e = µ 1 µ 1 φ 2 1 4φ 2 1 = = tl 2 tl S e = µ 1 LD e Lφ 2 1 = = t 2 S 2 D

29 So stores are too close with monopolistic competition. Excess Entry. Direction of the comparative statics the same

30 Issues Didn t specify this as a two stage game. Suppose try. Say a circle. Stage 1 N firms enter Stage 2. firms are equally spaced around the circle Stage 3. Price game. Straightforward to generalize the above analysis. Given discreteness, will in general have positive profits. (But next guy in makes profits negative).

31 Problem: model assumes firms are equally spaced. If firms are free to pick locations that aren t equally spaced, a pure strategy equilibrium may not exist in the price subgame. There is discontinuities in demand. (If assume transportation costs is quadratic rather than linear, no discontinuity.) See new paper by Jonathan Vogel (Plus new work by Wen-Tai Hsu)

32 Lecture 1D: Mankiw and Whinston Homogenous product market demand P (Q), Q total output. P 0 (Q) < 0 Fixed cost φ Variable costs c(q), c(0) = 0, c 0 (q) 0, c 00 (q) 0. Second stage, output per entrant is determined. Let q N be equilibrium output per firm, given N entrants (you pick model of competition). But assume (easy to check this is satisfied with Cournot and P 00 (Q) 0): Nq N > ˆN ˆq N, N> ˆN and lim N Nq N = M<

33 q N <qˆn,forn> ˆN. P (Nq N ) c 0 (q N ) > 0 for all N. First stage entry: N e,thenπ N e 0, andπ N e +1 < 0.

34 Social Planner Planner controls entry but not pricing given entry. Maximizes total surplus. So problem is max N W (N) = Z NqN 0 P (s)ds Nc(q N ) Nφ Ignore integer constraint, for now. The Planner s FONC is W 0 (N ) = P (Nq N ) N q N N + q N c(q N ) Nc 0 (q N ) q N N φ = [Pq N c φ]+n h P c 0i q N N = π N + N h P c 0i q N N = 0

35 Evaluate at N e,observethatπ N e = 0,soW 0 (N e ) < 0, (since P>c 0,and q N N < 0. Excessive entry. Intuition If impose the integer constraint then N e N 1.