EC537 Microeconomic Theory for Research Students, Part II: Lecture 5 - PowerPoint PPT Presentation

EC537 Microeconomic Theory for Research Students, Part II: Lecture 5 Leonardo Felli CLM.G.4 6 December 2011

Property Rights Theory The presence of inefficiencies due to the incompleteness of contracts naturally leads to the question: Do there exist institutions that ameliorates the inefficiencies that are generated by contractual incompleteness? The answer we are going to give is a positive one, in particular one of these institutions is the building block of modern economy: ownership of physical assets. The analysis of this institutions will also help us to answer a key question for economic analysis: What is a firm? What determines the boundaries of a firm? Leonardo Felli (LSE) EC537 Microeconomic Theory for Research Students, Part II: Lecture 5 6 December 2011 2 / 50

Property Rights Theory (2) We will see that while ownership rights are irrelevant when the Coase Theorem holds this is no longer the case when frictions prevent the Coase Theorem from holding at least at an ex-ante stage. The theory we present is known as property rights theory (Grossman and Hart 1986, Hart and Moore 1990) . Ingredients: incomplete contracts , and hence the presence of a potential hold-up problem, relationship specific investments, the lack of a well-functioning market for the good that embodies the parties’ investments. Leonardo Felli (LSE) EC537 Microeconomic Theory for Research Students, Part II: Lecture 5 6 December 2011 3 / 50

Specific Investments Question: why specificity plays a critical role. To understand this consider the following simple hold-up problem. A buyer and a seller engage in trade. At an ex-ante stage the seller can undertake an ex-ante investment e that enhances the quality of the unit of good to the buyer at a cost e 2 2 The value to the buyer is then v e Assume for simplicity that the delivery cost for the seller c = 0. Leonardo Felli (LSE) EC537 Microeconomic Theory for Research Students, Part II: Lecture 5 6 December 2011 4 / 50

Incomplete Contracts We assume an extreme incomplete contract framework: no contract will be drawn before the seller chooses the investment. Timing: The seller undertakes the ex-ante investment e ; A contract is agreed upon between the buyer and the seller to trade at a given price p ; Trade occurs. Leonardo Felli (LSE) EC537 Microeconomic Theory for Research Students, Part II: Lecture 5 6 December 2011 5 / 50

Efficient Outcome Ex-post efficiency requires that trade occurs as long as e ≥ 0 from v e ≥ 0. Ex-ante efficiency requires that e ∗ is the solution to the following problem: v e − e 2 e ∗ = v max 2 , or e Assume first that at the contracting stage the buyer makes a take-it-or-leave-it offer to the seller. We solve backward for the SPE of this simple game. Leonardo Felli (LSE) EC537 Microeconomic Theory for Research Students, Part II: Lecture 5 6 December 2011 6 / 50

Underinvestment Let e be given, at the contracting stage the gains from trade are: v e . The seller will accept the offer if and only if: p ≥ 0 The buyer’s offer is then obviously ¯ p = 0 The seller’s ex-ante investment is then such that: p − e 2 2 = − e 2 max ¯ 2 e In other words, the hold-up problem generated by incomplete contracts implies: e = 0 < e ∗ = v ¯ . Leonardo Felli (LSE) EC537 Microeconomic Theory for Research Students, Part II: Lecture 5 6 December 2011 7 / 50

Underinvestment (2) In general assume that the parties’ bargaining power is such that the seller gets λ of the gain from trade while the buyer gets (1 − λ ) of the gains from trade: λ ( v e ) , (1 − λ )( v e ) The seller’s investment problem is then: λ ( v e ) − e 2 max 2 e In other words we obtain that (hold-up problem): e ∗∗ = λ v ≤ e ∗ = v In particular, the equality will hold only if the seller has full bargaining power . Leonardo Felli (LSE) EC537 Microeconomic Theory for Research Students, Part II: Lecture 5 6 December 2011 8 / 50

Market for the Good Assume now that instead of selling to a unique buyer in a situation of bilateral monopolism, there is a market for the good. In particular, assume that there are two potential buyers for the good. Both buyers value the good v e and they Bertrand compete for the good. Let b i be the bid of buyer i ∈ { 1 , 2 } for the good. Leonardo Felli (LSE) EC537 Microeconomic Theory for Research Students, Part II: Lecture 5 6 December 2011 9 / 50

Bertrand Competition Extensive form of the Bertrand competition game: the good is allocated to the buyer who makes the highest bid, if the bids are equal buyer 1 gets the good; the buyer who gets the good pays his bid to the seller. Buyer i ’s expected payoff is then:  v e − b i if b i > b − i and if b i = b − i   and i gets the good  π i = 0 if b i < b − i and if b i = b − i   and i does not get the good  Leonardo Felli (LSE) EC537 Microeconomic Theory for Research Students, Part II: Lecture 5 6 December 2011 10 / 50

Bertrand Competition (2) Buyer i ’s best reply is then to choose:  v e > b i > b − i if b − i < v e and when b i = b − i   then i does not get the good    b i = b − i if b − i ≤ v e and when b i = b − i then i gets the good     b i < b − i if b − i ≥ v e  All Nash equilibria of this Bertrand competition game are such that: b i = b − i = v e Leonardo Felli (LSE) EC537 Microeconomic Theory for Research Students, Part II: Lecture 5 6 December 2011 11 / 50

General Investment Then the unique equilibrium price paid to the seller is: ˜ p = v e The seller’s ex-ante investment problem is then: p − e 2 2 = v e − e 2 max ˜ 2 e The first order conditions imply: e = v = e ∗ ˜ In other words, even in the presence of incomplete contracts the existence of a market for the commodity implies that the investment is efficient: ex-ante efficiency arises . Leonardo Felli (LSE) EC537 Microeconomic Theory for Research Students, Part II: Lecture 5 6 December 2011 12 / 50

Back to Specific Investments Assume now that the seller’s investment is specific to the buyer. The investment e has different returns depending on whether the buyer is 1 or 2: v ∈ { v 1 , v 2 } , v 1 > v 2 If buyer 1 buys the good then the returns are v 1 e while if buyer 2 buys the good the returns are v 2 e . Assume the same Bertrand competition game. Leonardo Felli (LSE) EC537 Microeconomic Theory for Research Students, Part II: Lecture 5 6 December 2011 13 / 50

Bertrand Competition Again Buyer i ’s expected payoff is then:  v i e − b i if b i > b − i and if b i = b − i   and i gets the good  π i = 0 if b i < b − i and if b i = b − i   and i does not get the good  Buyer i ’s best reply is then to choose:  v e > b i > b − i if b − i < v i e and when b i = b − i   then i does not get the good    b i = b − i if b − i ≤ v i e and when b i = b − i then i gets the good     b i < b − i if b − i ≥ v i e  Leonardo Felli (LSE) EC537 Microeconomic Theory for Research Students, Part II: Lecture 5 6 December 2011 14 / 50

Equilibrium of Bertrand Competition Then the unique (trembling-hand-perfect, cautious) Nash equilibria of this Bertrand competition game is such that: the buyers’ equilibrium bids are such that: b 1 = b 2 = v 2 e buyer 1 gets the good. Notice that the last condition implies ex-post efficiency . Leonardo Felli (LSE) EC537 Microeconomic Theory for Research Students, Part II: Lecture 5 6 December 2011 15 / 50

Underinvestment with a Market Notice that in this case the equilibrium price paid to the seller is such that: ˆ p = v 2 e The seller’s investment problem is then: p − e 2 2 = v 2 e − e 2 max ˆ 2 e The first order conditions of this problem imply: e = v 2 < e ∗ = v 1 ˆ In other words, specificity of the ex-ante investment implies a hold-up problem and hence ex-ante inefficiencies even in the presence of a market for the good . Leonardo Felli (LSE) EC537 Microeconomic Theory for Research Students, Part II: Lecture 5 6 December 2011 16 / 50

Competition Objective: to analyze the role that market competition for a match has in determining the parties’ outside option in the bargaining stage. Question: can this market competition reduce the inefficiency of the hold-up problem? Answer: yes but possibly at the cost of a related inefficiency. Coordination failure: a situation in which a group of agents can realise a mutual gain only by a change in behaviour by each member of the group. Ingredients: complementarities among parties’ investments and incomplete contracts. Leonardo Felli (LSE) EC537 Microeconomic Theory for Research Students, Part II: Lecture 5 6 December 2011 17 / 50

Ingredients Observation: given the specific nature of investments where is the competition coming from? Competition: Bertrand competition among heterogeneous agents. We assume that workers bid for firms. Specificity: we assume a discrete number of heterogeneous workers that matches with a discrete number of heterogeneous firms. Complementarity: Both workers and firms undertake complementary investments. Contracts: we take contracts to be incomplete, they are bilateral agreements to trade at a constant price (wage). Leonardo Felli (LSE) EC537 Microeconomic Theory for Research Students, Part II: Lecture 5 6 December 2011 18 / 50