CHAPTER 5. DYNAMIC CONTRACTING of i>0. Assume that R(0)>C,R(0)>2,limR()<1,R(i)>0,R"(t)<0,v Both parties are risk neutral and the interest rate is zero. Ignore issues of ownership The first best maximizes total surplus Earg max(r(i)-i-C*)3), where x=0.1 If surplus is divided using symmetric Nash bargaining solution, invest nent is sub-optimal(Grout, 1984) (2)∈ arg max{(R(i) Contractual solutions If the type of widget produced can be specified in the contract, the first best can be achieved If the level of investment can be specified in the contract, the first best can be achieved The large, finite number of S. A widget of type is needed in state s, that is, a widget of type s produces a return of R(i) state s and nothing in other states. The cost of production is C* for every type and state. The cost of writing a complete contract with a large number of states would be very high. The first best might be achieved as follows: Ml specifies the type of widget she wants at date 1; if M2 supplies that type, she receives P1: if she fails to deliver, she receives Po.(Note the type of widget must be verifiable). To implement the first best, put po >0 and P1 >Po +C*. Since MI gets the full marginal returns, investment will be optimal Renegotiation causes problems with this setup. For example, suppose that M2 has the opportunity to make a take-it-or-leave-it counter offer. Then M2 gets the surplus and again we have the holdup problem In any case, when there is renegotiation, the outcome is independent of the contract2 CHAPTER 5. DYNAMIC CONTRACTING of i ≥ 0. Assume that R(0) > C∗ , R0 (0) > 2, lim i→∞ R0 (i) < 1, R0 (i) > 0, R00(i) < 0, ∀i. Both parties are risk neutral and the interest rate is zero. Ignore issues of ownership. The first best maximizes total surplus: (i ∗ , x∗ ) ∈ arg max {(R(i) − i − C∗ ) x} , where x = 0, 1. If surplus is divided using symmetric Nash bargaining solution, invest￾ment is sub-optimal (Grout, 1984). (ˆı, xˆ) ∈ arg max ½1 2 (R(i) − i − C∗ ) x ¾ . Contractual solutions: • If the type of widget produced can be specified in the contract, the first best can be achieved. • If the level of investment can be specified in the contract, the first best can be achieved. There is a large, finite number of states s = 1, ..., S. A widget of type s is needed in state s, that is, a widget of type s produces a return of R(i) in state s and nothing in other states. The cost of production is C∗ for every type and state. The cost of writing a complete contract with a large number of states would be very high. The first best might be achieved as follows: M1 specifies the type of widget she wants at date 1; if M2 supplies that type, she receives p1; if she fails to deliver, she receives p0. (Note the type of widget must be verifiable). To implement the first best, put p0 ≥ 0 and p1 ≥ p0 + C∗. Since M1 gets the full marginal returns, investment will be optimal. Renegotiation causes problems with this setup. For example, suppose that M2 has the opportunity to make a take-it-or-leave-it counter offer. Then M2 gets the surplus and again we have the holdup problem. In any case, when there is renegotiation, the outcome is independent of the contract