twexamplefigures - ECO 387: Dynamic Contracts, Spring 2007....

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Unformatted text preview: ECO 387: Dynamic Contracts, Spring 2007. Department of Economics, University of Texas. Instructor: Dean Corbae Thomas Worrall Two State Example - Figures In Figures 1 and 2 we can see the value function that solves the problem and the constant K . It is verified that the guessed form is correct. The difference between the numerical solution and 1 1- log(- V- A ) is constant when A = V aut (1- ) , the value derived using the envelope condition.-1000-900-800-700-600-500-400-300-200-100 30 35 40 45 50 55 60 65 70 Value Function P(V) Initial Value (V) P(V) log(-V-A)/(1- ) Figure 1: Value Function 1- 1 0 0 0- 9 0 0- 8 0 0- 7 0 0- 6 0 0- 5 0 0- 4 0 0- 3 0 0- 2 0 0- 1 0 0- 0 .9- 0 .8 8- 0 .8 6- 0 .8 4- 0 .8 2- 0 .8- 0 .7 8- 0 .7 6- 0 .7 4- 0 .7 2 V a lu e P (V )- [1 /(1 - )]lo g (- V - A ) In itia l V a lu e (V ) Figure 2: K 1- = P ( V )- 1 1- log(- V- A ) The following pictures display the optimal promised values....
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twexamplefigures - ECO 387: Dynamic Contracts, Spring 2007....

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