Problem set 2 Exercise 1 129 Problem set

Problem set 2 Exercise 1 1/29 Problem set 2 By Thomas and Lars PS: Choose the environment, choose many pages per sheet. Laget av: Thomas Aanensen og Lars Solberg 17/09 -2007

Problem set 2 Exercise 1 2/29 1. The putting out system Laget av: Thomas Aanensen og Lars Solberg 17/09 -2007

Problem set 2 Exercise 1 3/29 (a) Show that in equilibrium: e = q = ½ Laget av: Thomas Aanensen og Lars Solberg 17/09 -2007

Problem set 2 Exercise 1 4/29 Because of the decision making structure the putter-out maximizes surplus given the home worker’s optimal response function. Laget av: Thomas Aanensen og Lars Solberg 17/09 -2007

Problem set 2 Exercise 1 5/29 Home worker’s maximation problem Laget av: Thomas Aanensen og Lars Solberg 17/09 -2007

Problem set 2 Exercise 1 6/29 The first order condition • This is also the optimal response function Laget av: Thomas Aanensen og Lars Solberg 17/09 -2007

Problem set 2 Exercise 1 7/29 The putter out’s maximation problem Laget av: Thomas Aanensen og Lars Solberg 17/09 -2007

Problem set 2 Exercise 1 8/29 First order condition Laget av: Thomas Aanensen og Lars Solberg 17/09 -2007

Problem set 2 Exercise 1 9/29 (b) Draw iso-profit and iso-utility curves, illustrate the equilibrium. Laget av: Thomas Aanensen og Lars Solberg 17/09 -2007

Problem set 2 Exercise 1 10/29 Laget av: Thomas Aanensen og Lars Solberg 17/09 -2007

Problem set 2 Exercise 1 11/29 (c) Explain the intuition behind U-shaped iso-utility curves. Laget av: Thomas Aanensen og Lars Solberg 17/09 -2007

Problem set 2 Exercise 1 12/29 • If income and effort are separated in the utility function, then we would have normal shaped iso-utility curves with prefered direction to the north-west. • But when the home worker increases his effort marginally, he effects his income as well. Thus, we do not have a single negative effect on his utility through this increase in effort, but also a positive effect through the income increase. Laget av: Thomas Aanensen og Lars Solberg 17/09 -2007

Problem set 2 Exercise 1 13/29 (d) For which values of q is a paretoimprovement possible, if e is set to 1? Laget av: Thomas Aanensen og Lars Solberg 17/09 -2007

Problem set 2 Exercise 1 14/29 Laget av: Thomas Aanensen og Lars Solberg 17/09 -2007

Problem set 2 Exercise 1 15/29 Laget av: Thomas Aanensen og Lars Solberg 17/09 -2007

Problem set 2 Exercise 1 16/29 When e is set to 1 we have that: Laget av: Thomas Aanensen og Lars Solberg 17/09 -2007

Problem set 2 Exercise 1 17/29 Pareto improvements are possible when: Laget av: Thomas Aanensen og Lars Solberg 17/09 -2007

Problem set 2 Exercise 1 18/29 e) Why isn’t such (e, q)-combinations incentive compatible? Laget av: Thomas Aanensen og Lars Solberg 17/09 -2007

Problem set 2 Exercise 1 19/29 The nature of the game makes any other values impossible. • We assume complete and perfect information in this one-shot game, given standard rationality assumptions. • The home worker maximizes his utility, and then the putter out maximizes his surplus given the worker’s optimal response. Thus, none of the players have an incentive to change his optimal strategy. Laget av: Thomas Aanensen og Lars Solberg 17/09 -2007

Problem set 2 Exercise 1 20/29 • If we had changed the nature of the game, by for example cooperation, then we could have achieved pareto improvements which were incentive compatible. Laget av: Thomas Aanensen og Lars Solberg 17/09 -2007

Problem set 2 Exercise 2 21/29 2. Contingent renewal The probability for contingent renewal: p = A + a*e, Laget av: Thomas Aanensen og Lars Solberg 17/09 -2007

Problem set 2 Exercise 2 22/29 (a) Derive the optimal effort of the worker as a function of w. (b) Show that; e = a. R / (1+r-p), where R = r (u (w, e) / r – Vu) is the unemployment rent. Laget av: Thomas Aanensen og Lars Solberg 17/09 -2007

Problem set 2 Exercise 2 23/29 Laget av: Thomas Aanensen og Lars Solberg 17/09 -2007

Problem set 2 Exercise 2 24/29 Laget av: Thomas Aanensen og Lars Solberg 17/09 -2007

Problem set 2 Exercise 2 25/29 Laget av: Thomas Aanensen og Lars Solberg 17/09 -2007

Problem set 2 Exercise 2 26/29 where Laget av: Thomas Aanensen og Lars Solberg 17/09 -2007

Problem set 2 Exercise 2 27/29 (c) Show that de /dw = a / (1+r-p) Laget av: Thomas Aanensen og Lars Solberg 17/09 -2007

Problem set 2 Exercise 2 28/29 d) Compare the equilibrium with the equilibrium in the putting-out system. Laget av: Thomas Aanensen og Lars Solberg 17/09 -2007

Problem set 2 Exercise 2 29/29 Comparing the two cases • The overall structure in these two cases has much in common, and that is why we have these similarities. • The employer/putter out can not monitor the worker completely, and in simular cases with monitoring you achive pareto optimality. • The worker decides his own effort in both cases, and he is in a way superior when choosing his strategy. If the employer/putter out could have dictated him to choose a higher effort, we would have achived a pareto optimal situation. Laget av: Thomas Aanensen og Lars Solberg 17/09 -2007