Problem set 2 By Thomas and Lars PS: Choose the environment, choose many pages per sheet. Problem set 2 Exercise 11/29 Laget av: Thomas Aanensen og Lars Solberg17/

1. The putting out system Problem set 2 Exercise 12/29 Laget av: Thomas Aanensen og Lars Solberg17/

(a) Show that in equilibrium: e = q = ½ Problem set 2 Exercise 13/29 Laget av: Thomas Aanensen og Lars Solberg17/

Because of the decision making structure the putter-out maximizes surplus given the home worker’s optimal response function. Problem set 2 Exercise 14/29 Laget av: Thomas Aanensen og Lars Solberg17/

Home worker’s maximation problem Problem set 2 Exercise 15/29 Laget av: Thomas Aanensen og Lars Solberg17/

The first order condition This is also the optimal response function Problem set 2 Exercise 16/29 Laget av: Thomas Aanensen og Lars Solberg17/

The putter out’s maximation problem Problem set 2 Exercise 17/29 Laget av: Thomas Aanensen og Lars Solberg17/

First order condition Problem set 2 Exercise 18/29 Laget av: Thomas Aanensen og Lars Solberg17/

(b) Draw iso-profit and iso-utility curves, illustrate the equilibrium. Problem set 2 Exercise 19/29 Laget av: Thomas Aanensen og Lars Solberg17/

Problem set 2 Exercise 110/29 Laget av: Thomas Aanensen og Lars Solberg17/

(c) Explain the intuition behind U-shaped iso-utility curves. Problem set 2 Exercise 111/29 Laget av: Thomas Aanensen og Lars Solberg17/

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. Problem set 2 Exercise 112/29 Laget av: Thomas Aanensen og Lars Solberg17/

(d) For which values of q is a pareto- improvement possible, if e is set to 1? Problem set 2 Exercise 113/29 Laget av: Thomas Aanensen og Lars Solberg17/

Problem set 2 Exercise 114/29 Laget av: Thomas Aanensen og Lars Solberg17/

Problem set 2 Exercise 115/29 Laget av: Thomas Aanensen og Lars Solberg17/

When e is set to 1 we have that: Problem set 2 Exercise 116/29 Laget av: Thomas Aanensen og Lars Solberg17/

Pareto improvements are possible when: Problem set 2 Exercise 117/29 Laget av: Thomas Aanensen og Lars Solberg17/

e) Why isn’t such (e,q)-combinations incentive compatible? Problem set 2 Exercise 118/29 Laget av: Thomas Aanensen og Lars Solberg17/

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. Problem set 2 Exercise 119/29 Laget av: Thomas Aanensen og Lars Solberg17/

If we had changed the nature of the game, by for example cooperation, then we could have achieved pareto improvements which were incentive compatible. Problem set 2 Exercise 120/29 Laget av: Thomas Aanensen og Lars Solberg17/

2. Contingent renewal The probability for contingent renewal: p = A + a*e, Problem set 2 Exercise 221/29 Laget av: Thomas Aanensen og Lars Solberg17/

(a) Derive the optimal effort of the worker as a function of w. (b) Show that; e = aR / (1+r-p), where R = r (u (w,e) / r – Vu) is the unemployment rent. Problem set 2 Exercise 222/29 Laget av: Thomas Aanensen og Lars Solberg17/

Problem set 2 Exercise 223/29 Laget av: Thomas Aanensen og Lars Solberg17/

Problem set 2 Exercise 224/29 Laget av: Thomas Aanensen og Lars Solberg17/

Problem set 2 Exercise 225/29 Laget av: Thomas Aanensen og Lars Solberg17/

where Problem set 2 Exercise 226/29 Laget av: Thomas Aanensen og Lars Solberg17/

(c) Show that de /dw = a / (1+r-p) Problem set 2 Exercise 227/29 Laget av: Thomas Aanensen og Lars Solberg17/

d) Compare the equilibrium with the equilibrium in the putting-out system. Problem set 2 Exercise 228/29 Laget av: Thomas Aanensen og Lars Solberg17/

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. Problem set 2 Exercise 229/29 Laget av: Thomas Aanensen og Lars Solberg17/