The Reservation Wage under CARA and Limited Borrowing

Abstract

A continuous-time sequential job search model with savings and CARA preferences is solved analytically without resorting to unlimited borrowing and real-valued consumption. I isolate the effects of limited borrowing and nonnegative consumption as well as risk-aversion on the reservation wage by using a system of ordinary differential equations.

• Item Type: Paper (Discussion Paper)
• Keywords: labor income risk, wealth-dependent reservation wage, borrowing limit
• Subjects: Economics; Economics > Discussion Papers in Economics; Economics > Discussion Papers in Economics > Macro-Economics; Economics > Discussion Papers in Economics > Labor; Economics > Discussion Papers in Economics > Mathematical Methods
• Dewey Classification: 300 Social sciences; 300 Social sciences > 330 Wirtschaft
• Journal of Economic Literature classification: C61, E21, D91, J64
• Language: English

References

Acemoglu, D., and R. Shimer (1999): "Efficient Unemployment Insurance," Journal of Political Economy, 107(5), 893-928.

Merton, R. C. (1969): "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," Review of Economics and Statistics, 51(3), 247-257.

Merton, R. C. (1971): "Optimum Consumption and Portfolio Rules in a Continuous-Time Model," Journal of Eco- nomic Theory, 3(4), 373-413.

Oksendal, B. (2003): Stochastic Dierential Equations: An Introduction with Applications. Springer.

Sennewald, K. (2007a): "Controlled Stochastic Dierential Equations under Poisson Uncertainty and with Unbounded Utility," Journal of Economic Dynamics and Control, 31(4), 1106-1131.

Sennewald, K. 2007b): Stochastic Control, Optimal Saving, and Job Search in Continuous Time. Dissertation, TU Dresden, Germany.

Sennewald, K., and K. Waelde (2006): "It^o's Lemma' and the Bellman Equation for Poisson Processes: An Applied View," Journal of Economics, 89(1), 1-36.

Shimer, R., and I. Werning (2007): "Reservation Wages and Unemployment Insurance," The Quarterly Journal of Economics, 122(3), 1145-1185.

Shimer, R., and I. Werning (2008): "Liquidity and Insurance for the Unemployed," American Economic Review, 98(5), 1922-1942.

Waelde, K. (2008): Applied Intertemporal Optimization. www.waelde.com/aio.