Unemployment There is a continuum of workers with identical probabilities λ of being fired each period when they are employed. With probability µ ∈ (0, 1), each unemployed worker receives one offer to work at wage w drawn from the cumulative distribution function F(w). If he accepts the offer, the worker receives the offered wage each period until he is fired. With probability 1 − µ, an unemployed worker receives no offer this employed and zero otherwise. There is no unemployment compensation. Each worker regards U as fixed and constant over time in making his decisions. a. For fixed U, write the Bellman equation for the worker. Argue that his optimal policy has the reservation wage property. b. Given the typical worker’s policy (i.e., his reservation wage), display a difference equation for the unemployment rate. Show that a stationary unemployment rate must satisfy c. Define a stationary equilibrium. d. Describe how to compute a stationary equilibrium. You don’t actually have to compute it.
Unemployment There is a continuum of workers with identical probabilities λ of being fired each period when they are employed. With probability µ ∈ (0, 1), each unemployed worker receives one offer to work at wage w drawn from the cumulative distribution function F(w). If he accepts the offer, the worker receives the offered wage each period until he is fired. With probability 1 − µ, an unemployed worker receives no offer this employed and zero otherwise. There is no unemployment compensation. Each worker regards U as fixed and constant over time in making his decisions. a. For fixed U, write the Bellman equation for the worker. Argue that his optimal policy has the reservation wage property. b. Given the typical worker’s policy (i.e., his reservation wage), display a difference equation for the unemployment rate. Show that a stationary unemployment rate must satisfy c. Define a stationary equilibrium. d. Describe how to compute a stationary equilibrium. You don’t actually have to compute it.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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employed and zero otherwise. There is no unemployment compensation. Each worker regards U as fixed and constant over time in making his decisions.
a. For fixed U, write the Bellman equation for the worker. Argue that his optimal policy has the reservation wage property.
b. Given the typical worker’s policy (i.e., his reservation wage), display a difference equation for the unemployment rate. Show that a stationary unemployment rate must satisfy
c. Define a stationary equilibrium.
d. Describe how to compute a stationary equilibrium. You don’t actually have to compute it.
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