1. Consider a one-sided search model. In this model, workers only have two states: unemployed (U) or employed (E), there

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1 Consider A One Sided Search Model In This Model Workers Only Have Two States Unemployed U Or Employed E There 1 (55.11 KiB) Viewed 19 times

1. Consider a one-sided search model. In this model, workers only have two states: unemployed (U) or employed (E), therefore U+E-1. Let V.(w) denote the value of being employed at wage w, and V, denote the value of an unemployed worker. Let s denote the separation rate, that is, s is the fraction of workers who will become randomly separated from their jobs every period. For V.(w), it is an increasing function of w, and the marginal value decreases as w increases. Obviously, the value of working will decrease if the separation rate s increases. Unemployed workers can claim a constant unemployment insurance of amount b. When unemployed, workers receive job offers at frequency p. That is, each period a fraction p of all the unemployed workers will receive job offers. Apparently, V, is increasing in band p. For an unemployed worker with job offer w, he/she decides whether to accept the offer or to remain unemployed. If V.(w) > V. worker accepts the job; if V.(w) <V, worker remains unemployed. (a) Illustrate Vand V.(w) on a graph with wage on the horizontal axis and V, and V (w) on the vertical axis. (b) Use the graph in part (a), find out the reservation wage w* so that if w >w*, worker takes the job, and if w <w*, worker remains unemployed. (c) During the pandemic, a lot of workers lost jobs because of economic shutdown. Which variable changed in the model? Illustrate the change in the graph in part (a). (d) Following the increasing unemployment numbers, the federal government became much more generous in distributing unemployment insurance benefits. What is the effect of this policy change on top of the effect in part (c)? Illustrate the change using the graph in part (e).