Exercise on the natural rate of unemployment Consider the bathtub model of unemployment. Let E, denote the employment level and U, the unemployment level in period t. Also, let L denote the (constant) labour force. Then, the model consists of the following two equations: AUt+1 = SEt - fut Et + Ut = [ where f denotes the probability with which unemployed people find jobs in a certain period, and s denotes the probability with which employed people lose their jobs in a certain period. In other words, s is the separation rate and f is the job finding rate. i) Consider a steady state situation, where neither employment nor unemployment change over time. Describe the unemployment rate in the steady state, as a function of s and f. Now suppose that the steady-state unemployment is described by the formula you provided in part i), but f, s are not constant. Here is how these variables are determined: The job finding rate is given by f(e) = e where e takes values in [0,1] and denotes the worker's effort. This effort is, in turn, given by e(b) = 0.5 - 0.05b, where b denotes the level of unemployment benefits. Assume that b takes values in [0, 10]. The job separation rate is given by s(c) = 0.1 - 0.02c, where c is the fee that a firm has to pay in order to terminate a work relationship (also known as a firing cost). Assume that c takes values in [0,5]. ii) What is the economic intuition behind the determination of the job finding rate and the job separation rate above? ii) Write the steady-state unemployment rate as a function of b, c. Does steady-state unemployment depend positively or negatively on b and c? Discuss. iv) If you were the policymaker, and your goal was to minimise unemployment, how would you set the policy variables b, c? v) If c = 2.5, how should the government set b in order to achieve unemployment equal to 10%? Notice that, by doing so, you have expressed the unemployment rate as a function of two policy variables (that is, two variables that are perfectly controlled by the government)