Consider homogeneous workers who search for jobs in a frictional labour market. The job offers arrive with probability = 0.8 in each period. Each job offer with a matching productivity is drawn from an exogenous probability density function, g() = /100 for [0, 10] and (20)/100 for [10, 20] There exists a minimum wage w in the market. A workers will only accept job offers if their productivity exceeds the minimum wage level. If rejecting a job offer, the worker will have to wait until the next period to receive a 1 (possible) new offer. If accepting a job, the wage of the job is determined by the following bargaining equation w = 0.5w 0.5 In every period, each current job is terminated with probability = 0.1. (a) Derive the unemployment rate without minimum wage w = 0 and with minimum wage w = 2.5. (b) Derive the probability density function for wage without (w = 0) and with minimum wage (w = 2.5). Calculate the average wages for the employed workers and for the labour force (include both employed and unemployed workers) in both cases