Unemployment Dynamics: Please answer parts A, B, C, D, & E accordingly.

Assume unemployment at date t + 1, Ut+1, is given by: Ut+1 = Ut Mt + St, (3) where Ut is unemployment at date )5, Mt are the number of unemployed who match with a job and S: are the number of employed people who separate from their job and enter unemployment at date 15. (A) (2 points) Interpret equation (3): Why does unemployment at date t+1 equal the expression 0n the right hand side? What if anything does the equation abstract from (i.e. leave out or ignore)? (B) (8 points) Assume a fraction a = 0.06 of the unemployed are matched each period: Mt = aUt. Assume also that a fraction d = 0.04 of the employed separate from their jobs each period: St = dEt. Assume that POP is the total working population (and everyone in this population either works or is unemployed), so that E + U: = POP = 1. Substitute these expressions into equation (3) and draw a plot with current unemployment U: on the horizontal axis and future unemployment Ut+1 on the vertical axis. Show the steady state level of unemployment in your plot, and derive an expression for the steady state level of unemployment . (C) (6 points) Find an equation for the equilibrium unemployment rate at the steady state. Then 00mpute the equilibrium unemployment and the equilibrium unemployment rate at the steady state. (D) (4 points) Now, suppose that as the economy evolvessay into more technical / intellectual prOperty producing industriesrms become less risky. In other words, imagine that rms go bankrupt less often and therefore people lose their job less often than they used to. At the same time, nothing changes for unemployed people looking for jobs. What happens to the equilibrium unemployment rate? Explain your reasoning. (E) (3 points) Now, suppose that a new online platform is developed allowing people looking for jobs to find it more easily. In other words, unemployed people are able to find jobs more often than they used to. At the same time, nothing changes for employed people: they have the same chance to lose their jobs. What happens to the equilibrium unemployment rate? Explain your reasoning