3. UNEMPLOYMENT AND THE BUSINESS CYCLE (25 POINTS) Take a simple search model as the one we saw in class. Workers can he either employed or unemployed. Let the total number of employed workers be E1 and the number of unemployed, Ut. Their sum, the labor force, is constant over time. E; + U; = L. Each period unemployed workers nd jobs at rate Ag, and employed workers lose their jobs at rate (it. For now assume that 5 and A are constant. The total number of unemployed evolves according to the equation Ut+1 = [I A) Ut + 513;. Finally, output in this economy follows Okun's law: 1/; = le\"(\"i\"nl, where A, o > 0? Kg denotes real GDP, at = Hf and an is the natural rate of unemployment.3 (a) Show that the difference equation for this economy that relates the unemployment rate at consecutive periods t and t + 1 equals \"1+1 = (1 Adlntld (h) {3% 1%) Find the steady state unemployment rate, um and steady state output. (c) {##) Analyze the effects of the following shocks in this economy on u: and 14,. Use the graphs nt+1vs \"at, at vs t and Yt vs t on your answer. (a) An expansion shock: A T and A T permanently. (b) The government imposes a ring tax: 5 J, and A J, permanently by the same proportion.4 (d) (##l Explain the mechanism behind a positive technology shock, A T, increases A: and why a ring tax decreases both (i and A. Note: these are outside from this model