The Beveridge Curve (job openings rate vs. unemployment rate), seasonally adjusted Click and drag within the chart to zoom in on time periods Dec 2000 to Feb 2001 Job openings rate Mar 2001 to Nov 2001* 8.0 - Dec 2001 to Nov 2007 Dec 2007 to June 2009* - July 2009 to Feb 2020 Mar 2020 to Apr 2020* 7.0 - May 2020 to Aug 2022 6.0 5.0 4.0 3.0 2.0 1.0 4.0 6.0 8.0 10.0 12.0 14.0 Unemployment rate Note: * represents recession, as determined by the National Bureau of Economic Research Source: U.S. Bureau of Labor Statistics. In this problem, we will use the Search Model of Unemployment to analyze the post-Covid recovery in the United States, the observed movements in the Beveridge Curve, and the possi- ble effects of increased matching frictions. Your goal, at the end of this question, is to plot the Beveridge Curve for a simulated economy. a Assume the economy starts at b1, Z1, e1. Provide two graphs which determine equilibrium j and Q. Write two equations which determine the equilibrium unemployment and vacancy rates. Call these initial values j1, Q1, uj and v1. b Suppose productivity falls from z1 to Z2 with z1 > Z2 (assuming the other parameters, b1, e1 do not change). On your previous graphs, demonstrate the effect of this change on equilibrium j and Q (call them j2 and Q2). Determine how u2 and v2 are related to uj and v1 (and explain how you know this)c Starting from b1, Z2, e1, suppose the matching efficiency increases to e2 > e1. Using two new graphs, show how j and Q change. (Your graphs should include j2, @2 and the newvalues jg, Q3. Determine how U3 and 03 are related to rig and '02 (and explain how you know this). (1 Suppose now the economy starts to recover so that productivity rises from 2:2 to 2:3 with 22