Econ 312: Unemployment & Reservation Wages - Lecture 23 by Noah Williams, UW-Madison - Pro, Study notes of Economics

Download Econ 312: Unemployment & Reservation Wages - Lecture 23 by Noah Williams, UW-Madison - Pro and more Study notes Economics in PDF only on Docsity! Lecture 23 More on Unemployment Noah Williams University of Wisconsin - Madison Economics 312 Spring 2009 Williams Economics 312 An Employed Worker An employed worker earns and consumes w. Next period, she is unemployed with probability s, otherwise she is still employed. This can be expressed recursively as Ve(w) = U (w) + β [sVu + (1− s)Ve(w)] Solving this for Ve(w) gives Ve(w) = U (w) + βsVu 1− β(1− s) So Ve(w) is increasing, assuming U is. Williams Economics 312 The recursive equation for employed workers implies Ve(wi) = U (wi) + βsVu 1− β(1− s) ⇒ Ve(wi)−Vu = U (wi)− (1− β)Vu 1− β(1− s) A worker accepts a job if U (wi) ≥ (1− β)Vu . The reservation wage satisfies Ve(w∗) = Vu or equivalently U (w∗) = (1− β)Vu Combine the earlier equations to get the reservation wage: (1− β)Vu = U (b) + βp N∑ i=n∗ πi ( Ve(wi)−Vu ) Ve(wi)−Vu = U (wi)− (1− β)Vu 1− β(1− s) Williams Economics 312 Determination of Reservation Wage Williams Economics 312 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 16-12 Figure 16.8 The Reservation Wage Williams Economics 312 Unemployment Rate Determination of the unemployment rate: Unemployed workers find jobs with probability p ∑N i=n∗ πi = pH (w∗) in book notation. Employed workers lose jobs with probability s. A fraction u of the workers are unemployed Job creation and destruction must balance. upH (w∗) = s(1− u) Williams Economics 312 Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 16-20 Figure 16.13 The Determination of the Reservation Wage and the Unemployment Rate in the Search Model Williams Economics 312 Changes in the Unemployment Rate What raises the unemployment rate? Anything raising reservation wage: higher unemployment benefits b, best jobs pay very high wages, workers are more patient β. Jobs are harder to find p (despite lower reservation wage). Separations are more s frequent (despite lower reserv. wage). Williams Economics 312 Cyclical and Cross-Sectional Unemployment If the job finding rate falls: Workers become less choosy: the reservation wage falls. Direct effect: fewer unemployed workers find jobs. Direct effect dominates, so unemployment rate rises and unemployment spells get longer. This seems to characterize the recent recessions. If unemployment benefits increase: Workers become more choosy: the reservation wage increases. No direct effect on separations or job finding rates. Unemployment rate rises and spells get longer. This seems to characterize differences between US and Europe. Williams Economics 312 NEW TOPIC: MONETARY POLICY Conduct of monetary policy may have dramatic implications for economic outcomes. Main example in US: The “Great Inflation” of the 1970s. Sustained double digit annual inflation rates, accompanied by slow economic growth and recession. Problems on much larger scales internationally. Hyperinflations in Latin America in 1980s had annual inflation rates in hundreds to thousands of percents. Bolivia: 1281% (1984), 11,750% (1985), 276% (1986). Argentina and Brazil in hundreds of percents. Even within US, much debate over how policy should be conducted. Williams Economics 312 Argentina: Inflation and Real Money 1970 1975 1980 1985 1990 1995 2000 2005 −1 0 1 2 Lo g va lu e of m on th ly g ro ss in fla tio n ra te 4 5 6 7 Lo g va lu e of r ea l ( ba se − m on ey ) ba la nc es Inflation Real balances Williams Economics 312 Laffer Curve Substituting back money demand: S = iL(r̄ + i, Ȳ ) How does seignorage revenue depend on inflation rate? Si = L(r̄ + i, Ȳ ) + iLR(r̄ + i, Ȳ ) L > 0 but LR < 0. For small i first term dominates, and Si > 0. For large i, Si < 0. Hence get a Laffer curve Cagan (1956) studied hyperinflations, used a particular functional form: log MP = a − bR + logY hence Si = (1− bi) exp(−bi). Maximal level S∗. Williams Economics 312 Abel/Bernanke, Macroeconomics, © 2001 Addison Wesley Longman, Inc. All rights reserved Figure 15.07a The determination of real seignorage revenue Williams Economics 312 Abel/Bernanke, Macroeconomics, © 2001 Addison Wesley Longman, Inc. All rights reserved Figure 15.07b The determination of real seignorage revenue Williams Economics 312 Seignorage Revenue: Argentina 1970 1975 1980 1985 1990 1995 2000 2005 −0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 Seigniorage: ratio of Diff money to nominal gdp Williams Economics 312 Seignorage Revenue: Brazil 1975 1980 1985 1990 1995 2000 2005 −0.01 0 0.01 0.02 0.03 0.04 0.05 Seigniorage: ratio of Diff money to nominal gdp Williams Economics 312 Seignorage and Hyperinflation If seignorage revenue maximized at hundreds of percents (or lower), why have we seen even higher inflation rates? Cagan’s answer: gradual adjustment of expected inflation and money holdings. Let desired real money holdings be m∗ = B exp(−bi). Suppose actual real money holdings m adjusts toward desired: ṁ m = β [logm ∗(t)− logm(t)] = β [logB − bi(t)− logm(t)] Now have i = g − ṁm = S/m − ṁ m substitute in and solve for ṁ m : ṁ m = β 1− bβ [ logB − b S(t)m(t) − logm(t) ] Williams Economics 312