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Date Created: 10/03/15
EC340 Labor Economics Woods College of Advancing Studies Boston College 412 A Derivation for Reservation Wage and Labor Market Participation Professor Ware A Reservation Wage Suppose a household has N gt 0 dollars of NonEarn Income per day D A and reserves 8 hours for leisure Here the household incurs Fixed Work Costs FWC that amount to D F per day as soon as it chooses to participate in the labor market and offer hours for market work H 16 I gt 0 at an hourly market wage w1 or wR Net Income Yn u118 Indifference curves uo uYnL 10 u u Yn L 18 Nonearn N A B C D Work Constraint A B H G K wl Work Constraint A B H G M wR Time 8 Reserve H I Yn NonEarnN FWC w1 16 1 or Yn NonEarnN FWC wR 16 1 l WR gt W1 l l DNonearn N l l l l l FNet NonEarn N FWC l l 7 l l l l l l l l l l l l l l l 0 1 2 3 4 5 6 397 8 9amp10111213141516aLeisure 16151413121110 9 8 756 5 4 3 2 1 OeHoursOffered He l l K 1 l l l Eur l FWC l G NonEarnFWC H B The smallest hourly Wage Rate w1 or wR e g in the picture above that will cause this household to choose to participate in the labor market and offer hours of work the household s Reservation Wage can be determined by analysis I39 Suppose the hourly wage rate is w1 and xed work costs are D F dollars per day Then the household s TWO IncomeLeisure Constraints are a A B E D at I 16 for H 0 hours offered to work and b A B H G K at I S 16 for H gt 0 hours offered to work Given these TWO constraints and wage rate wl consumption bundle El a Corner Solution is a utility maximizing choice on indifference curve u1 18 Clearl preferred to working at on u0 10 Total utility is u1L uN24 18 At bundle a M hours are offered to labor market activities H 16 I 16 16 0 and the household i3 n0t a labor market participant Suppose the hourly market wage rate rises to wR per hour Now the household s TWO incomeleisure constraints are a A B E D at L16 for H0 hours offered to work and b A B H G M at I S 16 for H gt 0 hours offered to work As opportunisticall illustrated the household is indi erent between utility maximizing consumption bundles at and on indifference curve u1 Total utility is u1L u1N24 18 for the bundle at E the same as u1 ENE uN FWC wR 16 933 9338 18 for the bundle at The household E a labor market participant at consumption bundle offering H 16 E 16 9 33 6 6397 hours of work at a wage rate of wR per hour Ceteris paribus the hourly wage rate hours offered combination wR 6 6397 is one coordinate point on this household s Supply Schedule of Labor Services The household i3 n0t a labor market participant at consumption bundle Ceterz39s paribus the hourly wage rate wR is this household s Reservation Wage the smallest hourly wage rate at which this household would be inalz erent between some labor market participation at and no labor market participation at El Other things the same a wage rate greater than wR increases the likelihood of labor market participation a wage rate smaller than wR e g W1 decreases the likelihood Notice that changes in Variable Work Costs such as in income and payroll tax would affect labor market participation in the same manner as changes in the gross hourly wage rate illustrated above Page 45 Edited 30Sep83 Printed 13Febo7 EC340 Handout d 412
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