Personnel Economics & Executive Compensation
Lazear Deferred Seniority Wage & Performance Bond Formula
Calculate Edward Lazear’s (1979) incentive-compatible senior wage w_2* = w_alt + s_shirk, junior underpayment performance bond VMP_1 - w_1*, and mandatory buyout/retirement surplus gap.
Explain steep seniority pay profiles and mandatory retirement without falling productivity!
Why do law partnerships, airlines, and corporations pay junior hires LESS than their marginal product (w_1 < VMP_1), pay senior employees MORE than their marginal product (w_2 > VMP_2), and historically enforce mandatory retirement or pension buyouts at career end? Edward Lazear (1979) solved all three puzzles simultaneously! When a senior worker in Period 2 can capture Shirking_Temptation s_shirk before dismissal into Outside/Leisure_Fallback w_alt,2, spot productivity pay w_2 = VMP_2 fails whenever VMP_2 - w_alt,2 < s_shirk! To deter shirking, the firm must set Senior Wage w_2* = MAX(VMP_2, w_alt,2 + s_shirk), financed in competitive zero-profit present value (at discount rate r) by Junior Wage w_1* = VMP_1 - (w_2* - VMP_2) / (1 + r)!
Verify on Discount_Rate r = 0.10 (10.0%, B2), Junior_Productivity VMP_1 = 80.00 ($k, B3), Senior_Productivity VMP_2 = 88.00 ($k, B4), Senior_Shirking_Gain s_shirk = 22.00 ($k, B5), and Senior_Outside_Reservation w_alt,2 = 77.00 ($k, B6 < VMP_2 = 88.00, so working Period 2 is socially efficient!): Spot pay w_2 = 88 leaves only 88 - 77 = 11 < 22 against shirking! Lazear’s No-Shirking Senior Wage rises to w_2* = 77 + 22 = 99.00 ($k, +11.00 above VMP_2!), Competitive Junior Wage drops to w_1* = 80.00 - (99.00 - 88.00) / 1.10 = 70.00 ($k, posting a 10.00 $k Junior Performance Bond!), and at the end of Period 2, w_2* = 99 > VMP_2 = 88 > w_alt = 77 explains why the worker will not quit voluntarily while the firm requires contractual retirement at Horizon T!
| Lazear (1979) Career Contract Metric (r=10%, VMP_1=80, VMP_2=88, s=22, w_alt=77) | Formula | Verified Output |
|---|---|---|
| No-Shirking Senior Wage (w_2*) | MAX(VMP_2, w_alt,2 + s_shirk) | $99.00k (+11k Over VMP_2) |
| Competitive Zero-Profit Junior Wage (w_1*) | VMP_1 - (w_2* - VMP_2) / (1 + r) | $70.00k (-10k Under VMP_1) |
| Implicit Junior Performance Bond Posted | VMP_1 - w_1* | $10.00k (Returned w/ 10% Interest) |
| Career-End Mandatory-Retirement Wedge | w_2* - VMP_2 | +$11.00k Excess Senior Wage |
Lazear Incentive-Compatible Senior & Junior Wage Profile Formula
Validate VMP_2 >= w_alt,2 (so Period-2 employment is socially efficient) and r > -1!
=LET(r_ds, B2, vm_1, B3, vm_2, B4, s_sk, B5, wa_2, B6, IF(OR(r_ds <= -1, vm_1 <= 0, vm_2 <= 0, s_sk < 0, wa_2 < 0, vm_2 < wa_2), "Invalid Career Contract", LET(w2_st, MAX(vm_2, wa_2 + s_sk), ROUND(vm_1 - (w2_st - vm_2) / (1 + r_ds), 2))))Implicit Junior Bond & Senior Overpayment Wedge Formula
Test s_shirk = 5 in cell B5 (77 + 5 = 82 <= VMP_2 = 88): spot productivity pay w_1* = 80, w_2* = 88 already deters shirking with zero deferred bond!
=IF(ISTEXT(E3), E3, ROUND(B3 - E3, 2))Try the example
Use the original values or change them to test your understanding.