Pareto Gains from Limiting Compensation Options

Debashis Pal; David E. M. Sappington; Iryna Topolyan

doi:10.2478/izajole-2023-0002

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Pareto Gains from Limiting Compensation Options

IZA Journal of Labor Economics

Volume 12 (2023): Issue 1 (January 2023)

By: Debashis Pal, David E. M. Sappington and Iryna Topolyan

Open Access

|Nov 2023

Figures & Tables

Timing in the Setting with Exogenous Ability.

Timing in the Setting with Endogenous Ability.

Table 1

The Effects of an SPP in Example 1.

θ_H	$\frac{θ_{H}}{θ_{L}}$	$ϕ_{H}^{*}$	$ϕ_{HS}^{*}$	$EU (ϕ_{H}^{*})$	${EU}_{S} (ϕ_{HS}^{*})$	$E Π (ϕ_{H}^{*})$	$E Π_{S} (ϕ_{HS}^{*})$
0.30	1.2	0.200	0.213	0.0025	0.0026	1.12524	1.12521
0.35	1.4	0.258	0.328	0.0066	0.0078	1.12658	1.12670
0.40	1.6	0.264	0.392	0.0099	0.0131	1.1285	1.12971
0.45	1.8	0.257	0.438	0.0125	0.0180	1.13055	1.13402
0.50	2.0	0.246	0.478	0.0145	0.0227	1.13258	1.13959
0.55	2.2	0.235	0.517	0.0161	0.0272	1.13453	1.14644
0.60	2.4	0.225	0.557	0.0174	0.0316	1.13638	1.15467
0.65	2.6	0.215	0.599	0.0185	0.0361	1.13813	1.16437
0.70	2.8	0.206	0.644	0.0194	0.0406	1.13978	1.17565
0.75	3.0	0.198	0.692	0.0202	0.0453	1.14134	1.18858
0.80	3.2	0.190	0.743	0.0209	0.0502	1.14281	1.20322

Table 2

The Minimum $\frac{θ_{H}}{θ_{L}}$ that Ensures Pareto Gains in Example 2.

k	$\hat{\frac{θ_{H}}{θ_{L}}}$	k	$\hat{\frac{θ_{H}}{θ_{L}}}$	k	$\hat{\frac{θ_{H}}{θ_{L}}}$
0.10	1.34	0.25	1.56	1.0	2.18
0.15	1.44	0.50	1.88	2.0	2.72
0.20	1.52	0.75	2.00	5.0	3.68

Table A1

Optimal Payments in the Setting of Example 1.

	θ_H = 0.3	θ_H = 0.4	θ_H = 0.5	θ_H = 0.6	θ_H = 0.7	θ_H = 0.8
${\underline{W}}_{L}$	− 0.113	− 0.085	− 0.071	− 0.063	− 0.058	− 0.054
${\bar{W}}_{L}$	0.839	0.738	0.683	0.648	0.623	0.605
Δ_L	0.952	0.823	0.754	0.711	0.681	0.659
${\underline{W}}_{H}$	− 0.127	− 0.149	− 0.179	− 0.212	− 0.246	− 0.280
${\bar{W}}_{H}$	0.873	0.851	0.821	0.788	0.754	0.720
Δ_H	1.0	1.0	1.0	1.0	1.0	1.0
$\underline{W}$	− 0.115	− 0.088	− 0.071	− 0.060	− 0.053	− 0.048
$\bar{W}$	0.845	0.752	0.684	0.635	0.598	0.570
Δ	0.961	0.840	0.756	0.695	0.651	0.617

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DOI: https://doi.org/10.2478/izajole-2023-0002 | Journal eISSN: 2193-8997

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Language: English

Submitted on: Feb 6, 2023

Published on: Nov 11, 2023

Published by: Sciendo

In partnership with: Paradigm Publishing Services

Keywords:

limited contract choice,

human capital investment

JEL:

D82,

J41,

K31

Related subjects:

Business and economics,

Mathematics and statistics for economists,

Econometrics

© 2023 Debashis Pal, David E. M. Sappington, Iryna Topolyan, published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 12 (2023): Issue 1 (January 2023)

Pareto Gains from Limiting Compensation Options

Figures & Tables

Figure 1

Figure 2

Table 1

Table 2

Table A1

Paradigm

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