Pareto Gains from Limiting Compensation Options

Figures & Tables

θ_H	θHθL \frac{{\boldsymbol {\theta _H}}}{{\boldsymbol {\theta _L}}}	ϕH* {\boldsymbol {\phi _H^*}}	ϕHS* {\boldsymbol {\phi _{HS}^*}}	EUϕH* {\boldsymbol {EU\left( {\phi _H^*} \right)}}	EUSϕHS* {\boldsymbol {E{U_S}\left( {\phi _{HS}^*} \right)}}	EΠϕH* {\boldsymbol {E\Pi \left( {\phi _H^*} \right)}}	EΠSϕHS* {\boldsymbol {E{\Pi _S}\left( {\phi _{HS}^*} \right)}}
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

	θ_H = 0.3	θ_H = 0.4	θ_H = 0.5	θ_H = 0.6	θ_H = 0.7	θ_H = 0.8
W_L {\boldsymbol {\underline W _L}}	− 0.113	− 0.085	− 0.071	− 0.063	− 0.058	− 0.054
W¯L {\boldsymbol {\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
W_H {\boldsymbol {\underline W _H}}	− 0.127	− 0.149	− 0.179	− 0.212	− 0.246	− 0.280
W¯H {\boldsymbol {\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
W_ {\boldsymbol {\underline W}}	− 0.115	− 0.088	− 0.071	− 0.060	− 0.053	− 0.048
W¯ {\boldsymbol {\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

k	θHθL^ {\boldsymbol {\widehat {\frac{{{\theta _H}}}{{{\theta _L}}}}}}	k	θHθL^ {\boldsymbol {\widehat {\frac{{{\theta _H}}}{{{\theta _L}}}}}}	k	θHθL^ {\boldsymbol {\widehat {\frac{{{\theta _H}}}{{{\theta _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