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Hình B.36: hợp đồng đầy đủ thông tin: Lao động cung cấp cho mỗi loại 8 Trong trường hợp này Bill làm việc chăm chỉ có một sự khuyến khích để xuyên tạc bản thân mình như là một loại a-: xem Hình B.37. Bill nhận ra rằng nếu anh ta được ale để sử dụng giới hạn ngân sách một loại unrestrictedly ông có thể đạt được cá trên cùng | 572 APPENDIX B. ANSWERS TO FOOTNOTE QUESTIONS 6. Follows from the assumption of zero income effects of the good under consideration. 7. a The budget constraint is h _ i yh wh h - Fh if 0 y y0h otherwise b Flipping Figure 11.4 and drawing in the budget constraint we have Figure B.36. The firm pays each worker his marginal product wa w and wb w the slope of the budget constraint in each part of the figure . It sets the up-front fees Fa and Fb so as to keep Alf and Bill on their reservation utility levels. Figure B.36 Full-information contracts Labour supply for each type 8 In this case hard-working Bill has an incentive to misrepresent himself as an a-type see Figure B.37. Bill realises that if he were ale to use the a-type budget constraint unrestrictedly he could achieve the topmost indifference curve depicted on the right-hand side of the figure and supply an amount b of work.@ 9. From 11.17 the condition that the b-type stays on the same utility level is given by b T-b A-b mbih mbI drb d 1 lAb dmb 1 Fb d.Fb b mb-ih mbI-mt Fb y p x Px x x 1 P P1 x 1 X 1 0 0 y p x pxi 0 which on simplification yields dF0b _ rj d -Tbp A b11 dx1 xb dp p dp T px x1 dp x1 Using 11.14 we get dFob dp xb B.11. INFORMATION 573 Figure B.37 Bill masquerades as an a-type in labour supply 10.Given that the a-type is mimicking an b-type s consumption we have dU x dp T x xb dp U b xb vb dx1 dp Ub xb vb xb dF0 x1 dp - p Using 11.23 and simplifying this becomes dU x dp dxb dp U b xb vb T x xi - p Using 11.14 then gives the result. 11.Conditions 11.22 and 11.29 imply that T xỉ - F Tb xị - Fb. Therefore if were to hold in 11.28 then also one would have T x F 0. 12. Assuming that holds then given 11.22 we have T x - F T x - Fb Tb xb - Fb 574 APPENDIX B. ANSWERS TO FOOTNOTE QUESTIONS In view of 11.31 this would imply that T v. x Fa 0. 13.In view of 11.22 and 11.32 we obtain Ta a - Fa Tb x - Fb and so from 11.31 T V a - Fa 0. 14.If the incentive-compatibility constraint 11.30 were binding as well as .
