HW XXXXXXXXXXPolitical Pressure XXXXXXXXXXAbe has 1 unit of wealth and Beatrice has 0, but a policy maker is considering a transfer ?? of wealth from Abe to Beatrice. The size of the transfer ?? =...

Please do thoroughly - thank you!


HW 25 (+16) Political Pressure 1. (+16) Abe has 1 unit of wealth and Beatrice has 0, but a policy maker is considering a transfer ?? of wealth from Abe to Beatrice. The size of the transfer ?? = ???? ????+???? will depend on the pressure ???? and ???? that Abe and Beatrice generate. Objective functions for Abe and Beatrice can therefore be written as follows, ???? = √1 − ?? − ???? ???? = √?? − ???? where the square root reflects a decreasing marginal benefit of wealth, and the negative terms −???? and −???? reflect the cost of pressuring the policy maker. a. (+4) Derive the first-order condition for the level of pressure that Abe will optimally exert on the policy maker, taking Beatrice’s pressure as given, as well as the first-order condition for the level of pressure that Beatrice will optimally exert on the policy maker, taking Abe’s pressure as given. b. (+4) The symmetry of the first-order conditions is such that any pair (????,????) of pressure levels that satisfies both first-order conditions must also satisfy ????∗ = ????∗ = ??∗. Use this fact to determine the level of pressure that both individuals exert in equilibrium. Also, determine the size ??(????∗ ,????∗ ) of the resulting transfer. c. (+4) Now suppose that the policy maker ignores pressure from Abe and Beatrice and chooses the level of transfers ?? to maximize utilitarian social welfare ?? = ???? + ????. What transfer policy is implemented in that case? How much pressure do Abe and Beatrice then exert? d. (+4) Use your answers above to discuss the welfare implications of setting policy in response to political pressure. HW 25 (+16) Political Pressure