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→A.2: Lobbying and policy choice
===A.1: Managerial Productivity & Incentives===
Consider Holmstrom's 1982 managerial model, except that the manager knows her productivity parameter from the start. The manager lives for two periods <math>(t = 1, 2)\,</math>. Once she is employed by a firm in period <math>t\,</math>, the firm's production cost is <math>C_t = \Beta - e_t\,</math>, where <math>\Beta\,</math> is the her productivity parameter and <math>e_t > \ge 0\,</math> is the effort she exerts at a cost of <math>\phi(e_t)\,</math> (with <math>\phi' > 0\,</math> and <math>\phi'' > O\,</math>). <math>C_t\,</math> is observable but not verifiable, but <math>\Beta\,</math> and <math>e_t\,</math> are not observed by the firms. The manager's utility is <math>\sum_{t=1}^2 \delta^{t-1}[I_t -\phi(e_t)]\,</math>, where <math>I_t\,</math> is her income at time <math>t\,</math> and <math>\delta\,</math> is her discount factor. Firms are competitive (they derive the same benefit from the manager's activity) and the manager cannot commit to staying with the same firm. It is common knowledge that <math>\Beta \in \{\underline{\Beta}, \overline{\Beta}\}\,</math>, where <math>\overline{\Beta} > \underline{\Beta} > 0\,</math>, and <math>Pr(\Beta = \overline{\Beta})=p\,</math>. Let <math>\Delta\Beta \equiv \overline{\Beta} - \underline{\Beta}\,</math>, and assume that <math>\phi(\Delta\Beta) < \delta\Delta\Beta\,</math>.
a.) Derive the best separating equilibrium for the manager (the manager offers the contract). In your answer, comment on the "intuitive criterion".
<math>V_i(x) - f_i - c_i\,</math>
with <math>V_1 = - x^2 + 1\,</math>, and <math>V_2 = -x^2 + 2x\,</math>. Note the fixed costs are a waste in that the policymalcer policymaker does not benefit from them (nor does anyone else).
The timing of interaction in this society is as follows. 1) Both interest groups decide, simultaneously and noncooperatively, whether to organize. 2) The organization decisions become known to everyone, and whomever is organized makes contributions <math>c(x)\,</math> to the policymaker in the form of a schedule of contributions contingent on the policy that is finally chosen. If both groups are organized, contributions are made simultaneously and noncooperatively, and you should assume that a Truthful Nash equilibrium is played. 3) Knowing the contributions offered, the policymaker selects policy. All payoff functions and the structure of the interaction are common knowledge.
