Changes

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 > 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{\B}\}\,<\/math>, where <math>\overline{\B} > \underline{\Beta} > 0\,<\/math>, and <math>Pr(\Beta = \overline{\B})=p\,<\/math>. Let <math>\Delta\Beta \equiv \overline{\B} - \underline{\Beta}\,<\/math>, and assume that <math>\phi(\Delta\Beta) < \delta\Delta\Beta\,<\/math>.

b) Show that if the firm wants to separate the two types, then in the first period it must offer cost targets <math>\underline{C}\,<\/math> and <math>\overline{C}\,<\/math> such that <math>(\underline{C} - \overline{C})\,<\/math> does not converge to zero as <math>\Delta\Beta\,<\/math> goes to zero. (Using a quadratic <math>\phi(\cdot)\,<\/math> may simplify the derivations. Hint: look at manager <math>\underline{B}\,<\/math>'s second period rent when she pretends to be <math>\overline{B}\,<\/math>. Write the two intertemporal incentive constraints).

c) Use an intuitive argument to conclude that the optimal scheme for the firm is to have the two types pool when <math>\Delta\Beta\,<\/math> is small.

Consider a society where a policy maker will select policy <math>x \in [0,1]\,<\/math>. There are two interest groups. Group 1 and Group 2. Both groups are willing to pay a fixed cost <math>f_i \ge 0, i=1,2\,<\/math> in order to set up lobbying capabilities, i.e., to "organize." A group that has organized is in a position to make contributions <math>c_i\,<\/math> to the policymaker in order to attempt to sway the decision of the latter. A group that is not organized cannot make contributions and hence cannot influence policy.

<math>U(x)+ c_1 - c_2 = -x^2 + x + c_1 + c_2\,<\/math>

<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 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.

c.) Suppose that <math>f_i=\epsilon, 1=1,2\,<\/math>, where <math>\epsilon\,<\/math> is a number strictly greater than zero but arbitrarily close to it. What is the subgame perfect equilibrium of the game in terms of organization decisions and implemented policy? Comment on the efficiency properties of this equilibrium, especially in relation to the efficiency properties of the equilibrium in Grossman and Helpman (1994).

d.) You are asked to participate in a debate on the ways to curb business influence on policy. The government can use one of two anticorruption measures, given its technical and enforcement capabilities. One thing the government can effectively do is stop one interest group from organizing altogether. Or it can make organization very tedious for both groups, raising the wasteful organization costs <math>f\,<\/math> for both groups. There is no limit to the government's ability to raise the fixed costs of organization. You are asked to select the anticorruption policy that would be more appropriate to eliminate inefficiency and waste. Briefly explain which measure would you favor and why.