Suppose that a legislature has to vote for one of two mutually exclusive proposals—proposal A or B. Two interest groups are willing to spend money on getting their preferred proposal implemented, with interest group 1 willing to pay up to y A to get A implemented and interest group 2 willing to pay up to yB to get proposal B passed. Both interest groups get payoff of zero if the opposing group’s project gets implemented. Legislators care first and foremost about campaign contributions — and will vote for the proposal whose supporters contributed more money, but they have a weak preference for project B in the sense that they will vote for B if they received equal amounts from both interest groups.
A: To simplify the analysis, suppose that there are only three legislators. Suppose further that interest group 1makes its contribution first, followed by interest group 2.
(a) If y A = yB, will any campaign contributions be made in a sub game-perfect equilibrium?
(b) Suppose 1.5yB > y A > yB. Does your answer to (a) change?
(c) Suppose y A > 1.5yB. What is the sub game-perfect equilibrium now?
(d) Suppose that project B is extending milk price support programs while project A is eliminating such programs, and suppose that yA > 1.5yB because milk price support programs are inefficient. Interest group 1 represents milk consumers and interest group 2 represents milk producers. Which interest group do you think will find it easier to mobilize its members to give the necessary funds to buy votes in the legislature?
(e) Suppose yA > 3yB. It costs interest group 2 exactly $1 for every dollar in contributions to a legislator, but — because of the transactions costs of organizing its members, it costs interest group 1 an amount $c per $1 contributed to a legislator. How high does c need to be in order for the inefficient project to be passed?
(f) How might the free rider problem be part of the transactions costs that affects interest group 1 disproportionately?
B: Consider the problem faced by the interest groups in light of results derived in Chapter 27. In particular, suppose that all members of interest group A have tastes uA(x, y) = xαy(1−α) where x is private consumption and y is a function of the likelihood that project A is implemented. Members of interest group B similarly have tastes uB (x, y) = xβy(1−β) where y is a function of the likelihood that project B is implemented. Suppose that interest groups have successfully persuaded members to believe y is equal to the sum of their contributions to the interest group. Everyone has income I, and there are NA members of interest group 1 and NB members of interest group 2.
(a) What is the equilibrium level of contributions to the two interest groups?
(b) Suppose again that B is a renewal of an inefficient government program with concentrated benefits and diffuse costs — and A is the elimination of the program. What does this imply about the relationship between NA and NB? What does it imply about the relationship between α and β?
(c) Suppose NA = 10,000, NB = 6, I = 1,000, α = 0.8 and β = 0.6. How much will each interest group raise? How does your answer change if NA is 100,000 instead? What if it is 1,000,000?
(d) Suppose that β is also 0.8 (and thus equal to α). If the vote-buying process is as described in part A, will legislation B pass even though there are 1,000,000 members of interest group 1 and only 6 in interest group 2?
(e) Finally, suppose that there is only a single beneficiary of B. How much will he contribute when β = 0.8? What if β = 0.6? Within this example, can even one concentrated beneficiary stop a project that benefits no one other than him?