Consider a politician who has to determine how much effort he will exert in his re-election campaign.
A: We can model such a politician as a “producer of good feelings among voters”.
(a) Begin with a graph that puts “effort” on the horizontal axis and the “good voter feelings” on the vertical axis. Assume that the marginal payoff from exerting effort initially increases with additional effort but eventually declines. Illustrate these politicians feasible “production plans”.
(b) Suppose that the politician dislikes expending effort but likes the higher probability of winning re-election that results from good voter feelings. Assume that tastes are rational, continuous and convex. Illustrate what indifference curves for this politician will look like.
(c) Combining your two graphs, illustrate the optimal level of effort expended by a politician during his re-election campaign.
(d) Now suppose that the politician’s opponent in the campaign has the same “production technology”. Suppose further that, at any “production plan” in the model, the opponent’s indifference curve has a shallower slope than the incumbent. Assuming the candidate who has produced better voter feelings will win, will the incumbent or the challenger win this election?
B: Let effort be denoted by ℓ and “good voter feelings” by x. Suppose that a politician’s tastes are defined by u(x, ℓ) = x −αℓ, and suppose that the production frontier for producing “good feelings” among voters is given by x = ℓ2 −0.25ℓ3.
(a) When effort ℓ is on the horizontal and x is on the vertical, what is the marginal rate of substitution for this politician?
(b) What does your answer imply for the shape of indifference curves?
(c) Setting this up similar to a profit maximization problem, solve for the politician’s optimal level of effort.
(e) Which one will win the election? Explain how this makes sense intuitively.