Seminar 4: Complementary institutions and bureaucratic agency (26.10)

Consider first Barth and Moene's (2011) paper:

1. The political support for publicly provided insurance
   1. What is an individual's expected utility when the instantaneous utility is given by (4) and consumption C = (1- t)w_i when the person is working, which happens with probability (1-e), and C = G when he is unemployed, which happens with probability e?
   2. The public budget constrain is kG=tw. Maximize the expected utility with regard to t, and try to derive a tractable expression for the individual's preferred tax rate.
   3. What is the individual's relative risk aversion (see almost any microeconomics book for definitions of relative risk aversion, e.g. Cowell's Microeconomics - Principles and Analysis, ch. 8.4)?
   4. What is the effect of an increase in an individuals income w_i, keeping average income w unchanged? How does this depend on the coefficient of relative risk aversion?
   5. The coefficient of relative risk aversion is often estitimated to be between 1 and 2. What is the effect of a mean preserving spread on political support for public insurance (assuming we can apply the median voter theorem)?
   6. Usually vulnerability (the probability of becoming unemplyed) is lower for higher wage groups. What would this imply for your answers to subquestions v. and vi.?
2. Bargaining over wages: A unemployed worker and an emplyer have been matched and bargain over the wage. The productivity of the worker in this job is p, which is to be shared among the worker and the employer. First the emplyer can suggest a wage w₀. If this is refused by the worker, the match is destroyed with probability δ, in which case the worker get G and the employer get 0. Otherwise, the worker can propose a wage w₁. Again if this is refused by the employer, the match is destroyed with probability δ, the worker get G and the employer get 0. If the job is not destroyed, it's again up to the employer to propose a wage w₃, and so on.
   1. Show the first three levels of the game three: Who draws, what can they do, what are the payoffs.
   2. Use that fact that step 3 is identical to step 1 to show that the game has a solution following a "Godfather principle". Find the emplyers offer in step 1.
   3. Would an increased G lead to more wage compression? What can be done to the model to explain

Some questions from Kalle's lecture on bureucracies and his model in Moene (1986):
The bureau has preferences U(X,Z) over activity X and slack Z where Z=B-C(X). Society's utility of activity is given by W(X), and the bureau's budget is given by B. We always have B<=W(X).
Assume here that U(X,Z)=X^βZ^1-β and C(X)=αX+C₀.

1. Calculate the socially optimal bureau
2. Calculate the bureau's X and B that exploit the situation with a complete information monopoly
3. Calculate X and B when the bureau chooses X for a given B and the politicians choose B given X=F(B) (where F is the optimal reaction of the bureau)
4. Discuss how this specific utility function can be interpreted as the outcome of conflict of interest between zealots (climbers), who prefer a large bureaucracy,  and conservers, who prefer leasure and slack on the job.
5. Assume now that social welfare depends on national income R, so W=W(X;R). Assume that W'_X is increasing in R. What does this mean, and does it seem like a plausible assumption? How are X and B affected by an increase in R?