Seminar 5: Bureaucratic agency and employment relations (9.11)

Some questions from Kalle's lecture on bureucracies and his model in Moene (1986) (almost identical to exercise for Seminar 4):
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)=(1/γ)X^γ, 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. What are appropriate values for γ?
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?

Exercises on emplyment relations