611
Game Economics Theoretic Microeconomics Spring 2007
Final Exam
All Syracuse University policies and procedures concerning academic honesty apply to
this course:
"Syracuse University students shall exhibit honesty in all academic endeavors. Cheating in any
form is not tolerated, nor is assisting another person to cheat. The submission of any work by a
student is taken as a guarantee that the thoughts and expressions in it are the student's own except
when properly credited to another. Violations of this principle include: giving or receiving aid in
an exam or where otherwise prohibited, fraud, plagiarism, the falsification or forgery of any
record, or any other deceptive act in connection with academic work. Plagiarism is the
representation of another's words, ideas, programs, formulae, opinions, or other products
of work as one's own either overtly or by failing to attribute them to their true source."
(Section 1.0, University Rules and Regulations)
WARNING!!!
While homework problems may have been done cooperatively, exams are individual
work. Do not communicate about this exam with anyone except the instructor [x3-2345 or email to [e-mail]]. Violation of this rule will result in a grade of 0 for the
exam. Any notices will be sent to you by e-mail; occasionally.
EXPLAIN check your answers carefully.
DUE: Noon, Tuesday, May 8th.
Economics 611 Game Theoretic Microeconomics
Final Exam
The three problems are each worth 33 points.
Spring 2007
1. (Principal-agent / moral hazard)
What is the effect of the functional form for detection probabilities in the effort example
at the beginning of Handout #8? Redo that example with (E) = 1 aEb], where 0 < a 1, and
output is given by (LE)c, where 0 < c < 1 In particular, answer the comparative statics questions:
How do effort, equilibrium wage, and labor hired, L, vary with a, b, and c?
2. (Insurance; moral hazard)
Later in Handout #8, we examined unemployment insurance for an example where the
probability of being laid off was .25, Y = 400, U(z) = (z), and (E) = e E/4. How important are
these particular functional forms? Re-do the analysis for U(z) = ln (1 + z). In particular, get the
analog of the diagram at the bottom of page 611.08-5.
3. (Optimization)
A. Min C = rK + wL subject to K 0, L 0, (K + 1)(L + 1) = Q for r,w > 0 and Q > 1.
B. f: + is continuous with f(a) 0 for some a in + and limx f(x) = 0. Show there
exists a global maximum for f on + .
Extra Credit. Think hard about the existence of a global minimum for the following
function of b1, ..., bK.