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Florida International University
ECO 4932 Topics in Theory – Spring 2015
Midterm #2 – 03/31/15 – Answer Key
Instructions: Please answer the questions in the answer sheets included with the exam.
Make sure to number the pages once you have finished your exam. All the questions are
about basic concepts covered in class and in the lecture notes. Please keep your answers
short and to the point. You can use equations in your answers if you think it will make the
argument more clear. Make sure I can understand your handwriting. If I can’t I will
assume that your answer is wrong. Good luck!
1. In many of the models we have seen in class the socially optimal policy (g*) is implemented,
while in other models a median-voter type of equilibrium results (gm). What is the typical
assumption that provides one or the other result? Explain.
2. Recall the models of Efficient and Inefficient Electoral Competition from chapter 4. What is
the level of public good (g) provided in each model and what is the level of rents (r)? Are the
levels of g and r different? If so, why?
3. Consider the model in which an independent and benevolent judiciary can verify and enforce
electoral promises. What type of policy can we expect to be implemented? What rents will
the candidates collect if elected?
4. Recall the Electoral Cycles Model from chapter 4. What is the level of rents in off-election
periods? What is the level of rents in on-election periods? Which one is greater? What is the
main incentive that determines the behavior of the incumbent?
Answer Key:
1. The key assumption that gives one or the other result is about the distribution of income. If
the distribution of income is uniform, given that all voters have the same preferences, they
will prefer the same level of g. The closer each candidate is to g* the higher is his probability
of winning. Therefore both candidates will offer g*. If the distribution of income is positively
skewed then the voter with median income becomes the pivotal voter. Any candidate that
offers gm can have at least half of the votes; therefore both candidates will offer gm.
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2. In the model of Efficient Electoral Competition, the median voter is pivotal therefore the
level of g = gm. Rents however are zero. Suppose a candidate offers r’ > 0. The other
candidate can increase his probability of winning by offering r” = r’ – ε. Rents are competed
away in a Bertrand type of competition and rm = 0. In the model of Inefficient Electoral
Competition the level of g = g* but rents are not zero. Rents are not competed away because
candidates have ideological attributes. They are not perfect substitutes of each other.
Therefore the policy platforms do not entirely determine the electoral outcome.
3. Candidates want to maximize their objective E  p   Pp  R   r  , augmented by the
uncertainty over  . Voters prefer the candidate whose platform gives the highest expected
utility E W  g   , r   ;  . Where E denotes expectations over  . Candidate A’s
probability of winning is
 0 if E W  g A   , rA   ;    W  g B   , rB   ; 

 


1
PA  
if E W  g A   , rA   ;    W  g B   , rB   ; 
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
 1 if E W  g A   , rA   ;    W  g B   , rB   ; 
The probability of candidate B is PB  1  PA , so both candidates face the same incentives.
Whoever moves closer to the state-contingent policy the voters desire increases his
probability of winning. The outcome is optimal with
g A    g B    g *  
rA    rB    0
4. In off-election periods, the incumbent faces no incentives to behave well, and rents are
maximal: rt  r. In on-election periods policy choices are shaped by the same incentives as in


the simplified two period model and rents are given by r1   y   R  r . Performance
improves just before the elections: wasteful spending decreases and the quality of public
consumption improves. Competent incumbents who are able to please the voters are
reappointed, and incompetent ones are ousted from office.
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