Econ 131
Monica Singhal
UC Davis
Assignment 4
Due at the beginning of Class on May 10, 2017
Students are encouraged to work on assignments in small groups of no more than four students.
Assignments must be written up separately and must include the names of the other group
members. Assignments should be handed in at the beginning of class on the due date. Late
assignments will not be accepted under any circumstances. 1. Optimal Redistribution
a) Consider a two person economy and the formula derived in class, that at the optimal level of
redistribution, MUpoor / MUrich = 1 + (MDWL/MR). Assume throughout this question that
the marginal utility of income is declining. Suppose that a tax produces no deadweight loss
and the poor and rich individual have the same utility function. What will optimal
redistribution look like in this case and why (with reference to the formula)?
b) Now consider again the case in which the tax produces no deadweight loss but suppose that
the rich and poor individuals have different utility functions. In particular, suppose that the
utility function of the rich individual is U(Y) = 2*ln(Y) and the utility function of the poor
individual is U(Y) = ln(Y), where ln is the natural log. What will optimal redistribution look
like in this case? (Hint: this utility function is easy to work with because the derivative of
ln(x) is 1/x. So if U(Y) = ln(Y), then MU(Y) = 1/Y.)
c) Explain intuitively why your results from (a) and (b) differ in the direction they do (2-3
sentences).
d) Now let’s suppose again that the two individuals have the same utility function but now taxes
do produce deadweight loss. What does this imply for the levels of after tax and transfer
income of the two individuals at the optimal level of redistribution? Explain with reference to
the formula. 2. Economic Mobility
a) Consider the transition matrix from the CBO report discussed in class: Based on this matrix, what is the probability that an individual who starts in the lowest
income quintile in 1996 moves to a higher income quintile by 2005? b) What is the probability that someone who starts in the top 1% in 1996 ends up in the top 1%
in 2006? What would we expect it to be if incomes for all individuals were completely
uncorrelated from year to year?
c) One of the arguments in the Mankiw reading is that we cannot necessarily interpret low rates
of intergenerational mobility as evidence of inequality of opportunity. Briefly summarize his
argument (1-2 sentences).
d) The Chetty et al. work documents a high degree of geographic variation in rates of
intergenerational mobility. Does this descriptive evidence on its own provide evidence
against the Mankiw point? Explain (1-2 sentences). 3. Equity-Efficiency Tradeoffs in Practice
a) Senator Jones makes the following statement: “People have blamed U.S. tax and transfer
policies for the fact that inequality is higher in the U.S. than in other countries. But pre-tax
income inequality is also higher in the U.S. Since this can’t be explained by tax and transfer
policies, we know that there must be other factors that explain why the U.S. is more unequal
than other countries.” How would you respond to this statement? b) You have been contacted by a reporter writing a piece on French President Hollande’s 75%
top marginal tax rate. The tax was enacted in 2012, lowered in 2013, and finally repealed in
2014 after failing to raise much revenue.1 “Some economists seem to think this is a crazy
policy but others seem to be arguing that the top rate could be higher than 75%. Can you
help me make sense of what the important issues and tradeoffs are? Why didn’t such a high
tax raise much revenue?”
Based on what we’ve done in class and the readings, please provide a short summary of the
relevant economic tradeoffs involved in such a policy, with a focus on efficiency, distribution
(particularly as it relates to the top 1%), and revenue (300-400 words). 1 http://www.theguardian.com/world/2014/dec/31/france-drops-75percent-supertax

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