ECON1001 (Macro): Homework 5
UCL Department of Economics, 2009–2010 Term 1
Lecturer: Nicola Pavoni. Due by Thursday, November the 26th.
An employer o¤ers his/her employee the option of shifting x units of income from
next year to this year. That is, the option is to reduce income next year by x units
and increase income this year by exactly x units.
a) Would the employee take this option? Carefully explain your answer. [Hint:
Use a diagram to address the question.]
b) Determine, using a diagram, how this shift in income will a¤ect consumption
this year and next year, and savings this year. Carefully explain your results.
Consider the two-period problem of the representative consumer and assume the
consumer has current-period income y = 150, future income y 0 = 180, current and
future taxes t = 40 and t0 = 48, respectively, and faces a market real interest rate of
r = 0:2 (or 20% per period). The consumer’ preferences over c and c0 are represented
by the following utility function:
U (c; c0 ) = min fc; c0 g :
a) Show the consumer’ lifetime budget constraint and indi¤erence curves in a
b) Calculate his or her lifetime wealth, optimal current-period and future-period
consumption, and optimal saving. Show these values in your diagram. Is the con-
sumer a lender or a borrower?
c) Suppose that everything remains unchanged, except that now t = 10 and
t0 = 84. Calculate the e¤ects on current and future consumption and on optimal
saving and show this in your diagram. Explain your results in light of the Ricardian
d) Now, assume that the consumer is faced with a credit market imperfection,
in that he or she cannot borrow at all, that is, any decision of consumption that
induces negative saving (s < 0) is not an option for the consumer, who is then forced
to set s = 0 instead. Clearly, consumption choices that induce s > 0 are perfectly
acceptable. Repeat parts (a) to (c) and explain any di¤erences.
e) Finally, go back to point (c). That is, assume that t = 0; and t0 = 96 and
that there are no credit market imperfections. Now assume that the government
introduces a tax x on interest earnings. That is, borrowers face a real interest
rate r before and after the tax is introduced, but lenders receive an interest rate
of (1 x) r on their savings. Determine the optimal choice of current and future-
period consumption and the saving of the consumer when the tax is set at 50%, that
is, x = :5; and show this in a diagram. Explain your results in terms of income and
substitution e¤ects. [Hint: Do not worry if you do not get whole numbers.]
f) How would your answer to point (e) change if taxes were as in the original
formulation of the model, that is, t = 40 and t0 = 48? Explain.
At high school some of you might have studied the Keynesian aggregate con-
sumption function, which - in its simplest form - takes the following expression
C = c0 + c1 (Y T);
where c0 and c1 are parameters and Y T is current aggregate disposable income.
The parameter c1 is assumed to be a number between zero and one, and it is denoted
as the marginal propensity to consume.
a) Given an economic explanation for the name given to the parameter c1 : What
the parameter c0 > 0 could represent instead?
b) Comment the above function in light of what we have seen is class. In par-
ticular, discuss whether the above function is a reasonable approximation for the
aggregate behavior of forward looking consumers who live more than one period.