ECON8026 Advanced Macroeconomic Analysis
Assignment 4
Semester 1, 2023
Question 1
Preference Shocks in the Consumption-Savings Model. In the two-period consumption-
savings model (in which the representative consumer has no control over his real labor in-
come y1 and y2), suppose the representative consumer’s utility function is u(c1, Bc2), where,
as usual, c1 denotes consumption in period 1, c2 denotes consumption in period 2, and B is
a preference parameter.
a. Use an indifference-curve/budget-constraint diagram to illustrate the effect of an
increase in B on the consumer’s optimal choice of period-1 consumption.
b. Illustrate the effect of an increase in B on the private savings function. Provide
economic interpretation for the result you find.
c. In the months preceding the U.S. invasion of Iraq, data shows that consumers de-
creased their consumption and increased their savings. Is an increase in B and the effects
you analyzed in parts a and b above consistent with the idea that consumption fell and
savings increased because of a looming war? If so, explain why; if not, explain why not.
d. Using a Lagrangian and assuming the utility function is u(c1, Bc2) = ln c1 + ln(Bc2)
, show how the representative consumer’s MRS (and hence optimal choices of consumption
over time) depends on B.
e. How would your analysis in parts a and b change if the consumer’s utility function
were u(Dc1, c2) (instead of u(c1, Bc2)) and you were told that the value D decreased? ( D
is simply some other measure of preference shocks.)
Question 2
Impulse Response Function and Labor Supply: Part 1. Suppose a one-time TFP
shock occurs, as shown below.
As we have studied, an increase in TFP leads to an outwards shift in labor demand (recall
this from our firm analysis unit), which, as long as the upward-sloping labor supply function
does not shift, leads to an increase in the real wage. Using an infinite-horizon (which,
recall, is a heuristic for a “many, many, many time-period” framework) of the combined
consumption-savings and consumption-labor framework (which is an extension of the brief
two-period framework of Chapter 5), qualitatively plot an impulse response function for
the representative consumer’s optimal labor supply that lines up with the impulse response
1
profile for TFP drawn above. Use the lifetime utility function
ln
(
ct − ψ
1 + ν
n1+νt
)
+ β ln
(
ct+1 − ψ
1 + ν
n1+νt+1
)
+ β2 ln
(
ct+2 − ψ
1 + ν
n1+νt+2
)
+
β3 ln
(
ct+3 − ψ
1 + ν
n1+νt+3
)
+ ...
in which the utility parameters ψ > 0 (the Greek lower-case letter “psi”) and ν > 0 (the
Greek lower-case letter “nu”) are exogenous to the representative consumer.
(You should be able to set up the appropriate budget constraints yourself, although you
don’t need to display them if you don’t think you need to.)
Provide brief justification for the impulse response you have sketched.