Advanced Macroeconomics - Problem Set 2
Spring 2022
Riccardo Franceschin
March 23, 2023
The due date for this assignment is Sunday April 9. It needs to
be delivered by 23:59.
• For any question write to riccardo.franceschin@sabanciuniv.edu
• Don’t forget to write the name on your first page
Exercise 1: TFP shock with different utility
Suppose that the utility function of the consumer is the following
N 1+φ
C 1−σ
−
U=
1−σ 1+φ
(1)
where σ > 0 and φ > 0.
For the rest, the economy is described as we saw in class for the New
Neoclassical Synthesis with flexible prices.
1. Find the first-order necessary conditions of the consumer’s problem for
consumption and work.
2. Represent the equilibrium in the labour market, both graphically and
analytically
3. Describe graphically and analytically the natural equilibrium. What is
the effect of variation of the TFP on the natural level of employment?
Derive and comment an expression for the natural level of consumption,
output and real wage. (Assume that the production function is the
usual Y = AN )
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4. Repeat the previous analysis on the effects of variations in the TFP
when prices are fully rigid. Comment.
Exercise 2: Tax on Interests
Take the Endowment economy with two-periods that we saw in class.
Suppose that the government introduces a tax only on interests. Therefore
the interest rate for borrowing remain the same and it will not be taxed. while
the net interest rate will become (1 − x)r, where x is the tax introduced.
1. Show graphically and analytically the effects of x on the intertemporal
budget constraint
2. Show how the government decision influences the consumer decision.
In particular, discuss the income and substitution effects and their role
and the different effects depending on the status of borrower or saver
3. Suppose that the government use taxes to finance a quantity G and
G′ of public spending, with G = G′ > 0. Before the introduction of
the tax, the government was using only lump-sum taxes. Does the
Ricardian Equivalence apply after the tax? Show it and discuss.
Exercise 3: Preference Shock
Suppose that the consumer has this utility function
U = logCt + βlogCt+1
(1)
Suppose that the government has G = T = 0 while the firm has the following
production function
Y = AN
1. Find the intertemporal budget constraint and the equilibrium consumption in the two periods
2. Analyze the effect of a positive shock to β. What will happen to Ct ?
3. Suppose that the interest rate adjusts in order to satisfy the condition B = 0 and the equilibrium in the credit market. How would the
previous answer change?
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