Problem set n°1; to be discussed in class by the students on Friday ...

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28 Οκτ 2013 (πριν από 3 χρόνια και 11 μήνες)

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MACROECONOMICS

Prof. Nicola Dimitri


The foll
owing proble
ms will be discussed by the stud
e
n
ts
in class next Friday May 24
th

h 16
-
18 and, if
necessary, also from h 18
-
20 of the same day.

1)

Show that if




and



are two solutions of the equation






(




|


)




then also








+
(



)



with






is also a solution of the equation.


2)

In the continuous time version of the Ramsey model discussed in class find the Hamiltonian,
the Ramsey
-
Keynes optimal conditions and discuss the
stationary states and phase diagram
under the following hypotheses on the population growth rate

a)



̇









b)

̇








c)

̇








d)

b)

̇











3)

Consider t
he following two variables, discrete time, dynamical
system





























Find the stationary state, the eigenvalue and eigenvectors of the transformation matrix



[




]


and discuss the asymptotic behavior of the system. If the stationary state is not a saddle point
s
uggest a matrix A that could have a saddle point.