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9

Eq. (2.64) can be written as (at first order) $$ k_{t+1} - k^* = \lambda (k_t - k^*) \tag{1a} $$ Define the quantity $\kappa_t$ as $$ \kappa_t \stackrel{\rm def}{=} k_t - k^* \tag{2} $$ So that $$ \kappa_{t+1} = \lambda \kappa_t \tag{1b} $$ This can be solved very easy by realizing that \begin{eqnarray} \kappa_1 &=&\lambda \kappa_0 \\ \...


6

Shell 1971 argues (in a ten page paper, so read it!) that the dynamic inefficiency stems from the double infinity of traders and goods, and not the dynamics. This allows us to do the Hilbert hotel switch. Therefore, even when all souls are able to transact business in the same Walrasian market, the absence of Pareto-optimality persists in the ...


4

A system is explosive if its coefficients are non-stationary. Stationary is an important property to have in dynamic models as it tells us that an equilibrium value is obtainable (which is important in finding the BGP). If your system is explosive no equilibrium (and BGP) exists. In your example where you have the equality: $$k_t-k^* \simeq \lambda^t (k_0-...


4

There is an unpublished 1982 working paper by Donald Brown and John Geanakoplos, called “Understanding Overlapping Generations Economies as a Lack of Market Clearing at Infinity” (a scan used to be available at Brown's homepage). The authors show that there is a one-to-one correspondence between the equilibria of an OLG economy and almost-equilibria in a ...


3

The interest component is already included. It was just their way of writing out the budget constraint that confused me. If anyone is interested: $\frac{B_{t-1}}{p_{t}} - \frac{B_{t}}{(1+i_{t})p_{t}} = \frac{i_{t}}{(1+i_{t})}\frac{B_{t}}{p_{t}} - \frac{B_{t}}{p_{t}} + \frac{B_{t-1}}{p_{t}}$. This is simply the interest on existing debt and the face value of ...


2

I would call this a mean-variance utility function. The agent likes higher mean values, which is the first term, but trades that off against higher variance, which is the second term. If the random variable of interest is normally distributed with mean $P_{t+1} + \delta_{t+1} - (1+r^f)P_t$ and covariance matrix $\Omega$, and if the agent has constant ...


2

Property rights and assuming away bequest motives (the Old do no care about the Young). Capital of the previous period belongs to the Old, and since they will die at the and of old age, the finite-horizon transversality condition for utility maximization requires that either all assets have been consumed at the time of death, or that they have no utility-...


2

You can find OLG models that do not classify as DSGE (in particular, the model might not be stochastic) as well as DSGE with overlapping generations (contrary to those with infinitely lived agents). You can find more detail on this on this working paper by Assous and Duarte (2017), as they note In the early 1980s, when the real business cycle ...


1

I think all the textbook is trying to say is that there can be no corner solutions to your maximization problem. Not refusing consumption in any period, I think translates to consumption in each period > 0.


1

I haven't read the paper in full detail (I should, it's interesting) but let me give you my interpretation of the paper's title. Blanchard uses a constant probability of instanteneous death for each agent. As mentioned in footnote one of the paper this is most realistic as assumption for people between 20 and 40. Agents in the model therefore are like young ...


1

I found the problem, and now I feel dumb but I suppose I should leave the question up so people can know the potential pitfall and prepare for it better than I did. The problem arose from me misreading (and clearly misunderstanding) the equilibrium conditions for the problem, where it states that the interest rate $r_t$ on loans issued today and paid back ...


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