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I have the following task:

At some moment of time (1953), the government of a country (Israel) signs an agreement with another country (West Germany) stipulating that West Germany would pay reparations to Israel during the following N years. For simplicity assume that N is large enough, that the amount or reparations is proportional to Israeli output, and that the economy of Israel reaches the new steady state while the reparations are stil paid.

Need to use Solow model. But I really do not understand what the change will happen. Probably it is the same as an increase in s. Help is needed.

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No, savings is a structural parameter in the Solow model and is not affected by income level. The basic differential equation of the Solow model is given by $$ \dot{k}=sk^{\alpha}-(\delta+n+g)k $$

In steady state, as you pointed out, both output and capital only depend on the structural parameters. What would happen is that the output would shoot beyond its steady state level till the time the reparations are being paid, and then go back to the original level. Logically you are right- The marginal propensity to save increases in income. However, in no way is this implied by the Solow model.

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What changes is the macroeconomic identity of the model: from $$F(K,L) = S + C$$ it becomes

$$F(K,L) + V = S+ C = (1+v)F(K,L) = S+C$$

where $V$ denotes the value of reparations per period, and the last expression reflects an assumption made in the question, that reparations are a constant proportion of domestic output.

"Using the Solow model" means I guess, using the standard Solow model, and so it implies that you don't change its basic assumptions. So there is no distributional issues related to this transfer payment from abroad, while also the savings rate remains fixed, and it is applied to the whole available income (irrespective of how it becomes available). I guess you can take it from here.

PS: It appears interesting to also consider a fixed level of $V$, which would reflect a situation where as time passes and the domestic economy grows, reparations become less important in relative size (which is a "reasonable" scenario, something like "we will help more when you are weak, and as you get economically stronger, helped also by the reparations, our contribution will diminish in relative importance")

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In which context did you have this question ? Is it an homework ? It is interesting.

What happens with this reparations ? Are they redistributed in the economy by some social system ? the more crucial question is if these reparations make increase savings of people.

Also, how this money is redistributed between different social classes ? as propensity to save changes according to social classes, the increase in savings will be different.

In the classical solow growth model, countries with different levels of savings will converge to their "own" steady state, which we name as "conditional convergence". So, the long term equilibrium is dependent on the structural characteristics of this economy. In this case, for sure, a country receving huge amounts of money will have another steady state. (by the channel of increase of savings, there could be other structural changes other than changes in savings)

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