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Consumption, tradable capital good, wages, interest rates, taxes

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Please see the attachment. I require very specific explanations for each part. If necessary, assumptions may be made but please make these explicit and make sure they are reasonable so that I can follow what you did. Also make the solutions as technical as possible.

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Solution Summary

The rate of interest is computed. The tradable capital goods, wages, interest rates and taxes for consumptions are discussed.

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Solutions:
a) The rate of interest is defined by
1/(1 + r) = p2/p1 = β(y1/y2).,
r - Rate of interest
P1, P2 - prices in the two periods
Y1,y2 - Endowments for the two periods
The general relationship between prices and rates of return:
1 + r =[payoff + resale price] / price ,
Where r is a one-period return.

b) Suppose that in the two-period production economy the consumer has
endowments y1 = y and y2 = 0 of the good, and endowment n2 = 1 of labor in the second
period. The consumer has log utility, as a function only of the two consumptions. There
is 100 percent depreciation, and the production function is f(k, n) = kαn1−α.
The changes in the real wage must come from shifts in the labor demand curve (or else changes in population or participation) in this ...

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