Question

1. Imagine that there is a technological advancement which increases the productivity of capital. Which variable in the model should we increase? (You may assume that increases the productivity of both capital and labor. In other words, don't mess with the exponents......) Show the effect of this on steady-state capital and output on the usual graph.

2. It turns out that the effect of a change in the savings rate on the steady-state consumption is ambiguous. Let's try to show this with the power of algebra! Let A=2, L=100, and d=1/4 but do not pick a value for s. Solve for the steady-state values of K, Y and C by just leaving an "s" in there. This means that you will get functions of s as your answer! You should be able to look at K*(s) and Y*(s) and see easily that they will be increasing in s. C*(s), should be a parabola. Economists call the savings rate which maximizes this function the "golden rule" savings rate. You will learn how to find it explicitly in intermediate macro (you have to use calculus). Notice what the value of C* is if s=0 and what it is if s=1.

Make sure to show your work. Also make your C* function clear and easy to identify without carefully going through it all so that I don't have to if it's wrong.....

Answer 1

Solution for the abve problems

1)

2)

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