Question

Suppose output is given by

Y = K ^{1/2} (AN) ^{1/2}

As in the basic model, the workforce grows at rate n, capital depreciates at rate d and the savings rate is s. In addition, suppose that TFP grows at a constant rate g. That is:

∆A/A = g

We will refer to the product AN as the “effective workforce”. It follows that the effective workforce grows at rate n + g.

a. Express the production in per “effective worker” terms by
letting y_{e} = Y/AN and k_{e} = K/AN .

b. The growth in capital per effective worker can be written as

∆k_{e} / k_{e} = ∆K/K − ∆A/A − ∆N/N

Using the same steps as described in class, derive the dynamics of capital per effective worker.

c. Illustrate the steady-state for this economy on a diagram and
derive an expression for the steady-state capital stock per
effective worker, k^{∗}_{e} . How does it depend on
g?

d. Derive an expression for the steady-state output per
effective worker, y ^{∗}_{e} . In this
steady-state, at what rate must output per worker, y = Y/N , be
growing?

Answer #1

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