Question

1. Consider Country Z, a country with an economy that behaves according to an entirely conventional Solow model. In 2018, it’s in steady state. In this low-productivity country, technology (A) never changes. In 2019, a philanthropist instantly gives Country Z a massive amount of physical capital as a one-time gift because he read on a blog that such a gift might "jump-start" Country Z's economy. The capital is used reasonably efficiently, so there are no public choice failures.

   1. Between 2018 and 2020, what will happen to Country Z's interest rate? Will it rise, fall, or remain unchanged?

   2. Between 2020 and 2030, what will happen to Country Z's interest rate: Rise, fall, or remain unchanged?   

   3. Between 2020 and 2030, what will happen to Country Z's wages: rise, fall or no change?

   4. In Z's post-2019 steady state, what will wages be like compared to 2018: higher, lower, or the same?

Answer 1

We can understand this problem from the basic Solow model diagram and equation, as given below

In the model capital accumulation per worker is

k sy (n d)k

here LHS is the change in capital per labor and s is the saving rate n is the population growth rate and d depreciation

DIAGRAM below is just the graphical representation of the above equation. At steady state $\dot{k}^{*}$ = 0

(n+d)k sy k

= 0) sy- (nd)k

Now when the philanthropist gives a one time capital aid of amount say M₀, this is what will happen.

See the second vertical line denoting the new k . At this level of capital per labor the savings are not enough to account for the growth in labor and depreciation. Thus eventually the economy will return to original steady state, denoted by the first vertical lin.

In the above diagram the intersection of the curve and line is the steady state equilibrium with zero growth. But now the one time stimulus has taken it to the second vertical line in the marker in value of k (as per capita capital has increased)

Firstly in the year 2018 there will be excess capital so demand for new capital will be less. Hence interest rate will fall. (2018-2020). But when the economy reaches the steady state by 2020-2030 interest rate will also rise to original level.

Till the new steady state is achieved in medium term (say 2030)  $k>{k}^{*}$ Equilibrium will be achieved when by action of labor force growth ,  $k={k}^{*}$ holds again (as shown by the arrow)

With the capital increase labor productivity will increase (given constant technology). Hence in the short term 2018-2020 wages will increase.

Eventually as the steady state is achieved wages decrease to original level as again   $k={k}^{*}$. Thus in longer term 2020-2030 wages will decrease to original level.