Question

Assume that the Solow model provides an accurate representation of the two Germanies around the late 80s and early 90s. Although in 1989 both countries re-unified, for this problem we will treat them as two separate economies and we will model the effects of the reunification as a one-time flow of resources (capital and/or labor) across the common border. Aside from being in steady state, assume that before the re-unification both economies had the same saving rate, the same rate of population growth, rate of depreciation, and capital was equally important for production in both countries with a common value of α=1/2 . Let’s focus on the period before the re-unification. In this period, output per capita in the West is twice the level than in the East. Use this information to calculate the ratio of Total Factor Productivity between the two economies. Explain carefully your derivations.

Answer 1

The ratio of Total Factor Productivity (TFP) between the two economies is 4:1.

Step-by-step explanation:

Before reunification, assuming steady state conditions and equal saving rates, population growth rates, depreciation rates, and production function parameters (α = 1/2) for both East and West Germany, the given information states that output per capita in the West is twice that in the East. Using the Solow model, we can relate the difference in output per capita to differences in capital per capita and Total Factor Productivity (TFP).

The Solow model's steady-state output per capita equation for a given economy is y = (A * k^α), where y is output per capita, A is Total Factor Productivity, k is capital per capita, and α is the capital share in production. Given that α = 1/2 for both economies, and the output per capita in the West is twice that in the East, we can infer that the capital per capita in the West is √2 times the capital per capita in the East.

Now, considering that the production function remains the same for both economies and the capital share (α) is equal, the remaining difference in output per capita is due to differences in Total Factor Productivity. As the West's capital per capita is √2 times that of the East and output per capita is twice, the ratio of TFP between the West and the East can be calculated as 2 / (√2) = 4:1.

This calculation suggests that TFP in the West is four times higher than in the East, accounting for the observed differences in output per capita before the reunification.