Question

Exercise 1: Solow model .
Consider an economy whose production function is defined by Y (t) = F (K (t), L (t)) = K (t) 1 − α · L (t) α.
with 0 <α <1. In this economy, the population grows at the following rate: L (t) = n + β where n and
β are strictly positive constants and k (t) represents capital per capita: k (t) = L (t). Moreover,
a constant part of the product is saved and is immediately invested: S (t) = I (t) = s · Y (t) with s
the savings rate. Finally, capital depreciates at the rate δ.

QUESTION: The economy has reached stable steady state (different from 0) if β = 0. This economy is experiencing an influx of migrants whose economic characteristics are identical to the natives (same savings rate, same mode of life, same natural growth rate). What are the immediate effects on steady state and per capita growth rate? Then, the effects on the growth rate of the economy in the long term?

Answer 1

Initially equilibrium is at E and steady state level of capital per capita and income per capita is given by Y and A.

The influx of migrants will mean a higher population growth as a result the immediate impact will be declining capital per capita.

In the long run the new steady state will be at lower than earlier level of both capital per capita and income per capita I.e corresponding to G . New steady state k will be Y₀ and y will be A_0.