Economics 3213

Professor Xavier

PROBLEM SET 2: THE JUNGLE BOOK

Question 1: The Bare Necessities.

(i) In the real world, between 1960 and 2006 the growth rate of real GDP per capita across countries shows little or NO relation to the level of real per capita GDP in 1960. In other words, it is NOT TRUE that, poor countries tend to grow faster than rich countries. Does this finding conflict with the neoclassical model of Solow and Swan?

(ii) Define the concepts of Absolute and Conditional Convergence. Does  the AK model of endogenous growth predict convergence (conditional or absolute)? Explain why.

Question 2: Colonel Hathi's March

In class we assumed that the savings rate "s" was a constant. This was true for the Solow-Swan growth model as well as for the AK model. Imagine now that the saving rate is a decreasing function of k.

(i) Can you give a reason why the saving rate is a decreasing function of k?

(ii) What would be the "convergence" prediction of a model with an AK technology and a saving rate which is a decreasing function of k?Would the model still predict NO convergence? If it predicts convergence, does it predict absolute or conditional convergence?

(iii) Would a version of the Solow-Swan model with decreasing saving rates still predict convergence? Would the prediction be faster or slower convergence than in the case of constant savings rate? Why?

Question 3: I Wanna be Like You.

In class we assumed that the rate of population growth "n" was a constant. This was true for the Solow-Swan growth model as well as for the AK model. Imagine now that the rate of population growth is a function of k.

(i) Do you think fertility should be an function of k? An increasing or decreasing function of k? (Think of the costs and benefits of having children, and the reasons that lead people to purchase and produce kids) In the real world, do rich societies have larger or smaller fertility rates?

(ii) Intuitively, do you think mortality should be an function of k? An increasing or decreasing function of k? In the real world, do rich societies have larger or smaller mortality rates?

(iii) Intuitively, do you think net migration is a function of k? An increasing or decreasing function of k? In the real world, do rich societies tend to receive or to send migrants?

Imagine that the rate of population growth "n" is an INCREASING function of k.

(iv) What would be the "convergence" prediction of a model with an AK technology and a population growth rate which is an increasing function of k? Would the model still predict NO convergence? If it did predict convergence, would it predict absolute or conditional convergence?

(v) Would a version of the Solow-Swan model with increasing population growth rates still predict convergence? Would the prediction be faster or slower convergence than in the case of constant population growth rate? Why?