2 Growth

2.1. You found in the data that Country 1 GDP per capita grew at 6% in the last decade. Country
2 GDP per capita grew at 1.5%. Assume that this average growth rate will go on for the next 50
years. Imagine that the span between two generations is 50 years approximately (the grandfather is
50 years older than his grandchild). How much the life improves in country 1 and country 2 (you
should use time to double rule)? Compare and discuss the effect of the difference in the growth rate
on the standard of living (proxied by GDP per capita) in these two countries.

2.2. Consider the Solow economy where households save a constant fraction of their income at
each period, It = sYt, and where the production function is

3/; : AK?.5Lo.5
and the capital accumulates according to
Kt+1_ Kt : It ~ dKt
where d is the depreciation rate. Assume that the economy is initially in the steady state K

a) Analyze graphically the effect of a decrease in the savings rate on the level of capital (many
developed economies experimented diminished savings rate lately). Make conclusions about the level
of GDP per worker. Note: We assume that the number of workers is constant. 30 the ratio y
increases when Y increases and viceversa.

b) Assume that the savings rate is s (the original one). Analyze the effect of an increase in
technology level, A’ > A, on the growth rate of GDP per worker. You can use a graph or an equation
to explain your reasons.

2.3. Consider the Solow economy where households save a constant fraction of their income at
each period, and where the production function is

5/; : AK;).5Lo.5
and the capital accumulates according to
[(734.1 – Kt : It

When the level of capital is lower than some threshold value K, Kt < K, households are able to save
a fraction 3L of their income. When the level of capital is higher or equal to K, Kt 2 K, households
are able to save a fraction SH > 3L. Draw a diagram and see how an economy which is poor, Kt < K,
cannot escape from a poverty trap without international aid or without technological progress.