Economic growth and economic development 178

Introduction to Modern Economic Growth
give a flavor of these models, consider the following simple game of investment:
everybody else → high investment
individual ↓
high investment
yH , yH
low investment

yL, yL − ε

low investment
y L − ε, y L
yL, yL

The top row indicates whether all individuals in the society choose high or low
investment (focusing on a symmetric equilibrium). The first column corresponds to
high investment by all agents, while the second corresponds to low investment. The
top row, on the other hand, corresponds to high investment by the individual in
question, and the bottom row is for low investment. In each cell, the first number
refers to the income of the individual in question, while the second number is the
payoff to each of the other agents in the economy. Suppose that y H > y L and ε > 0.
This payoff matrix implies that high investment is more profitable when others are
also undertaking high investment, because of technological complementarities or
other interactions.
It is then clear that there are two (pure-strategy) symmetric equilibria in this
game. In one, the individual expects all other agents to choose high investment and
he does so himself as well. In the other, the individual expects all others to choose
low investment and it is the best response for him to choose low investment. Since
the same calculus applies to each agent, this argument establishes the existence of
the two symmetric equilibria. This simple game captures, in a very reduced-form
way, the essence of the “Big Push” models we will study in Chapter 22.

Two points are worth noting. First, depending on the extent of complementarities and other economic interactions, y H can be quite large relative to y L , so there
may be significant income differences in the allocations implied by the two different
equilibria. Thus if we believe that such a game is a good approximation to reality
and different countries can end up in different equilibria, it could help in explaining
very large differences in income per capita. Second, the two equilibria in this game
are also “Pareto-ranked”–all individuals are better off in the equilibrium in which
everybody chooses high investment.
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