Economic growth and economic development 446

The increase in consumption for each generation can be allocated equally during the two periods of their lives, thus necessarily increasing the utility of all generations.. This variatio

Introduction to Modern Economic Growth (which is clearly feasible) This implies the following changes in consumption levels:

∆c (T ) = (1 + n) ∆k > 0

∆c (t) = − (f0(k∗ − ∆k) − (1 + n)) ∆k for all t > T The first expression reflects the direct increase in consumption due to the decrease in savings In addition, since k∗ > kgold, for small enough ∆k, f0(k∗− ∆k)−(1+n) < 0, thus ∆c (t) > 0 for all t ≥ T , and explains the second expression The increase in consumption for each generation can be allocated equally during the two periods of their lives, thus necessarily increasing the utility of all generations This variation clearly creates a Pareto improvement in which all generations are better off This establishes:

Proposition 9.6 In the baseline overlapping-generations economy, the com-petitive equilibrium is not necessarily Pareto optimal More specifically, whenever

r∗ < n and the economy is dynamically inefficient, it is possible to reduce the capital stock starting from the competitive steady state and increase the consumption level

of all generations

As the above derivation makes it clear, Pareto inefficiency of the competitive equilibrium is intimately linked with dynamic inefficiency Dynamic inefficiency, the rate of interest being less than the rate of population growth, is not a theoretical curiosity Exercise 9.8 shows that dynamic inefficiency can arise under reasonable circumstances

Loosely speaking, the intuition for dynamic inefficiency can be given as follows Individuals who live at time t face prices determined by the capital stock with which they are working This capital stock is the outcome of actions taken by previous generations Therefore, there is a pecuniary externality from the actions

of previous generations affecting the welfare of the current generation Pecuniary externalities are typically second-order and do not matter for welfare (in a sense this could be viewed as the essence of the First Welfare Theorem) This ceases to

be the case, however, when there are an infinite stream of newborn agents joining the economy These agents are affected by the pecuniary externalities created by

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