Economic growth and economic development 526

Introduction to Modern Economic Growth
equilibrium path in which consumption, capital and output all grow at the same rate
g ∗ ≡ (A − δ − ρ)/θ > 0 starting from any initial positive capital stock per worker
k (0), and the saving rate is endogenously determined by (11.17).

One important implication of the AK model is that since all markets are competitive, there is a representative household, and there are no externalities, the competitive equilibrium will be Pareto optimal. This can be proved either using First
Welfare Theorem type reasoning, or by directly constructing the optimal growth
solution.
Proposition 11.2. Consider the above-described AK economy, with a representative household with preferences given by (11.1), and the production technology
given by (11.6). Suppose that condition (11.12) holds. Then, the unique competitive
equilibrium is Pareto optimal.
Proof. See Exercise 11.2

Ô

11.1.4. The Role of Policy. It is straightforward to incorporate policy differences in to this framework and investigate their implications on the equilibrium
growth rate. The simplest and arguably one of the most relevant classes of policies
are, as also discussed above, those affecting the rate of return to accumulation. In
particular, suppose that there is an effective tax rate of τ on the rate of return from
capital income, so that the flow budget constraint of the representative household
becomes:
(11.18)

a˙ (t) = ((1 − τ ) r (t) − n)a (t) + w (t) − c (t) .

Repeating the analysis above immediately implies that this will adversely affect
the growth rate of the economy, which will now become (see Exercise 11.5):
(1 − τ ) (A − δ) − ρ
.
θ
Moreover, it can be calculated that the saving rate will now be

(1 − τ ) A − ρ + θn − (1 − τ − θ) δ
(11.20)
s=
,
θA
which is a decreasing function of τ if A − δ > 0. Therefore, in this model, the equi(11.19)

g=

librium saving rate is constant as in the basic Solow model, but in contrast to that
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