Economic growth and economic development 63
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Introduction to Modern Economic Growth
F(K, L, A)
F(K, L, A)
K
0
K
0
Panel B
Panel A
Figure 2.1. Production functions and the marginal product of capital. The example in Panel A satisfies the Inada conditions in Assumption 2, while the example in Panel B does not.
is given by
(2.7)
K (t + 1) = (1 − δ) K (t) + I (t) ,
where I (t) is investment at time t.
From national income accounting for a closed economy, we have that the total
amount of final goods in the economy must be either consumed or invested, thus
(2.8)
Y (t) = C (t) + I (t) ,
where C (t) is consumption.1 Using (2.1), (2.7) and (2.8), any feasible dynamic
allocation in this economy must satisfy
K (t + 1) ≤ F [K (t) , L (t) , A (t)] + (1 − δ) K (t) − C (t)
for t = 0, 1, .... The question now is to determine the equilibrium dynamic allocation
among the set of feasible dynamic allocations. Here the behavioral rule of the constant saving rate simplifies the structure of equilibrium considerably. It is important
to notice that the constant saving rate is a behavioral rule–it is not derived from
the maximization of a well-defined utility function. This means that any welfare
1In addition, we can introduce government spending G (t) on the right-hand side of (2.8).
Government spending does not play a major role in the Solow growth model, thus we set it equal
to 0 (see Exercise 2.3).
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