The literature has in general taken the model of capital accumulation with a unique final consumption good as a canonical framework to study the patterns of economic growth. In particular, this model has been widely used to analyze the dynamic effects of shocksin fundaments and, in special, for the economic policy analysis.
The main feature of this model is that the economic dynamics is fully driven by the returns to capital. As the seminal contribution of Ramsey (1928) states, the optimal intertemporal allocation of consumption and investment leads the growth of consumption expenditure to only depend on the net interest rate. In this paper we assert that this standard result can not be generalized to models that allow for several heterogeneous consumption goods. More precisely, the aforementioned benchmark model may be not appropriate to study the dynamic effects of those shocks that have permanent effect on the sectoral composition of consumption. To show this point, we characterize the properties of the transitional dynamics of a growth model where individuals derive utility from the consumption of two heterogeneous goods.
Recently, the growing interest for issues on structural change and trade has extended the use of multisector growth models with heterogeneous consumption goods. However, this literature in general obtains as a by product that the dynamics of the aggregate variables are identical to those predicted by the model with a unique consumption good: the growth rate of consumption expenditure only depends on the marginal product of capital.
According to this result, the process of convergence would thus only be determined by the returns to capital with independence of the number of consumption goods. We instead argue that this isomorphism between the two types of models is a consequence of the restricted assumptions taken in the multisector models: the utility function is additively separable in consumption goods, or goods are produced by using technologies with identical capital intensities. By relaxing these assumptions, we first demonstrate that the expenditure growth rate depends not only on the interest rate, but also on the growth rate of relative prices of goods. Therefore, the process of convergence in a general multisector growth model is directly driven by two forces: the returns to capital and the dynamic adjustment of the relative prices. Our main purpose in this paper is to analyze how the presence of the second force modifies the patterns of economic dynamics.
The effect of the interest rate on consumption growth is measured by the intertemporal elasticity of substitution (IES, henceforth), whereas the growth effect of the variation in the relative price of goods is measured the Edgeworth elasticity between goods. In fact, we show that how the growth rate of relative prices moves the expenditure growth rate depends on the sign of the Edgeworth elasticity. When the two consumption goods are Edgeworth substitutes (complementary), the variation of the relative prices affects positively (negatively) the expenditure growth rate. By the contrary, if the consumption goods are Edgeworth independent, then the growth rate of prices has not directly effect on the expenditure growth rate. Intuitively, the increase in the relative price of one good reduces the demand of this good, which increases (decreases) the demand of the substitute (complementary) goods.
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