Introduction to Modern Economic Growth where τ j is the tax on investment This tax varies across countries, for example because of policies or differences in institutions/property rights enforcement Notice that + τ j is also the relative price of investment goods (relative to consumption goods): one unit of consumption goods can only be transformed into 1/ (1 + τ j ) units of investment goods Note that the right hand side variable of (8.40) is still Yj , which implicitly assumes that τ j Ij is wasted, rather than simply redistributed to some other agents in the economy This is without any major consequence, since, as noted in Theorem 5.2 above, CRRA preferences as in (8.38) have the nice feature that they can be exactly aggregated across individuals, so we not have to worry about the distribution of income in the economy The competitive equilibrium can be characterized as the solution to the maximization of (8.38) subject to (8.40) and the capital accumulation equation With the same steps as above, the Euler equation of the representative household is ả ả à (1 ) AHj C˙ j = −δ−ρ Cj θ (1 + τ j ) Kj Consider the steady state Because A is assumed to be constant, the steady state corresponds to C˙ j /Cj = This immediately implies that Kj = (1 − α)1/α AHj [(1 + τ j ) (ρ + δ)]1/α So countries with higher taxes on investment will have a lower capital stock in steady state Equivalently, they will also have lower capital per worker, or a lower capital output ratio (using (8.39) the capital output ratio is simply K/Y = (K/AH)α ) Now substituting this into (8.39), and comparing two countries with different taxes (but the same human capital), we obtain the relative incomes as ả 1−α + τ0 α Y (τ ) = (8.41) Y (τ ) 1+τ So countries that tax investment, either directly or indirectly, at a higher rate will be poorer The advantage of using the neoclassical growth model for quantitative evaluation relative to the Solow growth model is that the extent to which different types of distortions (here captured by the tax rates on investment) will affect income 403