JOURNAL OF POLITICAL ECONOMY fraction of capital devoted to consumption, dr is constant, the relative price of capital declines at the rate g, =(a- 1)g2. Given that p, is not constant, the real interest rate for loans denominated in capital goods (ra)is different from that of consumption-denominated loans (ra). Since the (net) marginal productivity of capital in the sector that roduces capital goods is constant and equal to A-8,, equilibrium the capital market requires that rx =A-82.A standard arbitrage argument implies that the interest rate for consumption-denom- inated loans is related to ra by ra =ru+ ge. The steady-state value of ra is chen given by r =A-8+(a-1)g Faced wich this interest rate, households choose to expand con sumption at rate ge=(r-pa. Substituting r, by its expression and ge=ag, yield the steady-state value of income measured in terms of consumption goods, which is given by Y,=C,+Pl-8, Z, grows at rate There are three properties of the competitive equilibrium that are worth noting. First, this economy has no transitional dynamics;it expands always at rate gy. Second, the parameter B and the amount of land services available in each period()are absent from the growth rate expression. They determine che level of the consumption path but not the growth rate, suggesting that countries with different endowments of natural resources will have different income levels but not different growch rates. Third, although CI and I, grow at different rates, their relative price adjusts in such a manner that the shares of investment and consumption in output(p, L,/Y and C/ are conscant The influence of preferences and technology on the rate of expan sion of this economy is rather intuitive. The rate of growth is higher the greater the net marginal product of capital (A-8)and the elasticity of intertemporal substitution(1/o)and the lower the pure rate of time preference(). 3 Equation(2)provides no reason to believe that unceasing growth is more likely than perpetual regression; whether the economy grows )In order for lifetime utility (U in [11)to be finite, it is necessary that p >a( JXA-8, )to ensure that the growth rate of momentary utiliy, (1 a)ge is lower than the discount rate, p. If (1-ag. 2 p, there is a set of feasible paths among which houscholds are indifferent because they all yield infinite utility. The requirement p I -(A -8, )is also necessary and sufficient for the transversality condition assoc ated with the households' maximization problem to hold. In all the other models assumed to hold per, this type of condicion, although not stated explicitly, is implicitly studied in this
LONG-RUN POLICY ANALYSIS or regresses depends on whether A-8,-p is positive or negative However, in the derivation of (2), the irreversible nature of invest- ments in Z was ignored. This irreversibility implies that the lowest feasible growth rate of output is-a8,, which corresponds to the path in which investment is zero. When the value of g, implied by(2)is lower than -a8u, the economy reverts to a corner solution in which investment is zero and the growth rate is -a8 A. Long-Run Effects of Taxation To illustrate the effects of taxation on this model, two proportional taxes will be introduced: one on consumption at rate t, and the other n investment at rate T,. The analysis will be undertaken in a closed economy context, but it is valid in a world of open economies con nected by international capital markets if all countries follow the worldwide tax system. Government revenue, measured in terms of the consumption good is given by T,=T C:+7p.. To isolate the effects of taxation fr those of government expenditures, I assume throughout the paper that this revenue is used to finance the provision of goods that do not affect the marginal utility of private consumption or the production possibilities of the private sector The only equation used to derive (2)affected by the presence of taxation is the one that determine hich is not by (1+7)(1+r2)=A+(1-8)+r(1-8) The left-hand side of this expression represents the opportunity cost of investing one unit of capital. The right-hand side is the result of using that unit of capital to produce during one period and selling the nondepreciated capital. The term T,(I-8)reflects the invest ment tax refund associated with that sale The growth rate of income is in this case [A/(1+-)-8,-p -as where the possibility of a corner solution in which the nonnegativity estriction on investment is binding, and hence g2 --82, is made explicit. Expression(3) shows that the influence of an inctease in T, on the growth rate is the same as that of a decrease in A: a higher f According to this system, investors pay taxes in their own country on capital riginated abroad but receive credit for paid abroad on the same ee Jones and Manuelli(1990) and King and Rebelo(1990) for discussions cffects of taxation in open economies
JOURNAL OF POLITICAL E investment tax rate leads to a lower growth rate in economies with strictly positive investment levels. In contrast, permanent changes in T. have effects that are similar to changes in B: they do not affect the rate of growth but solely the level of the consumption path.A onsumption tax does not distort the only decision made by agents in this economy, the decision of consuming now versus later, it is equivalent to a lump-sum tax. Since a proportional tax on Income amounts to taxing consumption and investment at the same rate, an increase in the income tax rate induces a decrease in the rate of growth of this economy In Solows(1956)original version of the neoclassical growth model, the savings rate(s)was fixed at an exogenous level. In that context Solow concluded that the savings rate determines only the stead state levels of the diffetent variables but not their growth rates. In is model, although the speed of convergence toward the steady state depends on s, the steady-state growth rate is exogenous and all s does is determine the capital/labor ratio The simple model just described can be used to illustrate that this result is an artifact of the exogenous nature of steady-state growth in the neoclassical model. Suppose that the savings rate, defined as the fraction of net output devoted to net investment, is exogenously fxed t the level s 20 rather than being chosen to maximize(1).This implies that Z, -sY /p Following the same steps as before, we can compute the steady-state growth rate as This expression implies that higher savings rates lead to higher growth rates, which accords with the positive correlation of these wo variables in the data(see Romer 1987). The concept of savings employed here is, however, broader than usual since Z composite of physical and human capital and hence s is the fraction of total resources devoted to both of these accumulation activities. I der to study the effects of ch in che defined in stricter sense that encompasses only physical capital accumulation,it is necessary to distinguish between these two types of accumulation This is one of the objectives of the next section 'This is also the mechanism at work in Bo economy the production technology is lineat, so an i acts as