The Role of Money in a Simple Growth Model: Note - Marxsen, William B (American Economic Review, 1978)
In a recent article in this Review, David lIevhari and Don Patinkin (hereafter noted L-P) develop an equilibrium growth model for a simple economy in which money is treated as a productive factor, entering an aggregate production function. In their policy section, they are unable to determine the effects of an increase in the exogenously determined rate of inflation on the equilibrium capital and real-balance intensities. They are also unable to establish whether or not steady-state equilibrium is stable. The purpose of this note is to extend their dynamic analysis and to show that 1) the effects of a change in the rate of inflation are more or less predictable, and 2) steady-state equilibrium can be expected to be stable. The L-P model can be briefly summarized. Assume a growing neoclassical economy where Y = G(K, M/P, N), and where Y, K, M/P, and N represent real output, the stock of physical capital, the real money stock, and the labor force, respectively. Assume further that G is linear homogeneous and twice continuously differentiable. The function can therefore be written y = g(k, m), where y, k, and m are Y/N, K/N, and M/PN, respectively. Assume g is wellbehaved such that gi > 0, gii 0. Let the labor force grow at some exogenously determined exponential rate n. Money is costlessly produced by the government and injected into the economy via transfer payments to the public. In order to avoid stability problems noted by Miguel Sidrauski, it is assumed that the rate of nominal expansion is altered by the government in order to maintain a constant target rate of inflation.' The rate of nominal expansion is u = DM/M, where D denotes the time derivative of the variable which follows it. The rate of inflation is p = DP/P. It follows that D(M/P) = (u p)M/P. From this and the labor force growth assumption, it follows that the rate of growth of the real per capita money stock is