The Riccati System and a Diffusion-Type Equation

We discuss a method of constructing solution of the initial value problem for duffusion-type equations in terms of solutions of certain Riccati and Ermakov-type systems. A nonautonomous Burgers-type equation is also considered.Comment: 11 pages, no figure

Government financing in an endogenous growth model with financial market restrictions

In this paper we develop an endogenous growth model with market regulations on explicitly modeled financial intermediaries to examine the effects of alternative government financing schemes on growth, inflation, and welfare. ; We find that in the presence of binding legal reserve requirements, a marginal increase in government spending need not result in a reduction in the rate of economic growth if it is financed with an increase in the seigniorage tax rate. Raising the seigniorage tax base by means of an increase in the reserve requirement retards growth and has an ambiguous effect on inflation. An increase in income tax—financed government spending also suppresses growth and raises inflation although not to the extent that the required seigniorage tax rate alternative would. Switching from seigniorage to income taxation as a source of government finance is growth-reducing but deflationary. From a welfare perspective, the least distortionary way of financing an increase in the government spending requirements is by means of a marginal increase in the seigniorage tax rate. Finally, under the specification of logarithmic preferences, the optimal tax structure is indeterminate.Finance, Public ; Fiscal policy ; Financial markets

On The Harmonic Oscillator Group

We discuss the maximum kinematical invariance group of the quantum harmonic oscillator from a view point of the Ermakov-type system. A six parameter family of the square integrable oscillator wave functions, which seems cannot be obtained by the standard separation of variables, is presented as an example. The invariance group of generalized driven harmonic oscillator is shown to be isomorphic to the corresponding Schroedinger group of the free particle.Comment: 11 pages, no figure

On government credit programs

Credit rationing is a common feature of most developing economies. In response to it, the governments of these countries often operate extensive credit programs and lend, either directly or indirectly, to the private sector. We analyze the macroeconomic consequences of a typical government credit program in a small open economy. We show that such programs increase long-run production if the economy is in a development trap and that such programs often lead to endogenously arising aggregate volatility. On the other hand, they may eliminate certain indeterminacies created by endogenous credit market frictions.Banks and banking, Central ; Credit ; Productivity