Milton Friedman’s article on the optimum quantity of money has motivated much research since its publication. While most of the research has been on deterministic frameworks, a few models (e.g. Bewley 1983, Taub 1989) have extended the analysis to stochastic environments. The first two essays of the dissertation address the issue in two types of stochastic economies. In both the models, quadratic utility and linear constraints have been used to facilitate the use of Whiteman’s techniques (1985). The third essay introduces capital and derives the optimal rate of monetary policy in the presence of financial intermediaries. In the first essay a pure exchange model in which infinitely lived agents face stochastically varying endowments in each period is considered. In this model individuals can delay payment for purchases into the future with a credit card. It shows that the optimal rate of inflation is the same in a world where individuals are required to pay for their purchases immediately as in a world where they can delay payment with a credit card. Moreover, the optimal inflation rate may be positive or negative depending on the parameters of the model. Therefore, Bewley’s (1983) conjecture that deflation should proceed at a rate greater than the rate of time preference in a world of uncertainty is not generally true. The second essay derives the optimum quantity of money in a stochastic production economy. The optimum quantity of money literature largely ignores the effect of labor supply on money’s optimal rate of return. This paper examines the issue in an economy that is subject to stochastic shocks each period. It shows that incorporating production affects the optimal return on money in important ways. If there are individual specific shocks to preferences, then the optimal policy is highly inflationary. When individual preferences are subject to economy wide shocks, however, it is possible for either inflation or deflation to be optimal. The optimal policy depends on the weight individuals attach to the disutility of work and the weight individuals attach to the utility from holding money. Optimal policy responds positively to increases in the disutility from work and negatively to increases in the weight on consumption in the utility function. The paper therefore shows the sensitivity of the optimal policy on the way labor supply is modeled. Since such considerations do not arise in endowment economies, the optimal policy will generally change as one moves from endowment to production economies. In the third essay the Tobin effect and optimal monetary policy are analyzed when financial intermediaries develop endogenously. Providing a justification for the development of intermediaries similar to those found in the recent financial intermediation literature, we show that financial intermediation significantly affects investment decisions and monetary policy. In particular, the cost to intermediaries of providing substitutes of outside money play a critical role. Whether a decrease in the return on outside money will increase investment or not is found to depend on how the cost of providing alternative means of payment is affected. It is found that at low and moderate rates of inflation the Tobin effect remains valid. At high rates of inflation, however, the Tobin effect gets reversed. Further, since borrowers have private information regarding the outcome of the investment projects financed by the lenders, credit rationing may occur in equilibrium. We also derive the rate of return on money that maximizes social welfare. This optimal rate of return is not only dependent on the cost of the alternative means of payment, it also depends critically on whether credit is rationed in equilibrium or not. Finally, the paper highlights some of the distributional issues raised by a change in the rate of return on money. / Ph. D.