INTRODUCTION

Imagine a planner undertaking an inter-temporal optimization exercise. He is morally at ease with the objective function and he is confident that he has captured all technological and institutional constraints accurately. These institutional constraints consist of, among other things, the responses of the private sector to the planner's decisions. The extent to which the planner can exercise control in the economy can be great or small, depending on the economy in question. Assume next that there is no uncertainty. It is of course well known that if an optimum exists, then under certain circumstances (for example, the objective function is concave and the constraint sets are convex) it can be decentralized, in the sense that there exists a system of inter-temporal shadow prices which, if used in investment decisions, can sustain the desired programme. Let the planner choose a good as the numeraire. The shadow own rate of return on the numeraire is usually called the social rate of discount. It is the percentage rate at which the present-value shadow price of the numeraire falls at any given instant. Thus, let st denote the present-value shadow price of the numeraire at t (that is, the amount of numeraire at t = 0 to be paid for a unit of the numeraire to be delivered at t along the decentralized optimal programme). Then, assuming continuous time and a differentiable shadow price, – ṡt/st is the social rate of discount at t.