RESOURCE DEPLETION, NATIONAL-INCOME ACCOUNTING, AND THE VALUE OF OPTIMAL DYNAMIC PROGRAMS

Under assumptions satisfied by many economic problems, I derive a fund amental new equation for the time rate of change of the optimal value function of any optimal control problem. This is then applied to Hotel ling's model of the resource extracting firm. The precise differences between rent, depreciation, and depletion charges are discovered, the now and stock price appreciation rates are distinguished, and novel ch aracterizations of mind-value are derived. Most importantly, the corre ct contribution of mining to net national product (and to sustainable development) follows. In perfect foresight equilibrium, competitively managed mines can appreciate while being exhausted.