R & D Spending and product pricing

An optimal control model is developed that combines cost reduction through R & D with pricing. Price and R & D spending level are control variables and unit cost is a state variable. Analysis of the model reveals that if a firm has a positive discount rate, optimal R & D spending on cost reduction may grow to a peak before eventually declining. If the firm has a zero discount rate, optimal R & D spending declines monotonically across time. Optimal price declines monotonically in either case, in a direct relationship with unit cost.