Dynamic cash discounts when sales volume is stochastic

In this paper, a dynamic terms of sale model is developed which suggests deep cash discounts can be partially explained by the positive relationship between the shadow value of sales and the optimal cash discount. The effect of sales volume uncertainty on the magnitude of cash discounts is also explored. Numerical results suggest the relationship between uncertainty and cash discounts is nonlinear. The model is then re-cast as a dynamic, differential game between two competing suppliers who use cash discounts to entice buyers. The results suggest that when firms are allowed to behave strategically, cash discounts are always larger as a result.