Jannett Highfill, Ph.D., M.A., Economics, Bradley University, 1501 W Bradley Ave, Peoria, IL 61625 and Michael McAsey, Ph.D., Mathematics, Bradley University, 1501 West Bradley Avenue, Peoria, IL 61625.
Consider a dynamic duopoly model where R&D “buys” a more reliable product under two competitive scenarios: the home firm competes with either a “complacent” foreign firm that does no R&D whatsoever or a “lockstep” foreign firm that improves its product at a rate proportional to the home firm’s improvement. On the demand side, there is a distribution of customers’ reservation price for a perfect product; products with less than 100% reliability impose a cost on customers and they adjust their reservation prices accordingly. Their decision is thus based on a “full quality price” which includes the purchase price and the expected cost of product failure. For both firms to have positive sales, the full quality price must be the same for both firm’s output. Firms maximize total (discounted) profits over an exogenous planning period. At each moment in time the firms play a two-stage game with order of play as follows. First, product reliability is chosen (with two possible scenarios) and then each firm chooses its own quantity taking the other firm's quantity (and both firms' qualities) as given in a Cournot-type competition. Quantities determine prices and thus profit margins and variable profits. Total profits are variable profits less the expenditures on R&D. Continuous time is assumed, so the home firm’s optimization problem is characterized by an optimal control problem with the home firm’s R&D spending as the control variable and product reliability as the state variable. The primary goal of the paper is to compare various firm metrics between the home and the foreign firm. The questions to be explored include which firm produces more, charges the higher price, and has the greater profit margins and variable profits. It is shown that difference in sales between firms is closely related to differences in margins; market outcomes like market sales and full quality price are also closely related. The difference in firm profits is related to the product of the determinants of the difference in sales and the determinants of the full quality price. A Monte Carlo analysis is used to investigate the relationship between parameter sets and these firm metrics.