engleski

Stackelberg equilibrium of the client and the producer of embedded software

In the Stackelberg leadership model the follower firm acts like in the Cournot model and for the given level of production of the leader firm determines its own production level which maximizes economic profit. The leader firm chooses quantity knowing that the follower firm will react to it according to its reaction function. Many economic phenomena have Stackelberg model structure and in this paper the relationship between the client and the producer of embedded sofware is modeled using this approach. The product quality affects the likelihood of product safety and the consumers' utility but depends on the invested effort. The goal is to find an equilibrium in the Stackelberg model where the client is the leader, and the producer is the follower. In the first step, the producer chooses the number of units of labor for the given price of a product in order to maximize the expected profit. In this way the producer indirectly affects the software quality. In the paper the effect of the product price change on producer's reaction is analysed. The comparative statics results confirm our intuition. The higher the product price, the greater the level of labor units employed by the producer and the better the product. Increase in labor costs has opposite effect on the producer's decision. In the second step the consumer determines the product price in order to maximize his or her expected utility. This decision is affected by the producer's reaction or the price effect on the product quality. The consumer's utility and the software quality are usually directly related in the existing literature. In this paper, this relationship is complemented by the probability of product safety. Theoretical optimization models which are solved by the client and the producer are illustrated numerically and the total welfare in the Stackelberg and the cooperative equilibrium is compared. The effect of the change in relationship between the employed labor units and the software quality on the given results is analysed. According to our numerical example, the more favorable this relationship is, the higher is the client's and the producer's welfare in the Stackelberg equilibrium. Even though fewer workers are employed, produced software is better. The total welfare loss is smaller due to more dominant effect of more favorable relationship between employees and the software quality in the Stackelberg equilibrium than in the cooperative equilibrium. Given the sensitivity of the results, future research should be devoted to examining the functional relationship between given variables in specific phenomena. The cost of software maintenance could also be taken into account.

embedded software; Stackelberg equilibrium; producer's reaction function; comparative statics analysis; welfare loss

nije evidentirano