Sol Microsystems has recently invented a new language, Guava, which runs on a proprietary chip, the Guavachip. The chip can only be used to run Guava, and Guava can only run on the Guavachip. Sol estimates that if it sells the chip for a price pc and the language for a price pg, the demand for the chip-language system will be
x = 120 − (pc + pg).
(a) Sol initially sets up two independent subsidiaries, one to produce the chip and one to produce the language. Each of the subsidiaries will price its product so as to maximize its profits, while assuming that a change in its own price will not affect the pricing decision of the other subsidiary. Assume that marginal costs are negligible for each company. If the price of the language is set at pg, the chip company’s profit function (neglecting fixed costs) is
(b) Differentiate this profit function with respect to pc and set the result equal to zero to calculate the optimal choice of pc as a function of pg.
(c) Now consider the language subsidiary’s pricing decision. The optimal choice of pg as a function of pc is
(d) Solving these two equations in two unknowns, we find that pc = _________ and pg = ________, so that pc + pg = ____________
(e) Sol Microsystems decides that the independent subsidiary system is cumbersome, so it sets up Guava Computing which sells a bundled system consisting of the chip and the language. Let p be the price of the bundle. Guava Computing’s profit function is
(f) Differentiate this profit with respect to p and set the resulting expression to zero to determine p = ____________
(g) Compare the prices charged by the integrated system and the separate subsidiaries. Which is lower? ____________ Which is better for consumers? __________ Which makes
more profit? __________