1. Vertical Relations Suppose Volkswagen is the sole manufacturer of electric go-karts. The inverse demand for electric go-karts is: P = 10 - y The marginal and average cost of producing go-karts is $2 per go-kart. Volkswagen both sells and manufactures go-karts. The marginal cost of selling the go-kart is zero. (a) What is Volkswagen's profit maximizing price? How many go-karts would it sell and what are its profits? Now suppose Volkswagen only wishes to manufacture go-karts, not distribute them. Instead, it hires Zimbrick to be the sole distributor of its go-karts in Colubmus. Assume that the marginal cost of selling go-karts is zero for Zimbrick. Let W denote the wholesale price that Volkswagen charges Zimbrick per go-kart. (b) Formulate Zimbrick's profit maximization problem and determine its demand for go-karts treating the wholesale price W as a variable. (c) Formulate Volkswagen's optimization problem and determine the optimal whole- sale price for a go-kart. How many go-karts does Volkswagen sell and what are its profits? Explain why Volkswagen's profits are lower than in the first part of this question. (d) Suppose that Volkswagen allows any car dealership in Columbus to sell go-karts. How could Volkswagen benefit from more dealers? Can you think of reasons it might be hurt by selling to more dealers