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Suppose a consumer wants to buy a new house and has a budget of 50 million. The consumer cares only about the size (S) of the house and the quality of construction (Q) of the house. Assume that if the consumer wants one more unit of size, then the builder wants 10 million. If the consumer wants one more unit of quality, then the builder wants 5 million. (a) Draw the consumer's budget line for size and quality. Place size on the horizontal axis. (b) Suppose the consumer's preferences are such that the marginal rate of substitution is equal to (4S)/Q. What value of each index will the consumer like to have in her house? ' (c) Suppose the consumer's marginal rate of substitution is (S)/Q. What value of each index wil the consumer like to have in her house? The Pizza company's franchisees pay a royalty to the company that is typically equal to 4.5% of the revenues of the restaurant. Using your learnings from the managerial economics course, analyze the case and answer the following in detail - - Do you support the idea that the pizza company's franchises are losing money by selling $1 double cheese supreme pizza? What factors need to be considered in making this decision? - vr... are the relevant costs to a franchise for selling a double cheese supreme pizza? ( - Do you think that the goals of the pizza company and the franchises are different? If so, is there a problem with the misalignment of incentives? Can this be resolved