Problem Set 2 due Tuesday, Feb 24 Problem 1. Consider a monopolist (call them the manufacturer) who produces SOMA. SOMA is bought by another...

Problem 1. Consider a monopolist (call them the manufacturer) who produces SOMA.SOMA is bought by another monopolist (call them the retailer) who turns SOMA intoAMOS for sale to customers. 1 unit of SOMA can be turned into 1 unit of AMOS at nocost.If the retailer charges a price p for AMOS, the demand for AMOS will be 100 − p. Theelasticity of demand at price p in this case is p/(100 − p).1. Let c be the price per unit that the manufacturer charges the retailer for SOMA. Use themarkup formula to determine what price (as a function of c) the retailer should charge hercustomers so as to maximize profit.2. The manufacturer produces SOMA at a constant marginal cost of $1 a unit. What shouldhe set c at so as to maximize his profit? What will his maximum profit be?3. Now suppose that the manufacturer were to integrate with the retailer, .i.e., the manufacturersells AMOS directly to the customer. What will the maximum profit of the integratedenterprise be?Problem 2. An author has signed a contract in which the publisher promises to pay her$10,000 plus 20 percent of gross receipts from the sale of her book. Suppose both publisherand author care only for their individual financial return on the project. Is it true that theauthor will prefer a higher book price than the publisher? (Hint: Think about how the costsare different for them.)Problem 3. You are the monopoly seller of computers and monitors. Remarkably, the costsof production for both products are zero. You sell to a market consisting of two segments(A and B). The RP of each segment for computers and monitors are shown in the tablebelow.Computer MonitorA’s RP $2000 $200B’s RP $1500 $300There are an equal number in each segment. It is possible for a buyer to purchase one of theproducts and not the other.1. If you were selling computers and monitors separately, what price should you charge foreach to maximize revenue?2. If you were to bundle the computer and monitor together and sell only the bundle, whatprice should you set to maximize revenue?3. Could you generate more revenue than in parts (1) and (2) through mixed bundling?Problem 4. Robinson Crusoe is the monopoly seller of a goat that produces s units of milk.s is a number between 0 and 1 and is an indicator of quality of the goat. Friday is a potentialbuyer. If both of them know s, then Crusoe has a RP of θ1s while Friday has an RP of θ2s.Assume θ2 > θ1 and that these are commonly known. However while Crusoe perfectly knowsthe quality s, Friday only knows that s is a random draw from a uniform distribution on theinterval [0, 1].1. Suppose θ1 = 1.5 and θ2 = 2. Do Crusoe and Friday trade? Provide a clear explanation.2. Suppose θ1 = 1 and θ2 = 3. Do Crusoe and Friday trade? Provide a clear explanation.