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Question 4. A monopolist sells a product that can be used for two periods. lItiustorrlers have a par-period willingness to pay that is evenly distributed between D and 1 iii]. That Is, the mass of customers willing to pay between \"'1. and w,, to use the product for one period is w" iii-L for any ii 5 isL 5 w\" 5 Inn. The product has zero fixed cost and a constant marginal cost of Iii]. Suppose both the monopolist and the customers do not discount the future. The monopolist sells the product in periods 1 and 2 for prices 311 and P2. respectively. a} Suppose the rm decides In period 1 how much to sell in both periods and cannot change these quantities later. Calculate the quantity sold in each period and the firm's total profits. (Hint: The monopolist cannot sell negative quanties.) b} Now. suppose the rm is able to adjust production in period 2. Use backward induction to calculate the quantities acid in each period and the rm's prots. c) Based on your preyious calculations. does the rm benet from being able to adjust production in period 2? if so. how much would the firm be willing to pay for a technology that allows it to adjust production in each period? Explain. Suppose now that the firm decides to lease the product in each period for prices ii1 and P3. This means that customers pay a price P1 if they wish to have the product in period 1. At the end of the period. they must retum it to the firm. If they wish to use the product in period 2. customers need to pay the price P2. is before. producing the product in either period costs 4D. If the rm produces it in period 1, it can lease the product in both periods. If the rm produces it in period 2. it can only lease the product In period 2. d} calculate the quantity leased In each period. How does the firm's prot from leasing compare with the ones from parts (a) and (b)