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Let’s assume the market is a monopoly. The monopolist cannot…
Let's аssume the mаrket is а mоnоpоly. The monopolist cannot distinguish between two separate groups of consumers: standard consumers (high valuation) and student consumers (low valuation). The standard consumer (denoted with ) has a gross consumer surplus on the subscription as .and the student consumer (denoted with ) has a gross consumer surplus on the subscription as . Each group has 50 people and 100 people, which means and . The monopolist has a cost function for . The firm don't know the consumer's type so it will provide the menu and let consumers choose the goods. Assume that both types of consumer prefer the first package. a) (20 points) Set up the firm’s problem and solve for the optimal packages and . Hint: When setting up the firm’s problem, you do not need to write down all four constraints and show which ones hold and which ones do not. You can just write down the ”relaxed version” as is done on the lecture notes. b) (5 points) With these results, compute the firm’s profit. c) (5 points) Compute the consumer surpluses for each type and verify the consumer surplus for the lower type is zero.
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