a. show that consumer surplus for type i is equivalent to the increase in utilit

a. show that consumer surplus for type i is equivalent to the increase in utility at the optimal choice from optimally consuming q relative to q=0.
b. what are the profit maximizing uniform price quantities and profits.
c. if a monopolist can stop arbitrage between two types what are the prices quantities and profits if she practices market segmentation. Explain why output is the same and profits dont increase when the monopolist switches from a uniform price to market segmentation.
d. Suppose the monopolist can charge type-specific two-part tariffs. Find the meanu of profit-maximizing two part tariffs. Explain why it is not incentive compatible.
e. Find the profit maximizing two part tariff if the monopolist cannot distinquish types. Verify that the usage charge i greater than marginal cost but les than the monopoly price.
f. suppose that the monopolist cannot distingush consumers by typebut it can stop arbitrage between customers. How much does it profit increase if it makes the incentive compatibility constraint for the high types bind? Provide them with efficient output?
i. suppose that the monopolist cannot distinguish consumer by type but it can stop arbitrage between customers. What menu of payments and quantities should it offer its customers. Verify that consumption of the high types is efficient but consumption by the low type is too small.