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Suppose a firm faces two customers: Larry and James.

1. Suppose a firm faces two customers: Larry and James. Each of these consumers has the utility function u(x)+m, where x is the level of consumption of the good produced by the firm and m is the money left over for the other purchases. Both consumers initially have $100 to spend. For Larry, the function u is given by u(x)=6x-x2. For James, it is u(x)=8ln(x+1). This firm has constant marginal costs equal to $2.

a. For each consumers, what is the best (first-degree price discrimination, profit maximizing) offer to make to that consumer? What is the total profit dealing with these two consumers?
b. Suppose the firm sets an entry fee plus per-unit price for each consume. It can tailor the entry fee and the per-unit price to the individual consumer. What are the best (profit-maximizing) entry fees and per-unit prices for it to set? What is the total profit in this case?
c. Suppose the firm must charge a single linear price for its output, in nondiscriminatory fashion. What is the best (profit-maximizing) price for it to charge? What is the total profit?

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