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谁能帮我做一下这道题，不甚感激！！
An economy has two kinds of consumers and two goods. Type A and type B consumers have the following
utility functions
U A(x1, x2) = 4x1 −（x1）^2/2+ x2,
U B(x1, x2) = 2x1 −（x1）^2/2+ x2.
Consumers can only consume nonnegative quantities. The price of good 2 is 1 and all consumers have incomes
of 100. There are N type A consumers and N type B consumers.
(a) Suppose that a monopolist can produce good 1 at a constant unit cost of c per unit and cannot engage in
any kind of price discrimination. Find its optimal choice of price and quantity. For what values of c will
it be true that it chooses to sell to both types of consumers?
(b) Suppose that the monopolist uses a “two-part tariff” where a consumer must pay a lump sum k in order
to be able to buy as much as he likes at a price p per unit purchased. Consumers are not able to resell
good 1. For p < 4, what is the highest amount k that a type A is willing to pay for the privilege of buying
at price p? If a type A does pay the lump sum k to buy at price p, how many units will he demand?
Describe the function that determines demand for good 1 by type A consumers as a function of p and k.
What is the demand function for good 1 by type B consumers? Now describe the function that determines
total demand for good 1 by all consumers as a function of p and k.
(c) If the economy consisted only of N type A consumers and no type B consumers, what would be the
profit-maximizing choices of p and k?
(d) If c < 1, find the values of p and k that maximize the monopolist’s profit subject to the constraint that
both types of consumers buy from it.
(e) For c = 0 calculate consumer surplus, producer surplus, and dead weight loss for both c. and d.
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