2. Assume there are two types of consumers of rice. Type B has utility given by 4q - t where as type A has utility given by 3q -t, where q is the quantity consumed (pounds of rice perhaps) and t is the amount paid. The proportion of type B consumers is 1/2. His cost of producing q units is 1/2q2. (a) Assume the rice salesman can only sell one type of bundle. That is he offers quantity q at price t to all consumers. Which bundle will he offer? Hint: there are only two bundles in consideration. (b) Assume that the rice salesman can now offer two quantities of rice at different prices (qA, tA) and (qs, to). Write down the 4 inequalities on these parameters so that A buys (qA, tA) and B buys bundle (qs, to). (c) Solve for the optimal bundles (qa; tA) and (qs, to). (d) Which type receives positive consumer surplus? (e) What if the proportion of type B consumers was 9/10. What would be the optimal bundles (qA, tA) and (qa, ts)? (f) Assume again that the proportion of Type B consumers is 1/2. The type A consumer union gets together and approaches the rice salesman. They say we will give you the secret to identifying whether a consumer is of type A or B, if you make a payout to us type A consumers. After revealing the secret, the firm can engage in direct price discrimination. To be fair, the type A consumers demand that this payout be exactly type B's consumer surplus under the solution in c. This is a side payment and does not factor into the prices for type A or type B set after the secret is revealed. Would the salesman accept this trade? why or why not