Suppose a nonlinear price discriminating monopolist faces an inverse demand​ curve: P = 175 - Q​
and can set three prices depending on the quantity a consumer purchases. The​ firm's profit​ is: ​
pi = P1 Q1 + P2 (Q2 - Q1) + P3 (Q3 - Q2) - mQ3
where p1 is the high price charged on the first units Q1 ​(first block) and p2 is a lower price charged on the next (Q1 - Q2) units and is the lowest price charged on the remaining (Q3 - Q2) units. Q3 is the total number of units actually​ purchased, and m ​= ​$50 is the​ firm's constant marginal and average cost. Using​ calculus, determine the​ profit-maximizing values for p1, p2​, and p3​, and the​ firm's profits.

Mr. smith recently faced a choice between being (a) an economics profes-sor, which pays $60,000/yr, or (b) a safari leader, which pays $50,000/yr. after careful deliberation, smith took the safari job, but it was a close call. "for a dollar more," he said, "i'd have gone the other way."now smith's brother-in-law approaches him with a business proposition. the terms are as follows: - smith must resign his safari job to work full-time in his brother-in-law's business.- smith must give his brother-in-law an interest-free loan of $100,000, which will be repaid in full if and when smith leaves the business. (smith currently has much more than $100,000 in the the business will pay smith a salary of $70,000/yr. he will receive no other payment from the business. the interest rate is 10 percent per year. apart from salary considerations, smith feels that working in the business would be just as enjoyable as being an economics professor. for simplicity, assume there is no uncertainty regarding either smith's salary in the proposed business or the security of his monetary investment in it. should smith join his brother-in-law and, if so, how small would smith's salary from the business have to be to make it not worthwhile for him to join? if not, how large would smith's salary from the business have to be to make it worthwhile for him to join?

Benton company (bc), a calendar year entity, has one owner, who is in the 37% federal income tax bracket (any net capital gains or dividends would be taxed at a 20% rate). bc's gross income is $395,000, and its ordinary trade or business deductions are $245,000. ignore the standard deduction (or itemized deductions) and the deduction for qualified business income. if required, round computations to the nearest dollar. a. bc is operated as a proprietorship, and the owner withdraws $100,000 for personal use. bc's taxable income for the current year is $ , and the tax liability associated with the income from the sole proprietorship is $ . b. bc is operated as a c corporation, pays out $100,000 as salary, and pays no dividends to its shareholder. bc's taxable income for the current year is $ , and bc's tax liability is $ . the shareholder's tax liability is $ . c. bc is operated as a c corporation and pays out no salary or dividends to its shareholder. bc's taxable income for the current year is $ , and bc's tax liability is $ . d. bc is operated as a c corporation, pays out $100,000 as salary, and pays out the remainder of its earnings as dividends. bc's taxable income for the current year is $ , and bc's tax liability is $ .

An outside manufacturer has offered to produce 60,000 daks and ship them directly to andretti's customers. if andretti company accepts this offer, the facilities that it uses to produce daks would be idle; however, fixed manufacturing overhead costs would be reduced by 75%. because the outside manufacturer would pay for all shipping costs, the variable selling expenses would be only two-thirds of their present amount. what is andretti's avoidable cost per unit that it should compare to the price quoted by the outside manufacturer?