A utility function is homothetic if any straight line through the origin cuts all indifference curves at points of equal slope: The MRS depends on the ratio y/x.
Prove that if an individual’s tastes can be represented by a homothetic indifference map then price and quantity must move in opposite directions; that is, prove that Giffen’s paradox cannot occur.

Allie and sarah decided that they want to purchase renters insurance for the apartment they share. they made a list of all of the items to be covered by the insurance policy, along with their estimated values. if the items to be covered total more than $3000, the insurance company charges an annual premium of 23% of the total value of the items. if the items to be covered total $3000 or less, the insurance company charges an annual premium of 20% of the total value of the items.

Richardson hired j.c. flood company, a plumbing contractor, to correct a stoppage in the sewer line of her house. the plumbing company's 'snake' device, used to clear the line leading to the main sewer, became caught in the underground line. to release it, the company excavated a portion of the sewer line in richardson's backyard. in the process, the company discovered numerous leaks in a rusty, defective water pipe that ran parallel with the sewer line. to meet public regulations, the water pipe, of a type no longer approved for such service, had to be replaced either then or later, when the yard would have to be excavated again. the plumbing company proceeded to repair the water pipe. though richardson inspected the company's work daily and did not express any objection to the extra work involved in replacing the water pipe, she refused to pay any part of the total bill after the company completed the entire operation. j.c. flood company then sued richardson for the costs of labor and material it had furnished. (c) for what, if anything, should richardson be liable? explain."

Over the past decade, brands that were once available only to the wealthy have created more affordable product extensions, giving a far broader range of consumers a taste of the good life. jaguar, for instance, launched its x-type sedan, which starts at $30,000 and is meant for the "almost rich" consumer who aspires to live in luxury. by marketing to people who desire a luxurious lifestyle, jaguar is using: