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.

Azster inc. recorded sales revenue for the year that ended december 31, 2014 as $67,000. interest revenue of $5,300 and expenses of $14,000 were also recorded for the same period. what is aster’s net profit or loss?

The following transactions occurred during july: received $1,000 cash for services provided to a customer during july. received $4,000 cash investment from bob johnson, the owner of the business received $850 from a customer in partial payment of his account receivable which arose from sales in june. provided services to a customer on credit, $475. borrowed $7,000 from the bank by signing a promissory note. received $1,350 cash from a customer for services to be rendered next year. what was the amount of revenue for july?

Suppose you hold a portfolio consisting of a $10,000 investment in each of 8 different common stocks. the portfolio's beta is 1.25. now suppose you decided to sell one of your stocks that has a beta of 1.00 and to use the proceeds to buy a replacement stock with a beta of 1.55. what would the portfolio's new beta be? do not round your intermediate calculations.