In response to increased consumer demand for healthful beverages, companies like Coca-Cola and Pepsi introduced new product lines like fruit juice to their product mix.

Define the marginal rate of substitution between two goods (x and y). if a consumer’s preferences are given by u(x,y) = x3/4y1/4, compute the consumer’s marginal rate of substitution as a function of x and y. calculate the mrs if the consumer has chosen to consumer 48 units of x and 16 units of y. show your work. (use the back of the page if necessary.

With signals from no-claim bonuses and deductibles, a. the marginal cost curve for careful drivers lies to the left of the marginal cost curve for aggressive drivers b. auto insurance companies insure more aggressive drivers than careful drivers because aggressive drivers have a greater need for the insurance c. the market for car insurance has a separating equilibrium, and the market is efficient d. most drivers pay higher premiums than if the market had no signals

You are the manager of a large crude-oil refinery. as part of the refining process, a certain heat exchanger (operated at high temperatures and with abrasive material flowing through it) must be replaced every year. the replacement and downtime cost in the first year is $165 comma 000. this cost is expected to increase due to inflation at a rate of 7% per year for six years (i.e. until the eoy 7), at which time this particular heat exchanger will no longer be needed. if the company's cost of capital is 15% per year, how much could you afford to spend for a higher quality heat exchanger so that these annual replacement and downtime costs could be eliminated?