economics:-
\f14. Consumers in Georgia pay twice as much for avocados as they do for peaches. However, avocados and peaches are the same price in California. Ifconsumers in both states maximize utility, will the marginal rate of substitution of peaches for avocados be the same for consumers in both states? If not, which will be higher? l. Brenda wants to buy a new car and has a budget of $25Jlll. She has just found a magazine that assigns each car an index for styling and an index for gas mileage. Each index runs from l-l, with 1D representing either the most styling or the best gas mileage. While looking at the list of cars, Brenda observes that on average, as the style index increases by one unit, the price of the car increases by $5ll. She also observes that as the gas-mileage index rises by one unit= the price of the car increases by $EEDU. a. Illusin'ate the various combinations of style (S) and gas mileage (G) that Brenda could select with her $25,001:} budget- Place gas mileage on the horizontal axis. b- Suppose Brenda's preferences are such that she always receives three times as much satisfaction from an extra unit of styling as she does from gas mileage. What type of car will Brenda choose? c. Suppose that Brenda's marginal rate of substitution {of gas mileage for styling} is equal to SI{4G}. W'hat value of each index would she like to have in her car? d. Suppose that Brenda's marginal rate of substitution {of gas mileage for styling} is equal to (BSFG. TWhat value of each index would she like to have in her car? 18. Jane receives utility from days spent traveling on vacation domestically (D) and days spent traveling on vacation in a foreign country (F), as given by the utility function U (D, F) : 10DF. In addition, the price of a day spent traveling domestically is $100, the price of a day spent traveling in a foreign country is $400, and J ane's annual travel budget is $4000. a. Illustrate the indi'erence curve associated with a utility of 800 and the indifference curve associated with a utility of 1200. b. Graph J ane's budget line on the same graph. c. Can Jane afford any of the bundles that give her a utility of 800? What about a utility of 1200'? d. Find J ane's utility maximizing choice of days spent traveling domestically and days spent in a foreign country. 20. The utility that Meredith receives by consuming food F and clothing C is given by U (F, C) : FC. Suppose that Meredith's income in 1990 is $1200 and that the prices of food and clothing are $1 per unit for each. By 2000, however, the price of food has increased to $2 and the price of clothing to $3. Let 100 represent the cost of living index for 1990. Calculate the ideal and the Laspeyres cost-ofliving index for Meredith for 2000. (Hint: Meredith will spend equal amounts on food and clothing with these preferences.)
