Brenda wants to buy a new car and has a budget of \(\$ 25,000 .\) She has just
found a magazine that assigns each car an index for styling and an index for
gas mileage. Each index runs from 1 to 10 , with 10 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 \(\$ 5000\). She also observes that as the gas-
mileage index rises by one unit, the price of the car increases by \(\$ 2500\)
a. Illustrate the various combinations of style (S) and gas mileage (G) that
Brenda could select with her \(\$ 25,000\) 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 \(S /(4 G)\) What 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 \((3 S) / G\) What value of each index would she like to
have in her car?
