Question

You are indifferent between spending one hour commuting by bus (x_B) or one hour by car (x_C). However, the bus averages 30mph (due to frequent stops), while the car averages 60mph. Your utility is expressed in miles commuted, and depends on the hours spent in either vehicle: u = 30x_B + 60x_C.

1. Draw the indifference curves for u=900, u’=1200 and u’’=1500.

2. A bus ticket costs $3 for a 30 minute ride, so the price for 1 hour of bus is p_B=6. You spend $270/month for the car (lease, insurance, gas…), which is $9/day. Since you do not commute for more than one hour a day, this is also your price per hour of car: p_C=9. Suppose your monthly budget for transportation is $180 (m=180). Draw your budget constraint.

3. What is the demand function for bus hours, x_B(m,p_B), and the demand function for car hours, x_C(m,p_C)? Make sure to give the price range for which is positive.

4. At m=180, you can’t afford the $270/month car costs, so x_C would be zero and x_B would depend on your answer in part c. Now your transportation budget jumps to m’=270. What happens to the demand for bus hours, x_B? Does this make bus rides an inferior good?

   e. You get into a car accident and your auto insurance jumps up. You have m’270, but the new price for car hours is now p’=15. Draw the new budget constraint and highlight the new optimal consumption bundle (x_B,x_C).

Answer 1

Figure 1

Car rides U=1500 A 20 U=1350 Utility Budget U=900 U=1200 D Bus rides

, a b The Wility : u: 30B + 600 ics are depicted in figure below: Figure. 1] b) The . budget budget constraint constraint : PBB+ Pc c m 1163 +90 = 180 This is represented by AB. c) Now, MRS: mu se operates Now; MRS & PB/Pc his implies the consumer either buy Borc. for the demand ; if MU : muss me That is # wrility from a dollar spent in B is greater than utility from a dollar spent in c. The consumer buys only B. Then if mo. the consumer only buys c. NOW MUB = Is Then S Muc pole m=u if Similarly, *c : Pc is M :u if PB/Pn at

62 og for m=180, x=0, xg = 180 = 3060) m'=240, < MUB, I ;* x = 0 , 31 : Mg 28 : 45 (0) After income nises; bus ride rises to as. so as income nises bus ride rises. Then the bus ride is normal good. e). At =15, still here < ; then busride is still &B= 45 and xe=o. Optimal bundle - a