Question

answer part e please

Exercise 6. Price Changes (Perfect Complements) MLK weekend is coming up and you are planning a long- weekend retreat to a nearby island for all employees in your office. You can't get there and back without a plane ticket, and you are not even considering taking the trip without a hotel room for each of the three nights you are planning to stay. Your utility measures the number of employees you can take to the retreat. It is u = min(V2Xp,/3Xy), where x, is number of plane tickets you need, and Xy is the number of hotel nights you need. a) Draw indifference curves for u=12, u'=15, u"=20. b) What are the demand curves for airplane tickets, Xp(m,pp.p.) and for one-night hotel rooms, Xp(m,pp.P.)? c) Plane tickets cost $150 each way (pp=150) and hotel rooms cost $100/night (pH=100). You have a budget of $9,000 (m=9000). Draw the budget line and determine how many employees you will be taking. d) The hotel you are about to book informs you that for parties of 20 or more they have a 50% rate reduction on all rooms (pu'=50). How many more people can you take? e) You call back the airline to make your final reservation, but you are informed that prices have increased to po'=225. How many people do you invite now? (Remember, the hotel discount applies only over a threshold).

Answer 1

We have

u(top, 'n) = min(52p,

where Xp is number of plane tickets and Xh is number of hotel nights you need.

Now drawing indifference curve for u = 12

this implies either 1/2 Xp = 12 or 1/3Xh = 12 thus drawing,

Similarly for u = 15

100

and for u = 20 we have,

100 Xp

100 Xp

(b)

(6) Demand curves 11 u = min ( up, { xn) and Pp. upt Philh= m @ In equilibrium or at optimeen, - ſ mn 3 Mp 3 enn 17 & up a un mo ATO

New, putting ② in , 1. Pp. up this see up = m + apl 6 + 3 ) = m em * = aptsen and an email eppt 3 Ph оёр +2 P,

(c) Now we have,

P,= 150 and Ph = 100 with m = 9000

Thus our budget line will be,

150.1, +100ph = 9000

-100 -50 150 O 100

So, utility maximization problem will be,

So I will be taking 15 employees with me as with u =15 the IC just touches the budget line..i.e highest IC possible.

-100 -500 100 150