2+-+PPF+ Solutions

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Department of EconomicsSpring 2013University of California - Berkeley

Economics 1Professor Moretti Head GSIKatherine Murtha

Section Exercise 1

for 1/23/13 & 1/24/13

Suggested Solutions

Arjun, TJ, and Wen are roommates in college. They’ve ignored their choresfor a while and let the apartment deteriorate, so when Wen’s mum calls tosay she is coming to visit them tomorrow, they drop everything else and takeaction ASAP. There are 2 tasks: cleaning rooms and doing the laundry. Theyeach have the same amount of time today.If Arjun spends all of today doing chores, he can finish 2 batches of laundry,or clean 2 rooms. TJ can finish 2 batches of laundry or clean 4 rooms.Wen can finish 4 batches of laundry or clean 2 rooms. (One batch includesfolding, and Wen happens to be very fast at folding clothes)

a. Calculate how much of each chore is ‘produced’ under the followingcircumstances, which we label I, II, III, and IV.I: All three spend all their time doing laundryII: All three spend all their free time cleaningIII: All three spend half their time on each choreIV: Arjun spends half his time on each chore, TJ only cleans, and Wenonly does laundry.

Max #of batchesof laundrydone (if

spend alltime onlaundry)

Max # of roomscleaned (if spend all

time cleaning)

OpportunityCost of Cleaning (in

words)

Opportunitycost of cleaningin terms of batches of laundry (number)

Order toplotpoints(fromlowest tohighest OC)

Arjun 2 2 Give up 1meal for 1

room

1 2nd

TJ 2 4 Give up 1meal for 2rooms

.5 1st

Wen 4 2 Give up 2batches of laundry forone room

2 3rd

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Total 8 8

I: Batches of laundry 2+2+4=8, Rooms=0II: Batches of laundry=0, Rooms 2+4+2=8III: Batches of laundry 1+1+2=4, Rooms 1+2+1=4IV: Batches of laundry 1+0+4=5, Rooms 1+4+0=5

b. graph the production possibilities frontier for this household“economy.” Using your answers to part (a) identify the points I-IV onyour graph.

In order to graph the PPF start by putting the three people in order from

lowest opportunity cost to greatest. Mark the two end points of the graph. Then starting at one endpoint (let’s say rooms), take the person who cangive up the least rooms cleaned in order to do one more meal. Subtract theamount of rooms that person can clean, and add the number of batches of laundry they make. Then use the numbers of clean rooms and batches of laundry the person with the next smallest opportunity cost can make.

c. explain why the production possibilities frontier has the shape it does.Because they only have so much free time in a day, time is ascarce resource. You cannot spend all your time on doing ANDall your time on cleaning. That’s why the PPF slopes down.It is curved because as you travel from no rooms cleaned to

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more rooms cleaned, the more rooms you clean, the morebatches of laundry you have to give up. When you start

allocating people’s time to cleaning, you pick the person who dosmost efficiently first. The person who gives up the least doing toclean (TJ). The last person you allocate to cleaning is the personwho is the slowest at it.

d. Are any of the allocations of time (I-IV) inefficient? Explain.Yes – point III is inefficient because it is inside the PPF.

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