ECO 2013-01 August 31, 1998

1. Rhonda is an attorney who used to be a legal secretary. She can type 120 words a minute; as an attorney, she earns $40 an hour.

Ignoring tax issues etc., if Rhonda is considering hiring a typist, who will cost $10 an hour, is it worth Rhonda's while to hire the typist if the typist can type

a - 125 words a minute?

b - 115 words a minute?

c - 60 words a minute?

d - 31 words a minute?

e - 29 words a minute?

The answer is yes for a, b, c, or d; no for e. Her opportunity cost of typing [120 words a minute] is $40/hour. The typist costs her $10/hour. A typist who can type 30 words a minute (120 divided by [$40/$10]) will cost her exactly as much as typing herself. So any typist who types faster (more than 30 words a minute) leaves her better off (costs less than typing herself), a typist who types slower than 30 words a minute costs her more than typing herself.

2. Professor Alice Goofoff has a sabbatical for a semester to do research on ethnomusicology among the surfers in Kuta Beach, Bali. She has a condo in Tallahassee. The assessment and mortgage payment on the condo is $550 a month. Utilities will be $15 a month if she leaves it empty, her cable costs $26 a month, and the phone will cost $21 a month even if she does not use it. If she disconnects each of these, when she returns she would have to pay $50 to reconnect utilities, $50 for cable, and $50 for the phone. She will be away three months and was thinking of just leaving the condo empty while she was gone. However, her Chairman's daughter, Mary, an MBA student, offers to housesit the condo for her, paying for utilities, phone, and cable, if Alice will pay her $40 a month [she says, to cover her commuting costs]. Alice's initial reaction is to say no, she would want at least $550 in rent from Mary; but her friend Raul Economides tells her to think about it, using the idea of opportunity cost. Assuming that other than money, there is no difference to Alice between the condo being empty and having Mary house sit, is Alice monetarily better off leaving the condo empty or paying Mary to house sit? What is the most Alice should be willing to pay Mary and still be better off?

[Opportunity cost refers to the next best alternative; compare Alice's situation, in terms of money, (1) leaving utilities, cable, phone connected, compared with having them disconnected and then paying to reconnect; and then

(2) leaving the condo empty, compared with Mary house-sitting]

[Answer as though only money matters, i.e. ignore the hassle factors]

a $40 [or more precisely, $39.99]

b $50 [or more precisely, $49.99]

c This is nonsense, if Mary won’t pay rent, she should leave it empty

d $62 [or more precisely, $61.99]

e $48.33

This is a bit complicated, sufficiently so that at the end of class a couple of people had me almost convinced b was the right answer, when actually e is. You need to go through several steps:

The $550 is completely irrelevant, because she has to pay that each month whatever she does; it is unavoidable, a sunk cost she cannot avoid, so byegones are byegones, forget the $550 a month payment.

What is the least amount she would have to pay if she left the condo empty?

For phone, 3 x $21 = $63 > $50, she should turn phone off and pay the reconnect fee, $50

For cable, 3 x $26 = $78 > $50, she should turn cable off and pay the reconnect fee, $50

For utilities, 3 x $15 = $45 < $50, she should leave utilities on and pay 3 months at $15, $45.

So the least amount that she would pay, that she can avoid by having Mary there, if she leaves it empty is $50 + $50 + $45 = $145.

$145/3 = $48.33 1/3 a month. If she pays Mary $48.33 a month, she is out of pocket $144.99, 1 cent better than if she leaves it empty. So the most she will pay Mary is $48.33 a month.

People who said b omitted to spot that she does better leaving the utilities connected, paying out $45, than she would turning them off and paying a $50 reconnect fee. If she paid Mary $49.99 a month, she would have paid $149.97 over three months, $4.97 more than she needed to if she left it empty, so there is no reason for her to do that.

The key here is that opportunity cost is equivalent to "avoidable outlays" – we are doing a negative, we need to figure out what is the smallest outlay with the condo empty that Alice can avoid by having Mary in it. That figure is $145 over three months, not $150. Tricky, but you did have a chance to discuss it.