Problem:

Jack had a Summer job on a ferry between a French and a Dutch island in the Caribbean. As crew, he could take his knapsack through customs without inspection.

On the French island, wine costs 5 FF a bottle, beer 4 FF a bottle.

On the Dutch island, wine costs 10 guilders a bottle, beer 6 guilders a bottle.

Jack has friends who work in cafes in both harbors who will buy or sell wine and beer to him at those prices. How did Jack supplement his salary over the Summer?

Most people said something like "buy where its cheaper and sell where it is more expensive," without explaining concretely what that meant in this situation. Often, people are put off by the two different currencies (and yes, there actually are both Dutch and French islands in the Caribbean); but they DON"T MATTER. Profitable trade is possible if RELATIVE PRICES ARE DIFFERENT -- and they are, here. Let's look at an example of how he can make money, and then analyze the situation.

Suppose he starts off with 60 guilders, and buys ten bottles of beer in the Dutch island;

He goes to the French island, sells the ten bottles of beer for 40 francs; with 40 francs, he can buy eight bottles of wine. He goes back to the Dutch island, and can sell the eight bottles of wine for 80 guilders. On one round trip, he made a profit of 20 guilders.

Analytically, how can we figure out what to buy where, what to sell where?

We use Opportunity Cost:

On the French island, 5 FF buys one bottle of wine or 1.25 bottles of beer; so the opportunity cost of a bottle of wine is 1.25 bottles of beer, the opportunity cost of a bottle of beer is 0.8 bottles of wine.

On the Dutch island, 10 guilders buys one bottle of wine or 1 2/3 bottles of beer; the opportunity cost of a bottle of wine is 1 2/3 bottles of beer, the opportunity cost of a bottle of beer is 0.6 bottles of wine.

Now compare the opportunity costs across islands: beer has the lower opportunity cost on the Dutch island, wine has the lower opportunity cost on the French island.

The principle of COMPARATIVE ADVANTAGE says buy (export) the good with the low opportunity cost; so buy beer in the Dutch café, take it to the French one where it is worth more wine -- its opportunity cost in terms of wine is higher. Trade it for the wine, of which the French are the low opportunity cost producers, take that back to the Dutch island, where the wine is worth more (has the higher opportunity cost in terms of beer). Hence you make a profit. If relative prices differ, then (ignoring transport and transaction costs), a profit can always be made [by buying where opportunity cost low and selling where opportunity cost high].

Quickly, lets look at the other two examples of opportunity cost issues:

To fly to Atlanta takes one hour and costs $375;

to drive to Atlanta takes five hours and costs $75;

If the employer is paying and sending them in work time,

other things equal, would someone with hourly earnings of $25 be more likely to drive or fly?

Flying, total cost to employer is $375 plus one hour at $25 = $400;

Driving, total cost to employer is $75 plus five hours at $25 = $75 + $125 = $200.

Most likely, he drives.

How about someone with hourly earnings of $90?

Flying, total cost to employer is $375 + $90 = $465

Driving, total cost to employer is $75 + (5 x $90) = $75 + $450 = $525.

Most likely, she flies.

What would be the "break-even" hourly earnings?

Difference in cost of the travel is $375 - $75 = $300;

Difference in time is 5 hours - 1 hour = 4 hours;

So the break-even point is $300/4 = $75/hour earnings.
 
 
 
 

Mary is a lawyer who earns $50 an hour lawyering. She can also type 60 words a minute. Ignoring any taxes etc, if Sam is a typist who can type 15 words a minute, what is the highest possible wage per hour Mary could pay Sam and still be better off than doing her own typing? [Assume when typing, Mary cannot also be lawyering].

Mary types four times as fast as Sam. Mary's opportunity cost of typing is the earnings from lawyering she loses, i.e. $50 an hour. So she will hire Sam if the cost of Sam doing the typing is less than her opportunity cost; it takes Sam four hours to type what Mary can type in an hour, so for Mary to hire Sam she must be paying him no more than one-fourth of her opportunity cost of time, i.e. $50/4, the highest possible wage per hour Mary could pay Sam and still be better off than doing her own typing would be just under $12.50, say $12.49.