CLASS NOTES ARE LOCATED WHERE IT SAYS CLASS NOTES!
During the early 1700s, a sailing ship is wrecked on an uninhabited island in the Caribbean Sea. The passengers and crew survive but lose all their possessions. There is no source of fresh water on the island, but coconut palm trees are fairly abundant, and the survivors are able to drink milk harvested from coconuts. There are no mammals living on the island, but many birds roost there, and these become a source of meat. There are a number of mango trees that provide fruit. A long, tough form of sawgrass grows in a number of different places on the island. This grass can be woven into knee-length sleeveless shirts, which are the basic type of clothing for people of both genders. The people on this island have developed a simple system of direct market exchange. Currently, two mangos trade for five coconuts, six coconuts trade for a pound of meat, and three pounds of meat trade for four shirts.
1. Use a formula that was stated in class, and in my notes, to calculate the total number of distinct relative prices in the island’s economy. Note that when this formula is used to count relative prices, any given pair of goods is considered to have only one relative price. For example, if we count the price of a pound of meat in mangos as one relative price, then we don’t count the price of mangos in pounds of meat as a second relative price.
(Class Notes: In a barter economy with markets, each good should have a market price, per unit, in terms of each of the other goods: baskets of fish per bushel of apples, bags of coconuts per bushel of apples, etc. A price of this type – units of one good per unit of the other good – is called a relative price (alternatively, a barter price). If there are different goods traded in an economy, then there turn out to be relative prices for a merchant to keep track of, in each market he visits. Each of the n goods has unit prices: one for each of the other goods. We divide by two to avoid counting reciprocal duplicates: if it costs 2 bags of coconuts to buy a bushel of apples, then it costs 1/2 bushel of apples to buy a bag of coconuts, and so on. )
2. Use the price information you are given to calculate all the distinct relative prices. Remember that the prices we are interested in are unit prices. A unit price is the price of a single unit of one good in units of another good. For each pair of goods, use the order that produces the highest unit price. In the case of coconuts and shirts, for example, if the price of a shirt in coconuts is higher than the price of a coconut in shirts, then report the first price but not the second one. Note: In calculating unit prices, don’t worry about issues of divisibility. Assume that any good can be divided in any way, so that fractions or decimals can be components of unit prices.
3. For each relative price you just calculated, calculate the relative price if the order of the two items is switched. (In the scenario above, for example, you would now calculate the price of a coconut in shirts.) What very simple formula can you use to do this? Explain briefly.
4. Now suppose the people on this island start using mangos as money. The relative prices on the island do not change, and the absolute prices are consistent with them. a. Use a formula stated in class, and in my notes, to calculate the total number of absolute prices in the island’s economy. b. Report these absolute prices.
Class Notes: ( In a monetary economy, in contrast, each good has a single absolute price (alternatively, a money price), which is its unit price in terms of money: dollars per bushel of apples, etc. If we assume that one of the n goods is used as money, then a merchant only needs to keep track of absolute prices. As long as there are more than two different goods ( ), it turns out that , and the difference between these two numbers gets very big as n gets large. Even if there are only 10 different goods, then there are 45 relative prices and only 9 absolute prices. And if there are 100 different goods, which is a more realistic number, then there are 99 absolute prices but almost 5000 relative prices.)
5. Comment briefly on the potential advantages and disadvantages of using mangos as money, using our list of the desirable properties of money as a guide.
6. Suppose you are a merchant on this island, where mangos are used as money in the market (see Item 4 above). A competing merchant who dislikes using money in transactions is willing to trade coconuts for shirts (or vice-versa) directly, at a rate of five coconuts per shirt. Explain, carefully and completely, how you could use this merchant’s willingness to trade these two goods, at this rate, in order to make a profit of one unit of money for yourself by (1) using money to buy units of a good in the market, (2) trading those units of the good to this merchant, in exchange for units of another good, and (3) selling those units in the market for money. Identify the items traded and the quantities, and verify the amount of the profit. Finally, explain what you would need to do in order to make a larger profit (double, for example).
