...And More

To make the situation more interesting, we now need 2 women to survive a wreck and to let some time pass. Imagine now that a second generation has reached adulthood. There are 10 individuals, each specializing in some activities (fishing, rabbit hunting, shelter repairing, etc.). Golf balls are still used as currency, but now there is a possibility to save: a crate with paper has reached the island, and all of the inhabitants have decided to keep the paper for the purpose of writing bonds. Some people have more golf balls in some periods while others have less, and bonds are going to allow them to lend and borrow. Bonds have a one period (say, a month) maturity. Selling a bond for 1golf ball amounts to borrowing 1 golf ball today, and requires a repayment of (1+R) golf balls in the following period, where R is the nominal interest rate.

We thus have on this island two markets: one for commodities and one for bonds. Looking at the market for bonds is not very instructive, however, since for every golf ball that is lent, a golf ball has to be borrowed. If Robinson sells a bond with a 1 golf ball face value to Nick, Robinson holds -1 worth of bonds and Nick holds 1 worth of bond. Hence at the aggregate, the sum is zero. We assume that there is a possibility to hold interest-bearing bonds. So why would anyone want to hold money (golf balls, in this economy), which doesn't pay any interest? For this to happen, we must assume first that no one will exchange goods for bonds. The only mean of buying commodities is using golf balls. But we also need to assume that there is a cost of transforming bonds in liquidity. If we do not assume this, then people would just transform some bonds for the exact amount of money they need to buy their desired goods. There are two opposing effects on the demand for money: first, if the interest rate R increases, it is relatively better to hold bonds, even though you incur the cost of transforming back into money, so an increase in R will decrease the demand for money. But to consume more goods, one needs relatively more money; hence an increase in consumption entails an increase in the demand for money. (Notice that the money supply on our island is fixed: there is a fixed number of golf balls) An increase in the demand for money will tend to make the general worth (or buying power) of money higher, decreasing the price level. A decrease in the demand for money will tend to bring up the prices. If there is little demand for money, people want to get rid of their extra golf balls (the value of money has decreased), and the only way to do this is to buy more goods, which is going to make the price level go up - this is inflation.

How does one individual decide how much to consume today, and how much to save in bonds (and to consume tomorrow)? Well, if the interest rate is high, then the agent has incentives to save more today (thus consuming less and working more today), because he will get relatively more tomorrow. Hence, an increase in the interest rate R will increase production (by increasing work effort) and decrease consumption demand.

We now need to examine what will happen when there are shocks to the production function. An important distinction will be whether the shocks are permanent (they last forever, as a change in technology) or temporary (lasting only one period, as a natural cataclysm). Once again, we will try to decompose the effects into wealth and substitution effects.

After doing this, we will see what changes if we let people on the island organize a labor market.