Question

Consider an island where people use sand dollars (shells) as currency. For simplicity, assume that people consume only one good: fish. Currently, there are 400 sand dollars in circulation and there are 200 fish purchased each year. Based on this information, what is the price of fish? Now, suppose that a change in climate leads to new sand dollars washing ashore, leaving a total of 500 sand dollars. If there are still 200 fish purchased each year, what is the new price of fish? In order to prevent inflation, what would have to happen to the amount of fish purchased each year?

Answer 1

To answer this question, we can consider a simplified version of the quantity theory of money. The quantity theory of money is well represented by the following equation:

M . V = P . Y,

where M = currency in circulation in the economy, V = velocity of money, P = average price level, Y = real GDP.

Velocity of money refers to how many times a single unit of currency exchanges hands in an economy. For simplicity, assume in this case that it exchanges hands exactly once in this example of a small economy, so that V = 1.

The, our equation reduces to: M = P . Y

(a) Thus, in the first part of the question, M = 400, Y = 200. Using the simplified equation above, this gives us P = 2.

(b) In the next part, M increases to 500. Thus, with M = 500, Y = 200, we get P = 2.5. Clearly, the price has increased from 2 to 2.5, which we call safely call inflation.

In order to prevent the price from increasing, Y will have to increase so that P stays stable. Thus, with M = 500, P = 2, we need Y = 500/2 = 250. Thus, we need to catch more fish, 250 units to be exact, to prevent inflation in this single-good economy.