Capital

Until now, on this island, most goods were perishable goods: if you did not eat them or use them right away, then they would spoil. We even assumed that shelters were very basic, and counted them as consumption goods. Imagine that, after a while, inhabitants found ways to build goods that are useful in the production processes of their consumption goods. For instance, they managed to build a rowboat which they could use to fish, ladders which help pick fruit, and "machines" which turn the soil, flatten it and to build better shelters. All these goods are used as physical capital in the production process. Hence now, when deciding how much to produce, and individual must not only decide how much to work, but also how much capital to buy for the next period. People will now have to make an investment decision.

If you remember, we assumed that the marginal productivity of labor (the increase in production from working an extra hour) typically decreases. It seems natural to have a similar assumption regarding the marginal productivity of capital. We also assume that capital goods depreciate at a fixed rate: each period, because of usage, part of the capital breaks down. Hence, part of the investment serves just the purpose of replacing capital that no longer works, such as when a rowboat sinks. This is called depreciated capital. We usually call gross investment the total quantity of capital purchased. If we take away from gross investment the quantity that just replaces capital that no longer works (depreciated capital), then we have net investment.

How much will a person living on the island invest in capital? Well we now that the inhabitants of the island can always buy bonds, on which they have a return of R, the interest rate. It seems clear that when people decide where to place their money, they will compare the return on bonds to the return on capital investment. So what is the return on capital? Buying an extra unit of capital increases production by the marginal productivity of capital (which is diminishing, remember).

Buying a ladder allows the orange grower to generate 10 more golf balls a month. This is the return on the golf balls she paid for the ladder. If she paid 500 golf balls for the ladder, she gets 2% back each month (10), or a 24% annual return on capital. Pretty good. Diminishing returns means the second ladder may only generate a 10% return, for example.

If the orange grower is confidant she can get a 10 golf ball return, she would be willing to borrow money at a rate close to the 24% rate, leaving some difference to make it worthwhile. If she thinks it could be a broader range, say 6-14 golf balls of benefit, she will also want to ensure there is enough profit to take the risk if the return is only 6 golf balls.

So producers will continue to invest in new capital projects until the returns approach the bond returns. If bond returns are high, fewer capital projects will be invested in, and vice versa. If capital project risks decrease, more projects will be invested in as well.

What affects the demand for capital? It is clear that an increase in the interest rate will decrease the demand for capital goods, as more people buy bonds. But there are other factors that affect capital demand. Of course, if productivity of capital increases, then demand for capital will increase (this is similar to the effect of a change in labor productivity on labor demand). If depreciation increases, then the return on capital decreases (less money is made selling the capital after its use) and so this lowers the demand for capital. Finally, if a disaster (such as a typhoon) destroys a lot of the old stock of capital, then at the return on capital suddenly increases and the demand for capital increases as well.