Unit 9 Uneven development on a global scale

9.5 Investment and saving

What are the macroeconomic implications of the increases in capital per worker that have accompanied rising per capita incomes?

Equipping workers with a higher level of capital requires higher net investment. The economy’s gross fixed capital formation must provide each worker with a higher stock of capital, and also cover the depreciation of the existing capital stock. To increase the capital stock from \(K_0\) in year 0 to \(K_1\) in year 1 requires positive net investment:

\[\text{net investment} = K_1 − K_0\]

But if a proportion, \(𝛿\), of the capital stock is lost every year through depreciation, the total amount of output that must be invested to achieve this increase will have to be higher:

\[\begin{align*} \text{gross investment} &= \text{net investment} + \text{depreciation} \\ &= (K_1− K_0) + \delta K_0 \\ &= K_1− (1− \delta) K_0 \end{align*}\]

Investment and saving in a growth model

When the question is not ‘How can an economy get stuck in a recession?’ (Unit 3 to Unit 5, and the box in this section on ‘Recap: Investment and saving in the multiplier model’) but ‘How can an economy get stuck with a low level of capital per worker decade after decade?’ (this unit), we need to modify the model to address the new question. Although savings and investment decisions are made independently, they are linked in the longer term: as Unit 6 describes, the savings of households provide the funds for investment by firms. To model the long-run growth of the economy, we incorporate this link: we assume that savings are invested.

A physical model based on grain—like the model of Marco in Unit 9 of the microeconomics volume—can help us understand the link from savings, through investment, to income and consumption in the future. Here, we will treat Marco as a representative of the entire economy. To remember this, you can mentally swap the letters so that ‘Marco’ becomes ‘Macro’. There is only one good: grain, which fulfils the role of both consumption (it can be eaten) and investment (it can be planted to produce grain for next year). At the beginning of year 0, Marco has \(Y_0 = 100\) units of grain. He plants \(I_0\) units, leaving \(C_0 = 100 - I_0\) for consumption during the year.

We will assume that the rate of return is \(r = 1.5\) (that is, 150%). So at the end of the year, Marco’s investment of \(I_0\) units will produce a harvest of \(Y_1\) units of grain to be used for consumption and investment the following year (year 1):

\[Y_1=(1+r) I_0 = 2.5 I_0\]

Each year, by saving part of his output (which is also his income) for planting rather than consumption, Marco is making an investment that will enable him to consume in the future. We can think of this portion of grain as capital; it will be used as the input to production. Note that Marco’s capital depreciates completely in a year—the depreciation rate, \(𝛿\), is equal to 1. At the end of the year, he will have no capital left. In order to continue producing grain the following year, he will have to invest again by saving and investing some of the harvest. When \(𝛿\) equals 1, gross investment, \(I\), forms the capital stock, \(K\).

How much grain should he consume in year 0?

Figure 9.10a shows consumption, savings, and income in year 0 on the horizontal axis, and in year 1 on the vertical axis. If Marco consumes \(C_0 = 70\) units of grain in year 0, and plants the remaining 30, he will harvest 75 units at the end of the year (point P in the left-hand panel). If (as in Unit 9 of the microeconomics volume) he cared only about consumption in periods 0 and 1, he might be satisfied with this plan: 70 units in year 0, and 75 in year 1.

But he also needs to save for year 2—so it is not feasible to consume at the production point P. Planning ahead, he decides to save 30% of his output, \(Y_1\), for the following year. Then he can consume only 70%: his feasible consumption frontier is the flatter line in the left-hand panel.

One possibility is to plant 30% of his grain this year too, and consume at point A; 70 units this year, and only 52.5 next year. But should he plant more, to smooth his consumption? And if so, will saving 30% of output be enough for the following year?

To answer these questions it is helpful to work out how much of his initial 100 units of grain Marco should plant to maintain his income—that is, to produce 100 units, leaving him in a position to consume and save as much in year 1 as in year 0. The answer is shown by point Q in the right-hand panel. If he plants 40% of his grain now, and consumes 60, he will harvest 100 units—leaving him in exactly the same position at the beginning of year 1 as he is now.

So he can plan to invest 40% of his output again, for production in year 2. This plan allows him to consume at point B, where \(C_0 = C_1 = 60\). Investing 40% of income every year allows him to sustain an income of 100 units, and smooth consumption at 60 units per year, indefinitely. In this scenario, the capital stock remains constant from year to year: gross investment is just enough to offset depreciation, and net investment is zero.

The left-hand panel of Figure 9.10a illustrates that saving less than 40% of income every year results in a falling income—negative growth. And in Exercise 9.5, you can work through the opposite case: if Marco were to save and invest more than 40% every year, income and consumption in this economy would grow indefinitely from year to year.

This model demonstrates what is possible for Marco. What he actually chooses to do will depend on his preferences. The model from Unit 9 of the microeconomics volume tells us that for individuals, the choice will be a case of ‘doing the best you can’ given the feasible frontier, your preferences between higher consumption now and in the future (as you reap the rewards from investment). If Marco places a high value on future consumption and is willing to accept lower consumption now, he may be able to save enough to achieve a positive growth rate.

Escaping from low levels of capital and income

Now imagine that the Marco-economy is currently investing 40% of output every year. The economy is producing an annual income of 100 units of grain, with capital of 40 units. Suppose that 60 units of consumption is sufficient only to provide a basic standard of living. Why does Marco not save and invest more, in order to increase the capital stock and raise income and consumption in the future?

In this simple model, raising income and consumption appears to be quite simple. Figure 9.10b shows that if the savings rate is increased to 50% in year 0 only, maintaining a rate of 40% in all subsequent years, year 1 income can be increased to 125 units of grain (point R). The right-hand panel shows what happens from year 1 onwards: 75 units of grain can be consumed each year (point D), since investment of 50 units is sufficient to maintain annual income at the new, higher level (point S).

But there is a catch: in order to achieve this, Marco has to lower his consumption to 50 units in year 0. If he is already struggling to survive, he may be very reluctant to do so. If the subsistence level of consumption is at or close to 60 units, it may simply be infeasible. The economy remains poor, in a low-income trap with a zero growth rate.

However, suppose that there is a windfall harvest one year. The additional grain could be used for higher consumption the following year. Or it could all be saved and invested to increase next year’s income. With more income, Marco could increase consumption and save enough to maintain this higher level of income in future years. His future will then be similar to the one in Figure 9.10b, but he can achieve it without having to decrease consumption now. In Section 9.8, we develop a model of growth based on the idea that if output increases in one year, this provides resources that can be used for investment and further growth.

In the Marco-model, there is no difference between saving and investment—what is not consumed is by assumption saved and invested. Remember that this is a model of a closed economy. As a result, there can be no problem of inadequate aggregate demand. The assumption that all savings are invested as in the simple grain model is the basis of our study of the economy in the ‘long run’. In the long-run model, there is no paradox of thrift, as shown in Section 5.8: a decision to save more brings with it a decision to invest more, which means we overlook the short-term fluctuations in aggregate demand that cause the economy to move between booms and recessions.

In the sections that follow, we investigate why the share of output that is saved and invested differs across countries and how that affects the ability of countries to grow rapidly and escape a low-income trap.

Investment and saving in the data

Since higher saving and investment raises living standards in the Marco-economy, it is interesting to plot the data for countries around the world with the investment share on the horizontal axis and GDP per capita on the vertical. Follow the steps in Figure 9.11 to understand this data.

In the grain model of a closed economy, savings and investment are identical—whatever is saved is by assumption invested. However, when a country is open to economic interactions with the rest of the world then investment can differ from domestic savings as we discussed in the puzzle of why investment does not flow from rich to poor countries. In an open economy, poor countries can in principle borrow from the rest of the world and raise the level of investment above domestic savings. This appears to have been the case in South Korea’s phase of very rapid growth as shown by the excess of investment over savings in Figure 9.12 until the 1980s. From then on, savings often exceeded investment, which was reflected in a persistent current account surplus.