We learned in the previous chapter that two of the essential ingredients in economic growth are increases in the economy’s levels of human capital and physical capital. Human capital is largely provided by governments through public education. (In countries with a large private education sector, like the United States, private post-secondary education is also an important source of human capital.) But physical capital, with the exception of infrastructure, is mainly created through private investment spending—that is, spending by firms rather than by the government.

Who pays for private investment spending? In some cases it’s the people or corporations that actually do the spending—for example, a family that owns a business might use its own savings to buy new equipment or a new building, or a corporation might reinvest some of its own profits to build a new factory. In the modern economy, however, individuals and firms that create physical capital often do it with other people’s money—money that they borrow or raise by selling stock.

To understand how investment spending is financed, we need to look first at how savings and investment spending are related for the economy as a whole. Then we will examine how savings are allocated among investment spending projects.

The most basic point to understand about savings and investment spending is that they are always equal. This is not a theory; it’s a fact of accounting called the savings–investment spending identity.

To see why the savings–investment spending identity must be true, let’s look again at the national income accounting that we learned in Chapter 7. Recall that GDP is equal to total spending on domestically produced final goods and services, and that we can write the following equation (which is the same as Equation 7-1):

where C is spending by consumers, I is investment spending, G is government purchases of goods and services, X is the value of exports to other countries, and IM is spending on imports from other countries.

In a closed economy, there are no exports or imports. So X = 0 and IM = 0, which makes Equation 10-1 simpler. As we learned in Chapter 7, the overall income of this simplified economy would, by definition, equal total spending. Why? Recall one of the basic principles of economics from Chapter 1, that one person’s spending is another person’s income: the only way people can earn income is by selling something to someone else, and every dollar spent in the economy creates income for somebody. This is represented by Equation 10-2: on the left, GDP represents total income earned in the economy, and on the right, C + I + G represents total spending in the economy:

Now, what can be done with income? It can either be spent on consumption—consumer spending (C) plus government purchases of goods and services (G)—or saved (S). So it must be true that:

where S is savings. Meanwhile, as Equation 10-2 tells us, total spending consists of either consumption spending (C + G) or investment spending (I):

Putting Equations 10-3 and 10-4 together, we get:

Subtract consumption spending (C + G) from both sides, and we get:

As we said, then, it’s a basic accounting fact that savings equals investment spending for the economy as a whole.

Now, let’s take a closer look at savings. Households are not the only parties that can save in an economy. In any given year, the government can save, too, if it collects more tax revenue than it spends. When this occurs, the difference is called a budget surplus and is equivalent to savings by government. If, alternatively, government spending exceeds tax revenue, there is a budget deficit—a negative budget surplus. In this case, we often say that the government is “dissaving”: by spending more than its tax revenues, the government is engaged in the opposite of savings.

We’ll define the term budget balance to refer to both cases, with the understanding that the budget balance can be positive (a budget surplus) or negative (a budget deficit). The budget balance is defined as:

Where T is the value of tax revenues and TR is the value of government transfers. The budget balance is equivalent to savings by government—if it’s positive, the government is saving; if it’s negative, the government is dissaving. National savings, which we just called savings, for short, is equal to the sum of the budget balance and private savings, where private savings is disposable income (income after taxes) minus consumption. It is given by:

So Equations 10-6 and 10-8 tell us that, in a closed economy, the savings–investment spending identity has the following form:

The Savings–Investment Spending Identity in an Open Economy An open economy is an economy in which goods and money can flow into and out of the country. This changes the savings–investment spending identity because savings need not be spent on investment spending projects in the same country in which the savings are generated. That’s because the savings of people who live in any one country can be used to finance investment spending that takes place in other countries. So any given country can receive inflows of funds—foreign savings that finance investment spending in that country. Any given country can also generate outflows of funds—domestic savings that finance investment spending in another country.

The net effect of international inflows and outflows of funds on the total savings available for investment spending in any given country is known as the net capital inflow into that country, equal to the total inflow of foreign funds minus the total outflow of domestic funds to other countries. Like the budget balance, a net capital inflow can be negative—that is, more capital can flow out of a country than flows into it. In recent years, the United States has experienced a consistent positive net capital inflow from foreigners, who view our economy as an attractive place to put their savings. In 2013, for example, net capital inflows into the United States were $423 billion.

It’s important to note that, from a national perspective, a dollar generated by national savings and a dollar generated by capital inflow are not equivalent. Yes, they can both finance the same dollar’s worth of investment spending. But any dollar borrowed from a saver must eventually be repaid with interest. A dollar that comes from national savings is repaid with interest to someone domestically—either a private party or the government. But a dollar that comes as capital inflow must be repaid with interest to a foreigner. So a dollar of investment spending financed by a capital inflow comes at a higher national cost—the interest that must eventually be paid to a foreigner—than a dollar of investment spending financed by national savings.

The fact that a net capital inflow represents funds borrowed from foreigners is an important aspect of the savings–investment spending identity in an open economy. Consider an individual who spends more than his or her income; that person must borrow the difference from others. Similarly, a country that spends more on imports than it earns from exports must borrow the difference from foreigners. And that difference, the amount of funds borrowed from foreigners, is the country’s net capital inflow. As we will explain at greater length in Chapter 19, this means that the net capital inflow into a country is equal to the difference between imports and exports:

Rearranging Equation 10-1 we get:

Using Equations 10-3 and 10-9 we know that GDP − C − G is equal to National savings, so that:

So the application of the savings–investment spending identity to an economy that is open to inflows or outflows of capital means that investment spending is equal to savings, where savings is equal to national savings plus net capital inflow. That is, in an economy with a positive net capital inflow, some investment spending is funded by the savings of foreigners. And in an economy with a negative net capital inflow (that is, more capital is flowing out than flowing in), some portion of national savings is funding investment spending in other countries.

In the United States in 2013, investment spending totaled $3,244.3 billion. Private savings totaled $3,402 billion, offset by government savings of −$368 billion and supplemented by a net capital inflow of $423 billion. Notice that these numbers don’t quite add up; because data collection isn’t perfect, there is a “statistical discrepancy” of −$212 billion. But we know that this is an error in the data, not in the theory, because the savings–investment spending identity must hold in reality.

Figure 10-1 shows what the savings–investment spending identity looked like in 2013 for two of the world’s major economies, those of the United States and Germany. To make the two economies easier to compare, we’ve measured savings and investment spending as percentages of GDP. In each panel the orange bars on the left show total investment spending and the multicolored bars on the right show the components of savings. U.S. investment spending was 19.4% of GDP, financed by a combination of private savings (22.5% of GDP) and positive net capital inflow (2.7% of GDP) and partly offset by a government budget deficit (−5.8% of GDP). German investment spending was lower as a percentage of GDP, at 17.6%. It was financed by a higher level of private savings as a percentage of GDP (24%) and was offset by both a negative net capital inflow or capital outflow (−6% of GDP) and a small budget deficit (−0.4% of GDP).

The economy’s savings finance its investment spending. But how are these funds that are available for investment spending allocated among various projects? That is, what determines which projects get financed (such as Facebook’s server farms) and which don’t (such as Microsoft’s Courier tablet computer, an innovative concept that the software giant decided not to pursue)? We’ll see shortly that funds get allocated to investment spending projects using a familiar method: by the market, via supply and demand.

For the economy as a whole, savings always equals investment spending. In a closed economy, savings is equal to national savings. In an open economy, savings is equal to national savings plus capital inflow. At any given time, however, savers, the people with funds to lend, are usually not the same as borrowers, the people who want to borrow to finance their investment spending. How are savers and borrowers brought together?

Savers and borrowers are matched up with one another in much the same way producers and consumers are matched up: through markets governed by supply and demand. In Figure 7-1, the expanded circular-flow diagram, we noted that the financial markets channel the savings of households to businesses that want to borrow in order to purchase capital equipment. It’s now time to take a look at how those financial markets work.

To do this, it helps to consider a somewhat simplified version of reality. As we noted in Chapter 7, there are a large number of different financial markets in the financial system, such as the bond market and the stock market. However, economists often work with a simplified model in which they assume that there is just one market that brings together those who want to lend money (savers) and those who want to borrow (firms with investment spending projects). This hypothetical market is known as the loanable funds market. The price that is determined in the loanable funds market is the interest rate, denoted by r. As we noted in Chapter 8, loans typically specify a nominal interest rate. So although we call r “the interest rate,” it is with the understanding that r is a nominal interest rate—an interest rate that is unadjusted for inflation.

We’re not quite done simplifying things. There are, in reality, many different kinds of interest rates, because there are many different kinds of loans—short-term loans, long-term loans, loans made to corporate borrowers, loans made to governments, and so on. In the interest of simplicity, we’ll ignore those differences and assume that there is only one type of loan.

OK, now we’re ready to analyze how savings and investment get matched up.

The Demand for Loanable Funds Figure 10-2 illustrates a hypothetical demand curve for loanable funds, D, which slopes downward. On the horizontal axis we show the quantity of loanable funds demanded. On the vertical axis we show the interest rate, which is the “price” of borrowing. But why does the demand curve for loanable funds slope downward?

To answer this question, consider what a firm is doing when it engages in investment spending—say, by buying new equipment. Investment spending means laying out money right now, expecting that this outlay will lead to higher profits at some point in the future. In fact, however, the promise of a dollar five or ten years from now is worth less than an actual dollar right now. So an investment is worth making only if it generates a future return that is greater than the monetary cost of making the investment today. How much greater?

To answer that, we need to take into account the present value of the future return the firm expects to get. We examine the concept of present value in the accompanying For Inquiring Minds. Then, in the chapter’s appendix, we show how the concept of present value can be applied to dollars earned multiple years in the future. The appendix also addresses how present value is used to calculate the prices of shares of stock and bonds.

In present value calculations, we use the interest rate to determine how the value of a dollar in the future compares to the value of a dollar today. But the fact is that future dollars are worth less than a dollar today, and they are worth even less when the interest rate is higher.

The intuition behind present value calculations is simple. The interest rate measures the opportunity cost of investment spending that results in a future return: instead of spending money on an investment spending project, a company could simply put the money into the bank and earn interest on it. And the higher the interest rate, the more attractive it is to simply put money into the bank and let it earn interest instead of investing it in an investment spending project.

In other words, the higher the interest rate, the higher the opportunity cost of investment spending. And, the higher the opportunity cost of investment spending, the lower the number of investment spending projects firms want to carry out, and therefore the lower the quantity of loanable funds demanded. It is this insight (discussed in the accompanying For Inquiring Minds) that explains why the demand curve for loanable funds is downward sloping.

When businesses engage in investment spending, they spend money right now in return for an expected payoff in the future. To evaluate whether a particular investment spending project is worth undertaking, a business must compare the present value of the future payoff with the current cost of that project. If the present value of the future payoff is greater than the current cost, a project is profitable and worth investing in. If the interest rate falls, then the present value of any given project rises, so more projects pass that test. If the interest rate rises, then the present value of any given project falls, and fewer projects pass that test.

So total investment spending, and hence the demand for loanable funds to finance that spending, is negatively related to the interest rate. Thus, the demand curve for loanable funds slopes downward. You can see this in Figure 10-2. When the interest rate falls from 12% to 4%, the quantity of loanable funds demanded rises from $150 billion (point A) to $450 billion (point B).

The Supply of Loanable Funds Figure 10-3 shows a hypothetical supply curve for loanable funds, S. Again, the interest rate plays the same role that the price plays in ordinary supply and demand analysis. But why is this curve upward sloping?

The answer is that loanable funds are supplied by savers, and savers incur an opportunity cost when they lend to a business: the funds could instead be spent on consumption—say, a nice vacation. Whether a given saver becomes a lender by making funds available to borrowers depends on the interest rate received in return. By saving your money today and earning interest on it, you are rewarded with higher consumption in the future when the loan you made is repaid with interest. So it is a good assumption that more people are willing to forgo current consumption and make a loan to a borrower when the interest rate is higher.

As a result, our hypothetical supply curve of loanable funds slopes upward. In Figure 10-3, lenders will supply $150 billion to the loanable funds market at an interest rate of 4% (point X); if the interest rate rises to 12%, the quantity of loanable funds supplied will rise to $450 billion (point Y).

The Equilibrium Interest Rate The interest rate at which the quantity of loanable funds supplied equals the quantity of loanable funds demanded is called the equilibrium interest rate. As you can see in Figure 10-4, the equilibrium interest rate, r*, and the total quantity of lending, Q*, are determined by the intersection of the supply and demand curves, at point E. Here, the equilibrium interest rate is 8%, at which $300 billion is lent and borrowed. In this equilibrium, only investment spending projects that are profitable if the interest rate is 8% or higher are funded. Projects that would not be undertaken unless they are profitable only when the interest rate falls below 8% are not funded. Correspondingly, only lenders who are willing to accept an interest rate of 8% or less will have their offers to lend funds accepted; lenders who demand an interest rate higher than 8% do not have their offers to lend accepted.

Figure 10-4 shows how the market for loanable funds matches up desired savings with desired investment spending: in equilibrium, the quantity of funds that savers want to lend is equal to the quantity of funds that firms want to borrow. The figure also shows that this match-up is efficient, in two senses. First, the right investments get made: the investment spending projects that are actually financed have higher payoffs (in terms of present value) than those that do not get financed. Second, the right people do the saving and lending: the savers who actually lend funds are willing to lend for lower interest rates than those who do not.

The insight that the loanable funds market leads to an efficient use of savings, although drawn from a highly simplified model, has important implications for real life. As we’ll see shortly, it is the reason that a well-functioning financial system increases an economy’s long-run economic growth rate.

Before we get to that, let’s look at how the market for loanable funds responds to shifts of demand and supply. As in the standard model of supply and demand, where the equilibrium price changes in response to shifts of the demand or supply curves, here, the equilibrium interest rate changes when there are shifts of the demand curve for loanable funds, the supply curve for loanable funds, or both.

Shifts of the Demand for Loanable Funds Let’s start by looking at the causes and effects of changes in demand.

The factors that can cause the demand curve for loanable funds to shift include the following:

Figure 10-5 shows the effects of an increase in the demand for loanable funds. S is the supply of loanable funds, and D₁ is the initial demand curve. The initial equilibrium interest rate is r₁. An increase in the demand for loanable funds means that the quantity of funds demanded rises at any given interest rate, so the demand curve shifts rightward to D₂. As a result, the equilibrium interest rate rises to r₂.

The fact that an increase in the demand for loanable funds leads, other things equal, to a rise in the interest rate has one especially important implication: it tells us that increasing or persistent government budget deficits are cause for concern because an increase in the government’s deficit shifts the demand curve for loanable funds to the right, which leads to a higher interest rate. If the interest rate rises, businesses will cut back on their investment spending.

So, other things equal, a rise in the government budget deficit tends to reduce overall investment spending. Economists call the negative effect of government budget deficits on investment spending crowding out. Concerns about crowding out are one key reason to worry about increasing or persistent budget deficits.

However, it’s important to add a qualification here: crowding out may not occur if the economy is depressed. When the economy is operating far below full employment, government spending can lead to higher incomes, and these higher incomes lead to increased savings at any given interest rate. Higher savings allows the government to borrow without raising interest rates. Many economists believe, for example, that the large budget deficits that the U.S. government ran from 2008 to 2013 in the face of a depressed economy caused little if any crowding out.

Shifts of the Supply of Loanable Funds Like the demand for loanable funds, the supply of loanable funds can shift. Among the factors that can cause the supply of loanable funds to shift are the following:

Figure 10-6 shows the effects of an increase in the supply of loanable funds. D is the demand for loanable funds, and S₁ is the initial supply curve. The initial equilibrium interest rate is r₁. An increase in the supply of loanable funds means that the quantity of funds supplied rises at any given interest rate, so the supply curve shifts rightward to S₂. As a result, the equilibrium interest rate falls to r₂.

Inflation and Interest Rates Anything that shifts either the supply of loanable funds curve or the demand for loanable funds curve changes the interest rate. Historically, major changes in interest rates have been driven by many factors, including changes in government policy and technological innovations that created new investment opportunities.

However, arguably the most important factor affecting interest rates over time—the reason, for example, that interest rates today are much lower than they were in the late 1970s and early 1980s—is changing expectations about future inflation, which shift both the supply and the demand for loanable funds.

To understand the effect of expected future inflation on interest rates, recall our discussion in Chapter 8 of the way inflation creates winners and losers—for example, the way that higher than expected U.S. inflation in the 1970s and 1980s reduced the real value of homeowners’ mortgages, which was good for the homeowners but bad for the banks. We also learned that economists summarize the effect of inflation on borrowers and lenders by distinguishing between the nominal interest rate and the real interest rate, where the difference is:

Real interest rate = Nominal interest rate − Inflation rate

The true cost of borrowing is the real interest rate, not the nominal interest rate. To see why, suppose a firm borrows $10,000 for one year at a 10% nominal interest rate. At the end of the year, it must repay $11,000—the amount borrowed plus the interest. But suppose that over the course of the year the average level of prices increases by 10%, so that the real interest rate is zero. Then the $11,000 repayment has the same purchasing power as the original $10,000 loan. In real terms, the borrower has received a zero-interest loan.

Similarly, the true payoff to lending is the real interest rate, not the nominal interest rate. Suppose that a bank makes a $10,000 loan for one year at a 10% nominal interest rate. At the end of the year, the bank receives an $11,000 repayment. But if the average level of prices rises by 10% per year, the purchasing power of the money the bank gets back is no more than that of the money it lent out. In real terms, the bank has made a zero-interest loan.

Now we can add an important detail to our analysis of the loanable funds market. Figures 10-5 and 10-6 are drawn with the vertical axis measuring the nominal interest rate for a given expected future inflation rate. Why do we use the nominal interest rate rather than the real interest rate? Because in the real world neither borrowers nor lenders know what the future inflation rate will be when they make a deal. Actual loan contracts therefore specify a nominal interest rate rather than a real interest rate. Because we are holding the expected future inflation rate fixed in Figures 10-5 and 10-6, however, changes in the nominal interest rate also lead to changes in the real interest rate.

The expectations of borrowers and lenders about future inflation rates are normally based on recent experience. In the late 1970s, after a decade of high inflation, borrowers and lenders expected future inflation to be high. By the late 1990s, after a decade of fairly low inflation, borrowers and lenders expected future inflation to be low. And these changing expectations about future inflation had a strong effect on the nominal interest rate, largely explaining why nominal interest rates were much lower in the early years of the twenty-first century than they were in the early 1980s.

Let’s look at how changes in the expected future rate of inflation are reflected in the loanable funds model.

In Figure 10-7, the curves S₀ and D₀ show the supply and demand for loanable funds given that the expected future rate of inflation is 0%. In that case, equilibrium is at E₀, and the equilibrium nominal interest rate is 4%. Because expected future inflation is 0%, the equilibrium expected real interest rate over the life of the loan is also 4%.

Now suppose that the expected future inflation rate rises to 10%. The demand curve for loanable funds shifts upward to D₁₀: borrowers are now willing to borrow as much at a nominal interest rate of 14% as they were previously willing to borrow at 4%. That’s because with a 10% inflation rate, a 14% nominal interest rate corresponds to a 4% real interest rate. Similarly, the supply curve of loanable funds shifts upward to S₁₀: lenders require a nominal interest rate of 14% to persuade them to lend as much as they would previously have lent at 4%. The new equilibrium is at E₁₀: the result of an expected future inflation rate of 10% is that the equilibrium nominal interest rate rises from 4% to 14%.

This situation can be summarized as a general principle, known as the Fisher effect (after the American economist Irving Fisher, who proposed it in 1930): the expected real interest rate is unaffected by changes in expected future inflation. According to the Fisher effect, an increase in expected future inflation drives up the nominal interest rate, where each additional percentage point of expected future inflation drives up the nominal interest rate by 1 percentage point. The central point is that both lenders and borrowers base their decisions on the expected real interest rate. As a result, a change in the expected rate of inflation does not affect the equilibrium quantity of loanable funds or the expected real interest rate; all it affects is the equilibrium nominal interest rate.