**SOME IMPORTANT IDENTITIES**

Recall that gross domestic product (GDP) is both total income in an economy and the total expenditure on the economy’s output of goods and services. GDP (denoted as Y) is divided into four components of expenditure: consumption (C), investment (I), government purchases .(G), and net exports (NX). We write

y= C+I+ G+NX

This equation is an identity because every dollar of expenditure that shows up on the left side also shows up in one of the four components on the right side. Because of the way each of the variables is defamed and measured, this equation must always hold In this chapter we simplify our analysis by assuming that the economy we are examining is closed A closed economy is one that does not interact with other economies. In particular, a closed economy does not engage in international trade in goods and services, nor does it engage in international borrowing and lending. Actual economies are open economies that is, they interact with other economies around the world. Nonetheless, assuming a closed economy is a useful simplification with which we can learn some lessons that apply to all economies. Moreover, this assumption applies. perfectly to the world economy (for interplanetary trade is not yet common) Because a closed economy does not engage in international trade, imports and exports are exactly zero Therefore, net exports (NX) are also zero. In this case, we can write

Y= C+I+ G.

This equation states that GDP is the sum of consumption, investment, and government purchases. Each unit of output sold in a closed economy is consumed, invested, or bought by the government. To see what this identity can tell us about financial markets, subtract C and G from both sides of this equation. We obtain

The left side of this equation (Y – C – G) is the total income in the economy that remains after paying for consumption and government purchases: This amount is called national saving, or just saving, and is denoted S. Substituting S for Y – C – G, we can write the last equation as

This equation states that saving equals investment To understand the meaning of national saving, it is helpful to manipulate the definition a bit more. Let T denote the amount that the government collects from households in taxes minus the amount it pays back to households in the form of transfer payments (such as Social Security and welfare). We can then write national saving in either of two ways.

S=Y-C- G

or

S = (Y – T – C) + (T – G).

These equations are the same because the two Ts in the second equation cancel each other, but each reveals a different way of thinking .about national saving. In particular, the second equation separates national saving into two pieces: private saving (Y – T – C) and public saving (T – G). Consider each of these two pieces. Private saving is the amount of income that households have left after paying their taxes and paying for their consumption. In particular, because households receive income of Y, pay taxes of T, and spend C on consumption, private saving is Y – T – C. Public saving is the amount of tax revenue that the government has left after paying for its spending. The government receives T in tax revenue and spends G on goods and services. If T exceeds G, the government runs a budget surplus because it receives more money than it spends. This surplus of T – G represents public saving. If the government spends more than it receives in tax revenue, then G is larger than T. In this case, the government runs a budget deficit, and public saving T – G is a negative number Now consider how these accounting identities are related to financial markets. The equation S = f reveals an important fact: For the economy as a whole, saving must be equal to investment. Yet this fact raises some important questions: What mechanisms lie behind this identity? What coordinates those people who are deciding how much to save and those people who are deciding how much to invest? The answer is the financial system. The bond market, the stock market, banks, mutual funds, and other financial markets and intermediaries stand between the two sides of the S = I equation. They take in the nation’s saving and direct it to the nation’s investment.

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