For U.C. Berkeley instructional purposes only. Copyright 1999.
Version 2.0 1999-08-14
J. Bradford DeLong
Why do so many people find economics a relatively difficult subject?
Is economics a science?
Why do economists usesimplemathematical models?
What do economists models consist of?
Why does everything in an economics textbook seem to be repeated three timesonce in words, once in diagrams, and once in algebra?
Is there a point to thinking in this strange and new way?
Each time you learn a new subject you learn a new pattern of thought.
Every intellectual discipline has its own ways of thinking about the world. Thats what makes it a system of thought, a subject of study, something worth learning, and something that can be taught. Thus each intellectual discipline seems new and strange to those who have not seen it before: it is new and strange, because it is made up of newand initially strangepatterns of thought.
Economics is no exception.
Register this strangeness, for there is no way of avoiding it. It is sort of like learning a new language, and sort of like being initiated into a club. You will find that the economists ways of thinking that seemed strange at first allow you to see pieces of the economy more sharply and clearly than you could have imagined before.
(Of course, you will also find that economists ways of thinking lead themyouusto miss large pieces of what is going on in society. That is why economics is not the only social science, and we have sociologists, political scientists, historians, psychologists, and anthropologists as well.)
But there is a problem with your learning to think like an economist. Wethose who are teaching youyour gradersyour discussion and section leadersyour lectureryour (ahem!) textbook writerare people who have over the years become very, very used to thinking like an economist. For us the strangeness has melted away: ideas and assumptions that seem obvious and natural to your teachers will seem counterintuitive and strange to you. They may seem barely worth mentioning, or not worth mentioning at all, to themusme. But to you they may well seem badly in need of explication, and perhaps of defense.
This chapter tries to point out where some of these strangenesses lie.
Economics: it is a science?
If you are coming to economics from a background in the natural sciencesphysics, chemistry, and so onyou may think you have an idea of what economics is: economics is like a natural science, only less so. To the extent that it works, it must work more-or-less like physics. Its major problem is that it doesnt work very well: its predictions are often wrong, and its theories are unsettled.
If so, you are half right. Economics is a science, but economics is not a natural science, it is a social science. Its subject is not electrons or elements, but human beings: people and how they behave. This has a number of important consequences. Some of them make economics easier than a natural science, some of which make economics harder, and some of which make it just different.
[Graphic of some sort: physicists
on left hand side; economists on right]
First, because economics is a social science, intellectual debates within economics can last a lot longer than in the natural sciences, and are much less likely to come to clear and well-defined consensus conclusions. The major reason for this is that people care: people have very different views of what a free, a good, a just, or a well-ordered society would look like. (Indeed, they look for things in the economy that are in harmony with their vision of what a society should be. They ignoreor explain awayfacts they run across that turn out to be inconvenient for their particular political views.
People are, after all, only human.
Economists try to approach the objectivity that characterizes most work in the natural sciences. We should be able to reach broad areas of agreement. After all, what is, is; and what is not, is no. Even if wishful thinking or predispositions contaminate the results of one single study, successor studies and reexaminations can correct the error. But economists do not approach the unanimity with which physicists embraced the theory of relativity, chemists embraced the oxygen theory of combustion, and biologists rejected the Lamarckian inheritance of acquired characteristics.
Second, the fact that economics is about people means that economists cannot (or cannot ethically) undertake large-scale experiments. Economists cannot set up special situations in which potential sources of disturbance are reduced to a minimum, examine what happens, and then generalize from what happens in the experiment (where sources of disturbance are absent) to what happens in the world (where sources of disturbance are common).
The absence of the experimental method makes economics harder than many of the natural sciences. It makes economists conclusions much more tentative and subject to dispute.
Third, the things that economists studypeoplehave minds of their own. They take a look at what is going on around them, they plan for the future, they take steps to avoid future consequences that they foresee and fear will be unpleasant, and at times they do things just because they feel like it. This means that in economists analyses the present often appears to depend not just on the past but on the future, or rather on what people expect the future to be.
This additional wrinkle makes economics in some sense very hard. In the natural sciences you can almost always rely on the arrow of causality and influence flowing from the past to the future only. In economics expectations make the arrow of causality flow from the (anticipated) future back to the present almost as often as from the present to the future.
Economics is a quantitative social science
But spite of its political complications, its non-experimental nature, and its peculiar problems of temporal causality, economics remains a quantitative science. Most of what economists study comes in measurable form, with numbers attached. Thusas opposed to sociology and political scienceeconomics makes heavy use of arithmetic and algebra. Economics makes heavy use of arithmetic to measure economic variables of interest. In economics you can always ask, and usually answer, the question how much?
And answering the question how much? Requires counting things, requires arithmetic.
[Figure: financial markets data
Economics also makes very heavy use of algebra to formulate and analyze modelssmall, simplified sets of relationships that are intended to illuminate more complicated processes going on in the economy.
When economists are trying to analyze the implications of how people acthow, say, consumers change (or dont change) their spending in response to a change in incomethey will almost always write down (in algebra) a behavioral relationship: an equation giving a rule for how the effect (economy-wide consumption spending) reacts to the cause (total economy-wide incomes). For example, they will write down a consumption function:
Using "Ct" to stand for economy-wide Consumption spending in some particular year t, and "Yt" to stand for economy-wide total income. c0 and c are the parameters of this behavioral relationshipthey tell us exactly how consumption varies with income: raise total incomes by $1 and consumption will rise by $c; even if incomes were to fall to zero, total consumption spending would still be positive at $c0.
Analyzing the consequences of how people act by writing down these algebraic behavioral relationships has proven a powerful tool. But other kinds of equations appear in economic reasoning as well. There are equilibrium conditionsthings that must be true if the economy is to be in balance, and that if they do not hold then things must be changing rapidly.
In microeconomics the principal equilibrium condition is that supply must be equal to demand. If not, then either buyers who find themselves short are frantically raising their bids (and prices are rising) or sellers who find themselves with excess inventory are frantically trying to dump it (and prices are falling); only if supply equals demand can the price in a market be relatively stable. Similarly in macroeconomics: equilibrium conditions are as a rule simple statements that supply be equal to demand. For example, aggregate demandthe sum of consumption spending C, investment I, government purchases G, and net exports NX:
and aggregate supplyGross Domestic Product [GDP], which is the same thing as total economy-wide income:
must be equal:
If not, then either inventories are rising above or falling below desired levels, and businesses are about to take action by changing their production and sales strategies.
And there is a third kind of algebraic equation: the identity. An identity is something that hold true by definition, so that we cannot even conceive of how it could not be true.
The rhetoric of economics.
Economics is also heavily dependent on metaphors. This should be no surprise. Human beings think in metaphors. They understand something that they do not know by comparing and analogizing it to something that they do know. Economics is no exception.
In economics, curves "shift." Money has a "velocity": if total GDP of $10 trillion is supported by $1 trillion of cash and checking account balances, economists say that money has a "velocity" of 10 (because the average piece of money changes hands as part of a final demand-related transaction some ten times a year).
When the Federal Reserve raises interest rates and throws people out of work, it "pushes the economy down the Phillips curve." When the Federal Reserve lowers interest rates and the economy booms, it "pushes the economy up the Phillips curve"as if the economy were a dot on a diagram drawn on a piece of paper, as if it were constrained to move along a particular curve on the diagram called the Phillips curve, as if changes in Federal Reserve monetary policy really did push this dot drawn on the diagram up and to the left.
It is important for you to be conscious ofand a little bit critical ofthe metaphors that economists use for two reasons.
First, if you dont understand the metaphors and their place much of economics may simply be completely incomprehensible. All will become clear or at least clearer if you remember that a dominant metaphor in macroeconomics is the circular flow metaphor, that the flow (seethere it is, the metaphor) of spending is like the flow of some liquid through the economy, that if the total amount of spending increases but the quantity of money doesnt then the money must "flow" faster since the fixed quantity of pieces of money must change hands more often: hence money must have a higher velocity. Without the underlying context of the metaphor that spending is a circular flow of purchasing power through the economy, references to the "velocity" of money make no sense.
Most of the metaphors you will see in macroeconomics will fall into four classes:
- The first is made up of hydraulic metaphors connected with the dominant image of the circular flow of economic activity.
- The second is economists use of the word "market" to label intricate and decentralized processes of exchangeas if all the workers and all the jobs in the economy really were being matched to each other in a single open-air market.
- The third is economists fondness for the idea of "equilibrium": their thinking about economic processes as if they were somehow bringing the two pans of an old-fashioned scale into balance (thats what "equilibrium" means: equi-librium, equal weights on the two pans of the balance)
- The fourth and last is the way of metaphorical thinking that is the branch of mathematics called analytic geometryeconomists use of graphs and diagrams as an alternative to algebraic equations by identifying equations with curves, equilibrium with points, and changes in parameter values as shifts in the positions of curves on a diagram. This use of metaphor is central enough to economics that it is discussed not in this but the next section of this chapter.
The Circular Flow of Economic Activity
The most frequently encountered metaphor in economics is the metaphor of thecircular flow of economic activity. When economists speak of the "circular flow" of economic activity through the economy, they have a definite picture in their minds eye. Patterns of spending, income, and production are seen as flows of some liquid through different sets of pipes. Categories of actors in the economythe set of all businesses, or the government, or the set of all householdsare seen as pools into and out of which the fluid of purchasing power (i.e., money) flows.
Businesses pay incomes to households in return for the factors of productionthe labor-power of their workers, the capital on which they pay interest (or to whose owners they distribute profits), and so forth. Households pay some of their incomes in taxes to the government, and split the rest between consumption and saving. The government takes the taxes (and any money it borrows from the pool of savings), uses some it to augment households incomes through transfer payments like Social Security, and uses the rest to purchase goods and services for its own purposes. Businesses seeking to invest draw on the pool of savings to gain financing to purchase capital goods to expand their productive capacity. And exports serve as an addition to (and imports a subtraction from) total demand for domestically-made products.
All of these flows of spending then show up as purchases of goods and services from the same businesses that we started from: the businesses that pay incomes to households in return for the resources that they need to make the products to satisfy demand.
This is the circular flow of economic activity.
One benefit of this hydraulic metaphor is to help us see that the economy is made up of ongoing and ever-repeated patterns of activity: not one act of exchange or production, but a continuous process of the exchange and transformation of flows of purchasing power and resources: patterns of activity that both persist and change over time. The hydraulic metaphor is apt in that it reminds us that economic variables like consumption spending or GDP are ongoing flowssee, there the metaphor is.
The circular flow metaphor contains another important truththat every piece of economic activity has two sides. When a business produces and sells something of value, the money earned by the business is then paid out as income to someonethe workers, the suppliers, the bosses, or all three. When a household earns income, that purchasing power is then used somehowtaxed away by the government, spent on consumption goods the household finds useful, or loaned to a bank (or to the U.S. Treasury, if you take the cash and hide it under your mattress) which then uses that purchasing power somehow.
Economists talk as if all economic activityall purchases and acts of exchangetake place in something like the great open-air marketplaces of the merchant cities of the preindustrial past.
[Graphic: Picture of large open-air
They speak offhandedly of how all contracts between workers and bosses are made in the "labor market," of how all the borrowing of money from and the depositing of money into banks take place in the "money market," of how supply and demand have to balance in the "goods market." In the market square of a trading city of the pre-industrial past you could survey all the buyers and all the sellers, and pretty quickly have a good idea of just what was being sold for how much, and what quality it was.
In using the open-air markets of the pre-industrial past as metaphors for the complex processes of matching and exchange that take place in our modern industrial economy, economists are placing an intellectual bet: they are betting that information travels fast enough and that buyers and sellers are well informed enough that the prices and quantities that prevail in our modern economy are as if we actually could walk around the perimeter of the marketplace and examine all buyers and sellers in an hour. In most cases this will be a good intellectual bet to makebut sometimes (for example, in situations of so-called structural unemployment) it may not be.
Economists spend most of their time looking for equilibriumpoints of balance in which some quantity or set of quantities have no tendency to either rise or fall. The dominant metaphor is of an old-fashioned two-pan scale in balance. Equilibrium. Equi-libriumliterally, "even weights" so that both pans of the two-pan scale are at the same height.
This search for equilibrium is a way to try to greatly simplify the process of analyzing an ever changing, dynamic, complicated system. The underlying principle is that things are much easier to analyze if you can first figure out "points of rest," positions and states of affairs where pressures for economic quantities to rise and to fall are evenly balancedsee, there is the metaphor again. Once you have identified the potential points of rest, you can then figure out how fast your stripped-down picture of the economy will converge to those points of equilibrium.
This search for points of equilibrium, followed by an analysis of the speed of adjustment to equilibrium, is perhaps the most common way of proceeding in any economic analysis.
But do not forget: these metaphors are just aids to understanding theories and principles. They are not the theories and principles themselves. And the theories and principles in turn are also just aids to understanding the realityand are not themselves the reality.
The relationship between algebra and geometry
The fourth class of metaphors are drawn from analytic geometry. Its inventor, Rene Descartes (1596-1650), spent a good chunk of his life proving that graphs and algebra are identically useful ways of proceeding: that there is a natural way of identifying an equation with a curve, or a soluation with a point.
Thus metaphors that use analytic geometry portray behavioral relationshipschains of cause and effectlinks between one economic variable and anotheras lines drawn on a graph with axes.
Metaphors that use analytic geometry portray situations of balancesituations in which the economy has reached a stable positionas points on the graph where different curves happen to cross. We use graphs to plot two economic variables on the two axes. We draw one line (or "curve") for each behavioral relationship or equilibrium condition. The point where the curves cross will be the solution: the values at which the two economic quantities that you did not know are consistent with peoples behavior and market equilibrium.
Economics courses use analytic geometrylots of diagrams with curves and intersecting pointsin large part because Paul Samuelson had the good idea back at the end of World War II that many students would be more comfortable manipulating diagrams than manipulating algebraic equations. And he was rightwith diagrams, you can see what is going on. It is often easier to think of how a particular curve would shift than to think of the consequences of changing the value of the constant term in an equation.
Now if you find analytic geometry easy and intuitive, then Paul Samuelsons intellectual innovation makes economics very accessible to you. Understanding economists theories and arguments becomes as simple as moving lines and curves around on a graph, and looking for places where the right two curves cross. It becomes easy to graphically solve systems of equations, and to see how changing the presuppositions of the problem changes the answer. If you are comfortable with analytic geometry, economists reliance on lines, curves, and graphs makes understanding economics relatively easy.
If not not
Then you need to find other tools to help you think like an economist.
Dont get me wrong: these metaphors from analytic geometry are very useful in understanding the economy. It is truly helpful to think about changes in behavioral relationships as if they were curves on a graph that shift about. And it is helpful to think about positions of equilibrium as if the whole economy was a dot on a grapha dot located where two curves describing behavioral relationships cross, and thus where both behavioral relationships are satisfied. And it is helpful to think about changes in the state of the economy as movements on a graph of a dota dot that represents the state of the economy as a point on a diagram, and a dot that spends its time crawling around from one position to another.
But remember that these too are metaphors, not the reality. They are tools to aid your understanding. If the graphs are confusing, then you need to become better at understanding and manipulating algebra, or better at following the verbal descriptions of the argument. But use whichever feels most comfortable: grab hold of whichever makes most sense to you, and recognize that these are really three ways of trying to make the same points and reach the same conclusions.
that doesnt allow for the responsiveness of consumption to a change in total incomes to vary as the economy becomes richer or poorer.
Prices Always Go on the Vertical Axis
Again, dont let this bug you, and dont let this surprise you when you see it.
Simplify, Simplify, Oversimplify
The American economy is complex: 130 million workers, 10 million firms, and 90 million households buying and selling $24 trillion worth of goods and services a year. Economists have placed the intellectual bet that the best way to understand this complexity is to simplify. Restrict your attention to a very few behavioral relationshipscause-and-effect links from one set of economic quantities to anotherand a handful of equilibrium conditionsconditions that must be satisfied for economic activity to be stable and for supply and demand to be in balance in different markets. Capture these behavioral relationships and equilibrium conditions in simple algebraic equations (and analytic-geometric diagrams). See how the mathematical system made up of those equations behaves. Then try to apply the properties of the system back to the real world.
And all along hope that all the quantifying and simplifying have not made the model a bad guide to how the world really works.
Economists call this process of stripping-down of the complexity and variation of the economy into a handful of equations "building a model." And economists then use these models that they have built to try to understand what is going on in the real, complex economy out there..
It is important to understand that economists do not just use modelssystems of equations that in some way are supposed to mimic the behavior of people and institutionseconomists use simple models. Economists use simple models for two reasons. First, no one can understand what is going on inside complicated models. A model is of little use if it generates a prediction, but if you then do not understand the logic behind the prediction.
Second, predictions generated from simple models are nearly as good as ones from complex models. The economic models used in real life by the Federal Reserve or the Congressional Budget Office are more complex than the models in this textbook. But at the bottom they are clearly cousins of the models used here.
The same Phillips curves, IS curves, and consumption functions you see in your textbook underpin staffwork behind meetings of the Federal Reserve Open Market Committtee [FOMC] when it tries to decide whether the management of the economy requires a change in the level of interest rates.
If you hear someone say that economics is more of an art than a science, they are saying that the rules for how to build effective and useful modelsmodels that omit unnecessary detail but retain the necessary and important factorsare nowhere written down. In this important aspect of economics, economists tend to learn by doingor learn not at all.
The Utility of Algebra
This way of model building is a powerful way of thinkingif the detail that you omitted is indeed unnecessary, and if the features that your particular model focuses its attention on are in fact the most important features for analyzing the issues at hand. But the odds that this will be a fruitful intellectual strategy are good because the tools are powerful.
Algebraic equations are the best way to summarize cause-and-effect behavioral relationships in economics. Because so many of the concepts that economics deals with are easily counted, it is natural to use the fact that they can be counted: natural to say not just that consumption spending was strong, but that it was $6.25 trillion dollars that year. But arithmetic reaches limits. For example, it would be very cumbersome to carry around a large table telling you what economy-wide consumption spending is likely to be for each of a thousand different possible values of total economy-wide household incomes. It is easier to remember and to work with a single algebraic equation. As before, with Ct standing for consumption spending in some year t and Yt standing for total incomes in some year t, economists might write:
(with both consumption and income in
billions of dollars)
if it is indeed the case that consumption spending is likely to be $2 trillion even if incomes were to fall to zero, and if it is indeed the case that a $1 increase in income induces a $0.50 increase in consumption spending. Thus a single equation with fixed and known coefficients (the $2,000, and the 0.5) can take the place of a very large table detailing the relationship between income and consumption for some of the many possible values of income.
Table: The Relationship between Income and Consumption
(in billions of dollars)
But algebra has yet another advantage. Algebra allows you to do more than just think about the consequences of the one particular systematic relationship between consumption and income, like:
(with both consumption and income in
billions of dollars)
Algebra allows you to think about the consequences of a host of different possible systematic relationships:
Algebra does this by replacing the fixed and known coefficients $2,000 and the 0.5 in the first equation above with unspecified (and potentially varying) parameters, in this case call them c0 and c:
Using algebra to analyze the single equation above implicitly allows you to manipulate and analyze all at oncein shorthand formall of the long class of systematic relationships with different parameter values above, and all of the tables that they summarize, all at once.
Moreover, it is easy to move back from the abstract to the specific when you want to consider one particular case with one particular set of values for the parameters. Then just substitute the numerical values for that particular case ($2,000, and 0.5) for theabstractparameters (c0 and c).
The Power of Algebra
allow us to do comparative statics. They let us see what would happen to the equilibrium level of Yt if the parameters were a little bit different: a $1 increase in c0 increases equilibrium total output Yt by 1/(1-c) dollars, no matter what value c happens to take on.
Economics No Longer Focused on Description
Economics could have developed as a descriptive science: courses in economics could contain long lists of economic institutions and practices, and could be devoted to cataloguing and detailing the institutional structure of the economy. But it has developed as a more abstract science: courses spend most of their time on relatively abstract and general principles that nevertheless had proved useful in studying a number of situations.
Thus a remarkably large part of what economists have to say is tied up in their particular set of tools: a particular way of thinking about the world that is closely tied up with a particular technical language and a particular set of data that are most often examined. It is possible (at least, I have found it possible) to get a lot out of sociology and political science courses without learning to think like a sociologist or a political scientist because of their focus on the detailed analysis and description of institutions. It is much less possible to get a lot out of an economics course without learning to think like an economist.
The power of algebra is a principal reason that modern economics has become more of an abstract, tool-applying discipline. Had economists in the first half of the twentieth century found that their mathematical tools were less useful than they in fact turned out to be, economists in the second half of the twentieth century would have developed the field in different directions
Unfortunately for some of you, many students who wish to learn economics do not especially like algebra: the relationship between the equations with their Cts and their Its and their Ds and the real economy quickly becomes obscure. Economists have developed a number of tools (mostly graphics and diagrams) to try to make the algebra more intelligible. But they have had mixed success
Keys to Model Building
Ignore Differences Between People
One simplification that macroeconomistsbut not microeconomistsinvoke at almost every opportunity is the simplification that all participants in the economy are the same, or rather that the differences between businesses and workers do not matter much for the issues that macroeconomists study. The convention is to analyze a situation by examining the decision-making process that would be followed by a single representative agenta single representative business, representative worker, representative saver, whateverand then generalize to the economy as a whole the conclusions reached about how the decisions of that single representative agent are affected by the economic environment.
This use of the construct of the representative agent makes macroeconomics much simpler.
Difficulties with "Representative Agents"
As I wrote at the beginning of this chapter, every intellectual discipline sees some things very clearly and some things very fuzzily or not at all: distribution and its impact on social welfare is one thing that macroeconomics has trouble bringing into focus.
Look at Opportunity Costs
Perhaps the most fundamental principle of economics is that there is always a choice and that making a choice excludes alternatives. If you keep your wealth in the form of easily-spendable cash, you pass up the chance to keep it earning interest in the form of bonds. If you keep your wealth in the form of interest-earning bonds, you pass up the capability of immediately spending it on something that suddenly strikes your fancy. If you spend on consumption goods, you pass up the opportunity to save.
Economists call the value of the best alternative to any choice that someone is making that choices opportunity cost.
At the root of every behavioral relationship in an economic model will be somebodys decision. In analyzing that decisionand thus building up the behavioral relationshipeconomists will always think about the decision makers opportunity costs: if you do or get this, what opportunities and choices are you thereby excluding? How much of X will the decision maker choose given his or her other alternatives?
A substantial number of students make economics a lot harder than it has to be by not remembering that this opportunity cost way-of-thinking is at the heart of every behavioral relationship in an economic model.
Focus on Expectations
Much of the time the opportunity cost of taking some action today will not be an alternative use of the same resources today, but will involve some saving or husbanding of resources for the future. A worker trying to decide whether to quit his or her job and search for another will be thinking about what the future wages will be in the job that will be found in the future, after a period of searching. A consumer trying to decide whether to spend or save will be thinking about the rate-of-return on saving, which depends on what the rate of inflation and the level of the stock market will be in the future.
But no one knows what the future will be. At best we can form more-or-less rational-and-reasonable expectations of what the future might be.
Hence nearly every behavioral relationship in an economic model will depend on expectations of the future. The processes by which expectations are formedthe amount of time that individuals have to devote to thinking about what the future might be like, the information they have to process, and the rules-of-thumb they use to turn the information they have into expectationsare a central, perhaps the central piece of macroeconomics.
Economists tend to consider three types of expectations:
- Static expectationsin which the future in the relevant dimension is not thought to be uncertain or predictable enough that it is worth spending any time thinking systematically about how the future will be different.
- Adaptive expectationsin which time and attention is spent thinking about the future, and the rules-of-thumb adopted relate expectations of the future values of variables to their values now and in the recent past.
- Rational expectationsin which a lot of time and attention is spent thinking about the future, and in which the decision-makers in the economic model know as much (or more) about the structure and behavior of the economy as the economist building the model does.
Depending on which type of expectations is believed to hold, the behavior of the economic model can be very, very different.
As I wrote above, the fact that behavioral relationships depend on opportunity coststhat opportunity costs depend on expectations of the futurethat expectations are formed by individuals and decision-makers who are as smart as we are (indeed, they are us)makes economics potentially complicated and hard. The present depends on what people expect the future to be, and peoples expectations of the future are almost surely tied up with what is going on in the present. Analyzing situations in which cause-and-effect are potentially scrambled in this way can become very difficult very quickly.
An example: a simple model.
The Keynesian cross.
We have already presented the bulk of one of the simplest models used by macroeconomiststhe income-expenditure model, the so-called Keynesian Crossin the earlier sections of this chapter. It consists of the consumption function:
the national income identity:
and the statement that investment It, government purchases Gt, and net exports NXt are exogenousexo-genous, literally "outside-generated." To say of a quantity that it is exogenous is to say that it is generated outside of the model. Such quantities are things that the model doesnt try to account for. Instead, the model takes them as its inputs: as features that have already been determined and set by outside forces.
The assumptions (a) that I, G, and NX are generated outside the model by forces separate and unconnected with the determinants of consumption, and (b) that consumption spending has the simple systematic behavioral relationship of the consumption function are simplifying assumptions. They are not literally true: the level of consumption spending is determined by the decisions made by a hundred million households, not by a simple linear algebraic equation. But these simplifying assumptions do make it possible to analyze the model. And we hope that the simplifying assumptions we have to make in order to make the analysis tractable have not dropped so much of reality out of the model as to make it useless.
The consumption function is a behavioral relationshipa cause-and-effect prediction that if income is at level X consumption will be at level Y, and that if income changes by an amount DX (where "D" is a Greek letter, capital delta, often used as a shorthand for "change in") then consumption will change by an amount DY.
The national income identity is an equilibrium conditionsomething that must hold for the economy to be in balance. All economic models have behavioral relationships in themspecifications of how groups of economic agents will react to a range of conditions. And all have equilibrium conditions.
Solving the model three different ways.
We can analyze this model in any of three ways.
First, we can draw the so-called income-expenditure diagram, with the sum of spending (C+I+G+NX) on the vertical axis and the level of total income Y on the horizontal axis. Then we can use the consumption function and the exogenously-given values of I, G, and NX to draw a line representing the expenditure function: how much total spending (C+I+G+NX) there is for each possible value of total income Y. And the point at which the expenditure function lies on a 45-degree line along which the national income identity is satisfiedalong which C+I+G+NX=Yis the economys equilibrium position.
Thus we can use analytic geometry to analyze this model. And if our hand is steady enough and our eye good enough, we can read quantitative answers off of our graph.
Second, we canas was done abovedo the algebra: combine the national income identity and the consumption function to produce:
Then simply substitute in the (exogenously-given) values of the variables on the right-hand side and the two parameters c0 and c to solve the model and determine the level of total income Y.
Thus we can use algebra to analyze this model.
Third, we can talk through this modelwe can use our words:
In order for the economy to be in equilibrium, total spending must be equal to total income. Total spending is made up of four components, three of which (investment, government purchases, and net exports) are determined outside this simple model.
The fourth component of spending, consumption spending, is an increasing function of income: the higher are total incomes, the higher is consumption spending, but consumption spending increases less than dollar-for-dollar with increases in income.
Thus to determine the equilibrium level of total spending and income, start with the level that total spending would have if income were zero. In this first round, at this level of incomezerototal spending would be greater than total income, and since total income is equal to total production, more would be being purchased by consumers and others than is being produced. So this cannot be a stable position for the economy. Supply does not equal demand, and so the equilibrium condition is not satisfied. Things would change rapidly. In this case, assume that businesses would react to the fact that there inventories are falling by increasing productionhiring workers and buying materials until total production (and total incomes) would be equal to the first-round level of spending.
This takes us to the second round.
Consider what would happen if income were at a level equal to first-round spending. In this second round income would still be less than spendingbecause spending in this second round would be higher because incomes are higher, and higher incomes generate higher consumption spending.
So next, in the third round, consider income at a level equal to the level of second-round spending.
Continue this process. Eventuallybecause each dollar increase in income increases spending by less than a dollaryou will find the equilibrium level of income (and spending) to be that at which total spending (as a function of the level of total income) is equal to the level of total income itself.
All three ways of proceeding are equally valid and correct. Some ways may be easier or more useful to us at certain times or in certain circumstances. Some ways may be just plain easier for certain ones of us.
Verbal descriptions get the causal chain clear, but are less good at arriving at quantitative answers. The algebra is the quickest road to an answer, but may leave you wondering why it is the answer. The diagrams are wonderful if you think like Rene Descartes, but you may then have a hard time untangling the metaphor to get back from shifting curves and moving points of equilibrium to real people changing how they behave and how they live.
Whatever, all three ways are different ways of describing the same processes. Make this availability in macroeconomics of these multiple points of view your friend; dont let it be an obstacle to your understanding.
Thus you will find economics textbooks putting forward concepts and ideas in no fewer than three ways. The concepts and ideas will be presented first in verbal descriptions, second in equations, and third in the lines and curves of graphs and diagrams. Much of the time the principal weight of the discussion and explanation will happen in the graphical partthe lines and curves on graphs and diagrams. But all three are useful, and unless you understand all three your knowledge is partial and imperfect.
An Example: Consumers Become More Pessimistic
These are all three different views of the same process, the same thing. Either we say that consumers become pessimistic and spend less, we reduce the value of a parametera numberin an algebraic equation is reduced, we shift a line on a diagram downward.
The first uses words, the second uses algebra, and the third uses analytic geometry. The first tells what consumers do, the second describes the change in the algebraic behavioral relationship that economists use to model consumer behavior, and the third uses the metaphors of analytic geometrythe behavioral relationship between consumers incomes and spending is seen as a line on a graph that can and does change position as circumstances change.
1. Dont be surprised to find economists ways of thinking strange and newthat is always the case when you learn any new intellectual discipline.
2. Dont be surprised to find economics riddled with metaphorical thinkingthe velocity of money, curves that shift, and most important the idea of the circular flow of economic activity.
3. Dont be surprised to find economics more abstract than you had thought. Todays economics courses focus more on analytic tools and chains of reasoning and less on institutional descriptions.
4. Economics is a relatively mathematical subject because so much of what it analyzes can be measured. Thus economists use arithmetic to count things, and use algebra because it is the best way to analyze and understand arithmetic.
5. When macroeconomists build models, they usually follow four key strategies:
- Strip down a complicated process to a very few economy-wide behavioral relationships and equilibrium conditions.
- Simplifyignore differences between people in the economy
- Look at opportunity costs as ways to understand behavioral relationships.
- Focus on expectations of the future, and how such expectations affect the present
6. In economics, you will find that arguments are repeated in three different forms: once in words, once in equations, and once in the form of diagrams on which lines (or curves) shift and points of stable equilibrium are found "where the curves cross."
[To be written]
[To be written, and revised for each year within editions]