In comparison, the misery of the Great Depression reached a peak in the UK in 1932. The rate of unemployment topped out at 22 per cent, although output measured by GDP fell by only about 5 per cent over the preceding years. The next worst recessions, in the early 1980s and 1990s, by contrast, were characterised by persistent high unemployment, peaking at 10 per cent, but falls in GDP of only 3 per cent and 1.5 per cent each.
As a witness to the Great Depression, Keynes obviously wanted to figure out what caused such a drastic economic downturn – and what may prevent such devastation from happening again.
Adjusting inventories instead of prices
Not only did Keynes figure out that sticky prices cause recessions, but he also developed a hugely influential model that’s still presented in many macroeconomics textbooks. This model is a small part of a larger approach to managing the macroeconomy that came to be called Keynesianism – an
approach that favoured large government interventions into the economy rather than the sort of laissez-faire policies of non-intervention preferred by other people. (For a discussion of the costs and benefits of having the gov- ernment intervene in the economy, see Chapter 3.)
To be fair, we have to point out that Keynesianism has attracted a lot of critics and is not the be-all-end-all of macroeconomics. But the part of it we present here is not controversial. This aspect of Keynesianism explains how an economy adjusts to equilibrium – a place where aggregate supply matches aggregate demand – in the extreme short run after an economic shock when prices can’t change at all.
Look back at Figure 6-4 for a moment. The Keynesian model elaborates on exactly how an economy moves from producing at output level Yo to produc- ing at output level Y1 when a shock to aggregate demand happens and prices are fixed at level Po.
Keynes’s model focuses our attention on firms’ inventories of goods that have been made but not yet sold. According to Keynes, changes in invento- ries guide firms to increase or decrease output during situations in which prices are sticky and can’t serve as signals of what to do.
To see the novelty of Keynes’s inventory idea, understand that if prices were able to change, prices (not inventories) would guide firm decisions about how much to produce:
✓ If prices are rising, a firm knows that its product is popular and that it should increase output.
✓ If prices are falling, the firm knows that the product isn’t doing well and that it should probably cut output (and maybe get into another line of business!).
In an economy with fixed prices, however, firms need some other way of deciding whether to increase or decrease production. Keynes realised that the guiding force would be changes in inventories.
Keeping an eye on target inventory levels
Inventories are constantly turning over, with goods flowing both in and out.
New production increases inventories, while new sales decrease inventories.
The two factors interact to determine whether inventories are rising, falling or staying the same. For example, if new production equals new sales, inventory levels stay constant. If new production exceeds new sales, inventories rise.
The interaction of new production and new sales is important because each firm has a target level of inventories that it likes to keep on hand to meet
situations in which sales temporarily run faster than the firm can produce output. The target level is determined by the costs and benefits of having a bigger or smaller inventory on hand.
Having less inventory than the target level is dangerous because the firm may not be able to keep up with sales spikes. Having more inventory than the target level is wasteful because there’s no point in having stuff sitting around unsold, year after year. Each firm weighs these costs and benefits to come up with its own target inventory level.
Target inventory levels may vary from year to year depending on whether firms are expecting strong or weak sales. If managers are expecting strong sales, they may plan on increasing inventories, whereas if they are expecting weak sales, they may plan on decreasing inventories.
Keynes realised that aggregate demand shocks (which are, by definition, unexpected) would show up as unexpected changes in firm inventories.
✓ Unexpectedly low aggregate demand means that sales slow so much that inventories increase and reach levels higher than firms had planned on.
✓ Unexpectedly high aggregate demand means that sales increase so much that inventories decrease and reach levels lower than firms had planned on.
Increasing or decreasing output as inventories fluctuate
Unexpectedly large changes in inventories cause firms to change their output levels as follows.
✓ If inventories rise above target levels, firms respond by cutting produc- tion. By reducing production rates to less than sales rates, inventories begin to fall down toward target levels.
✓ If inventories fall below target levels, firms respond by raising produc- tion. By increasing production rates to more than sales rates, invento- ries begin to rise toward target levels.
The changes in output levels caused by changes in inventories are hugely important because they determine not only whether output (Y) is increasing or decreasing, but also whether unemployment is rising or falling.
For example, if firms increase production because inventories have fallen below target levels, they need to hire more workers, and unemployment falls.
If, on the other hand, firms decrease production because inventories rise above target levels, they need to lay off workers, and unemployment rises.
Adjusting inventories based on planned and actual expenditures
The Keynesian model differentiates between planned expenditures and actual expenditures as follows:
✓ Planned expenditures are the amount of money that households, busi- nesses, the government and foreigners want to spend on domestically produced goods and services.
✓ Actual expenditures are equal to gross domestic product (GDP), which we discuss in Chapter 4; they are what households, businesses, the gov- ernment and foreigners actually end up spending on domestically pro- duced goods and services.
What happens when actual expenditures are different from planned expendi- tures? Inventories automatically change. For example, if more money is spent on goods and services than was planned, people are buying up more output than is currently being produced. This situation is possible because firms sell goods from their inventories that were produced in previous periods. On the flip side, if people spend less money on goods and services than was planned, firm inventories rise because firms have to store up all the output that they can’t sell.
Keynes represented planned expenditures, PE, algebraically with the follow- ing equation:
PE = C + IP + G + NX (1)
What do all these letters mean? We discuss them in detail in Chapter 4, but here’s the short version:
✓ C stands for the amount of output that consumers want to consume.
✓ IP stands for the amount of output that firms plan to buy as investment goods, such as new factories and equipment, as well as any inventory changes that firms plan to make.
If, later on, firms have to increase or decrease inventories more than they planned, actual investment, I, doesn’t equal planned investment, IP. ✓ G stands for how much output the government wants to buy for things
such as building schools or ensuring an adequate supply of paper for paperwork.
✓ NX stands for net exports – the value of our exports minus the value of our imports. NX tells us the net demand that the foreign sector of the economy has for stuff that we make domestically.
For actual expenditures, Y, Keynes used the same equation that we use to calculate gross domestic product (which we discuss in Chapter 4):
Y = C + I + G + NX (2) Why can we use the GDP equation to calculate actual expenditures? As we explain in Chapter 4, actual expenditure is equal to national income because every penny of expenditure made in the economy is income to somebody.
Furthermore, actual expenditure is also equal to the pound value of all goods and services produced in the economy because every bit of output produced is sold to someone. (This process is actually part of the way that stock is valued for accounting purposes: any output that a firm makes but can’t sell to customers is counted as being ‘sold’ by the firm to itself as that output is placed into inventory. These inventory changes are known as inventory investment and are totalled up in GDP as part of the total investment, I.) Having three ways of looking at Y is actually very handy as you become famil- iar with the Keynesian model. Sometimes, understanding the model is easier if you think of Y as being actual expenditures; at other times understand- ing is easier if you think of Y as being national income or output. We switch between these three definitions whenever doing so helps make understand- ing the model easier.
The only difference between the right-hand sides of equation (1) and equa- tion (2) is the investment variable, which is planned investment (IP) in the first equation and actual investment (I) in the second. In other words, Y and PE differ only because of differences in investments caused by inventories increasing or decreasing unexpectedly when sales are more or less than planned.
Bringing some algebra into the mix
You knew the time was coming: here’s where things get algebraic. Our goal?
To identify the Keynesian model’s economic equilibrium by using our math- ematical superpowers. (Quick – to the nearest surviving public telephone box!)
First, we need to define a consumption function – a way to calculate total con- sumption – that we can substitute into equation (1). In Chapter 4, we present the following formula for calculating consumption:
C = Co + c(1 – t)Y (3)
For all the details, look back at Chapter 4. For now, what you really need to know about this formula is that higher income (Y) leads to higher consump- tion (C).
If you substitute equation (3) into equation (1), you get:
PE = Co + c(1 – t)Y + IP + G + NX (4)
If you look carefully, you see that this equation shows that the total planned expenditure on goods and services in the economy (PE) depends on the total income in the economy (Y). The higher the total income, the more money people are going to plan to spend.
A good way to simplify this equation is to create a variable called A and to define it as follows:
A = Co + IP + G + NX
When you do that, equation (3) looks a little more palatable:
PE = A + c(1 – t)Y (5) The variable A stands for autonomous expenditures, by which economists mean the part of planned expenditures that doesn’t depend on income (Y).
The part of planned expenditures that does depend on income, c(1 – t)Y, is known as induced expenditures.
To understand induced expenditures, you need to realise that because t stands for the income tax rate, (1 – t)Y is what people have left over to spend after the government taxes them. And of that amount, the fraction c gets spent on consumption, so that c(1 – t)Y tells you how much expenditure is
‘induced’ by an income of size Y.
Figure 6-6 graphs equation (5) and labels it the planned expenditure line.
To find the specific equilibrium of the Keynesian model, understand that all possible equilibriums are captured by the following equation:
PE = Y (6)
Figure 6-6:
The planned expenditure line.
Planned Expenditures
Planned Expenditures PE = A + c(1 − t)Y
Income, Output, Y PE
This equation can be read as ‘planned expenditures equal actual expendi- tures’. (Remember that Y equals both total income and total expenditure in the economy because all expenditures are income to somebody.)
Any situation where PE = Y is an equilibrium. Why? Because if the economy can get to the point where PE = Y, nobody has any reason to change behav- iour. Consumers are consuming as much as they planned to consume (C).
The government is buying up as much output as it wanted to buy (G).
Foreigners are buying as much stuff from us as they intended (NX). And, most importantly, firms are spending exactly as much on investment as they planned – implying that inventories aren’t changing unexpectedly.
If planned expenditures equal actual expenditures, you truly have an equi- librium because everybody is getting what they want, and nobody has any incentive to change behaviour.
You can solve the equilibrium value of output, which we call ~
Y, by substitut- ing equation (5) into equation (6). If you do so, you get the following:
Y = A + c(1 – t)Y (7)~
Showing equilibrium graphically
If the last equation is just too frightening, stick with us because finding the Keynesian model’s equilibrium graphically is much easier. To do so, you plot the PE = Y equation on the same graph as the PE = A + c(1 – t)Y equation, as we do in Figure 6-7. The point where the two lines cross is the equilibrium.
At that point, planned expenditures exactly equal actual expenditures in the economy.
Figure 6-7:
The Keynesian model’s equi- librium, ~
Y.
Planned Expenditures
Planned Expenditures PE =A+ c(1 − t)Y Actual Expenditures
PE= Y
Income, Output, Y PE
~Y 45°
This equilibrium is stable, by which we mean that if the economy starts out at any income level other than ~
Y, it soon moves back to ~
Y. The thing that returns the economy to ~
Y is inventory changes.
To see why this is true, look at Figure 6-8, which exploits a nifty geometric trick about the PE = Y line to show how the economy behaves when it’s not producing at the equilibrium output level, ~
Y.
Figure 6-8:
How inventory adjustments always move output back toward ~
Y.
Y1 PE
Y2 Y1 Income, Output, Y
PE1
PE2 Y2 Planned Expenditures
Planned Expenditures Actual Expenditures
~Y 45°
Falling Inventories Cause Output to Increase
Increasing Inventories Cause Output to Fall
The trick is that the PE = Y line shows up on the graph at a 45-degree angle, meaning that it can be used to draw squares – shapes whose sides have the same length. That means you can transpose any value of Y onto the vertical axis. To do so, take any value of Y, go straight up until you hit the 45-degree line, and then go straight sideways until you hit the vertical axis. The point you hit represents as many pounds vertically as Y represents horizontally.
For example, in Figure 6-8, start on the horizontal axis at output level Y2, which is less than the equilibrium output level ~
Y. If you go up vertically to the 45-degree line and then to the left, you can plot output level Y2 onto the verti- cal axis. Why is this useful? Because Y2 can then be compared directly with the level of planned expenditures, PE2, which you get by starting at output level Y2 on the horizontal axis.
As you can see, PE2 > Y2, meaning that planned expenditures exceed output in the economy. This situation means that inventories are going to drop unex- pectedly as firms sell part of their stockpiles of inventory to make up for the fact that people are buying up more stuff than firms are currently producing.
This drop in inventories returns the economy to equilibrium.
As inventories fall unexpectedly, firms increase production. As a result, Y increases. Furthermore, Y continues to increase until it reaches ~
Y because for any value of Y < ~
Y, you can see from the graph that planned expenditures continue to exceed output.
Inventory adjustments also return the economy to equilibrium if it starts out at an output level like Y1, which is greater than ~
Y. As you can see in Figure 6-8, by using the 45-degree line, actual output, Y1, exceeds planned expenditures, PE1. In other words, people are buying less (PE1) than firms are currently pro- ducing (Y1), so inventories are going to start to rise.
Firms respond to increases in inventories by reducing output. They lay off workers and cut production. As a result, Y falls. Y continues to fall until it reaches ~
Y because for any value of Y > ~
Y, you can see from the graph that output is going to continue to exceed actual expenditures.
Boosting GDP in the Keynesian model
Keynes didn’t just invent his model to explain how economies with sticky prices reach a stable equilibrium. What he really wanted to do was to use it to show what governments can do during a recession to make things better.
For example, consider Figure 6-8 once again. Suppose that inventory adjust- ments have carried the economy to equilibrium income, ~
Y, but that ~ Y is less than the economy’s full-employment output level, Y*. In such a case, Keynes asked, what – if anything – should governments do?
Governments can choose to do nothing. Eventually, because ~
Y< Y*, prices will fall and the economy will return to full employment (as it does moving from point B to point C in Figure 6-5). But Keynes argued that governments would be able to speed up the recovery by boosting planned expenditures.
For example, suppose that the government decides to increase G, govern- ment spending on goods and services. If it does so, PE in equation (4) clearly gets bigger. Because G is a part of autonomous expenditures (A), the increase in G means an increase in A in equation (5). Graphically, a larger A means that the planned expenditure line shifts vertically from PE1 to PE2, as shown in Figure 6-9. Given the fact that the actual expenditure line (PE = Y) doesn’t change, the vertical shift in the planned expenditure line causes equi- librium output to increase from ~
Y1 to ~ Y2.
Figure 6-9:
Increasing government expen- ditures increases equilibrium output from Y~1 to ~
Y2. PE
Income, Output, Y Planned
Expenditures
Actual Expenditures
Planned Expenditures After G Increases, PE2
Initial Planned Expenditures, PE1
~Y1 ~
Y2 45°
Keynes suggested using government policy to increase planned expenditures by whatever amount was necessary to increase the economy’s short-run, sticky-price equilibrium, ~
Y, all the way to the full-employment output level, Y*. (Famously, he extended this idea to paying some people to dig holes in the ground and others to fill them in again – in other words, any action is better than no action!) In Chapter 7, we discuss such policies in greater detail, including why they don’t always work so well in practice.