Basic Macroeconomics - What causes unemployment?

 

        We will honor tradition and begin with a discussion of Say’s law - an old and simple idea that still stirs strong passions.  Conservatives often claim Say as one of their own and defend him mightily.  See 

http://www.libertyhaven.com/theoreticalorphilosophicalissues/economics/keynesianism/sayslaw.shtml

The most authoritative source on virtually any dead economist is at

http://cepa.newschool.edu/het/index.htm

 

We will let Say speak for himself:

 


"It is worth while to remark, that a product is no sooner created, than it, from that instant, affords a market for other products to the full extent of its own value. When the producer has put the finishing hand to his product, he is most anxious to sell it immediately, lest its value should diminish in his hands. Nor is he less anxious to dispose of the money he may get for it; for the value of money is also perishable. But the only way of getting rid of money is in the purchase of some product or other. Thus the mere circumstance of creation of one product immediately opens a vent for other products." (J.B. Say, 1803: p.138-9)

 

Lets consider the statement a bit. Production is said to create demand equal in value.  The $20,000 you pay for a car is divided up in payments to autoworkers, steelworkers, rent on land, machinery and profits.  All funds go to a person who then decides to go to the movies, buy books, travel, buy stocks, bonds, deposit the funds in a bank or start their own company. While if all these possibilities are considered demand, it is clear supply and demand must be the same but the supply and demand for autos certainly need not be the same. Even the supply and demand for goods need not be the same once goods are separated out from financial instruments.  All recognize this distinction between the identity of aggregate demand and supply and the components of supply and demand. 

 

However conservatives question whether there can be a general lack of demand.  This is puzzling given that Say was quite clear on the point. 

 

“In a community city province or nation, that produces abundantly…almost all the branches of commerce… yield handsome profits, because the demand is great… And vice versa, wherever, by reasons of the blunders of the nation or its government, production is stationary, or does not keep pace with consumption, the demand gradually declines, the value of the product is less than the charges of its production; no productive exertion is properly rewarded; profits and wages decrease;… Depopulation misery and returning barbarism, occupy the place of abundance and happiness” (p. 21-22 of the 1832 English translation) 

 

However, the brief quote evokes several other controversies as well. Say claims the producer is anxious to sell immediately.  Unless production is intended for inventory, this is of course true.  However, the producer’s anxiety may well stem from his recognition that there is no guarantee the product will ever sell.  It is quite possible products intended to be sold get held by the producer in a warehouse as unintended inventory investment. 

The next line “Nor is he less anxious to dispose of the money” is a reference to the oldest theory of depressions.  Fear was said to cause people to hoard money and thereby depress demand. Say’s theory connects money with production.  Any disruption of the money flow affects production and any disruption of production affects the flow of money.  Whether we choose to focus on money or production is in some ways arbitrary but historically quite important.

 

 


The Great Depression begins in England in the mid 1920’s and in the US in 1929.  By 1930 it was clear periods of several years could pass with persistently high unemployment – not just in specific fields but in most fields generally. However there was no clear theory underlying the experience. The key idea comes from Richard Kahn in a 1931 Economic Journal article introducing the income-expenditure multiplier that provides a simple multiple-equilibrium theory.  John Maynard Keynes, the editor of the EJ, was searching for just a concept as its absence from his Treatise on Money had led to scathing criticism, even from his friends.  The final product is The General Theory of Employment Interest and Money which is a mainstay in Macro.   Keynes was also a rather good mathematician, and if you are interested in this aspect of his work, consult

http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Keynes.html

 

 

        The General Theory is widely considered to be difficult to read and texts rarely make direct use of Keynesian arguments. Instead, simple graphical explanations have evolved that capture the ideas to some degree.  We begin with the circular flow. 

       

 

 

 

 

 

 

 

 

 

 

 

 

 

 


When a business produces it must pay workers for their time, the owners of land for use of the property, buy machinery and distribute profits to owners.  Therefore every dollar taken in is allocated to some person and that person is a member of a household.  In the diagram, $2000 worth of goods are produced and households are paid $2000.  Not everything business produce though are sold to households.  Goods may be kept on store shelves or sold to other businesses, this is called investment. Note that in this context investment refers to goods and services not sold to households, it does not include stocks or bonds.  The investment may serve some useful purpose or it may not.  Customers are unlikely to return to a store if it does not have what they need, therefore inventory is important in maintaining long term relationships with customers.  Businesses may well build new factories with the hope of producing and selling goods in the future. However it is possible the firm intended to sell the goods and could not, that is unintended investment.   The top flow represents goods sold to households, $1600.


    Similarly, households do not spend all the income they receive.  Some funds are set aside for retirement, education of children or a car they want to buy next year.  The point of the circular flow diagram is simply that what households choose to save must equal what businesses actually invest – whether they want to or not. The difference between the top flow of $1600 and the bottom flow of $2000 is $400, whether we measure it from the households or the businessman’s point of view.  The reason is simple, businesses do not sell what households do not buy.  What businesses do not sell is investment, what households do not buy is savings.

 

        This idea is represented as Y = C+I = C+S.  Y is total income, the $2000.  C is what households spend and businesses sell to households, $1600.  I is investment and S is savings.  The concept is that as businesses produce goods to be sold to households or business they generate income.  Then that income is divided between consumption and savings.  After cancelling out C we  have I = S.  This is an identity, it is true by construction.  The difficulty is that it is possible that given the current business climate, businesses do not think additional plant or inventories are likely to be profitable and may want to invest only $300.   What will they do? 

        In the Keynesian version of the story they cut production and workers are laid off producing unemployment.  In the classical version, prices fall, consumers buy more and there is no unemployment.  Clearly it makes quite a difference which is true.  We will gradually allow more and more discussion of price flexibility but for the moment we follow the Keynesian lead and assume output is reduced. 

 

        We have an identity linking the household and business sector and we have a crude theory of behavior of firms – if there is unintended inventory accumulation they cut production.  All we need is a theory of household behavior and we will have our first macroeconomic model.  The theory is households spend most of what they earn.  In symbols:

 

Model 1:

Y = C + I = C + S    (identity linking sectors)

Id = If       (desired investment is equal to some fixed amount)

C = Co + mpcY  (Consumption is some initial amount plus a fraction of income)

mpc = maginal propensity to consume

 

 

We will construct more and more complex models, but the structure above will be maintained.  Identities will link sectors and theories of behavior will be constructed in each sector.  In the last 30 years simple rules of thumb have come into disfavor, carefully specifying the objective function and constraints decision-makers face is more popular.

 

The model may be solved in several ways.  First we will try it as a game, then solve graphically, then solve algebraically. 

 

The Game:

Let there be 4 capitalists, each wishes to invest $100.

 

Each capitalist also decides how many to employ.  A production line employs four workers and each capitalist has the equipment for 3 lines.  Therefore there are production facilities capable of employing 3x4x4 = 48 people. 

 

Let there be 40 workers.  If the worker is employed he earns $50 and spends $35.  If the worker is unemployed he earns nothing but spends $10.  Therefore the consumption function of a particular worker is C = $10 +.5y, for the class of workers as a whole it is $400+.5Y, where y is individual income and Y is the sum of income over the forty workers. 

 

We need four volunteers to be capitalists, these people will decide how many lines to run, and therefore how many workers to employ.  The basic requirement for being a capitalist is that you can pick a number between 0 and 3, we will work out the implications of the choices together.  The following table will keep track of our progress. 

 

lines used

workers hired = L

Y = 50L

C = 400 +.5Y

S = Y-C

I

Id

cut back or expand

0

 

 

 

 

 

 

 

4

 

 

 

 

 

 

 

7

 

 

 

 

 

 

 

8

 

 

 

 

 

 

 

9

 

 

 

 

 

 

 

10

 

 

 

 

 

 

 

11

 

 

 

 

 

 

 

 

If you are doing this on your own, treat it like an exercise, given the different number of lines operating, how many workers are hired?  What is aggregate income? Aggregate savings? Since actual investment equals savings we can compare actual investment to the desired investment level of $400.  If actual > desired firms cut back.  Where is the equilibrium?  

 

The other way to find the equilibrium is graphically. Each block in the grid below represents $100.  A 45-degree line and the sum of C+Id has been plotted.  From the circular flow we know that when Y = C +Id  S = Id and firms neither expand or contract.  Therefore where the red and yellow lines cross is the equilibrium marked in green, which agrees with the result in the table.  To sum up, if  1600 is produced, consumption is 400+.5(1600) = 1200, adding the 400 of desired investment demand is 1600.  Therefore, at Y = 1600, all production finds a willing buyer.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Finding the Equilibrium Algebraically

 

Y = C + Id

Id = 400

C = 400 +.5 Y

 

Therefore:

Y = 800+.5Y

.5Y = 800

Y = 1600

 

We will learn a bit more if we leave the equations in symbolic form.  Let

Y = C + Id

Id = If

C = Co+mpcY

 

Then

Y = Co+mpcY + If

Y(1-mpc) = If + Co

Y = (If+Co)/(1-mpc)

 

The equation says equilibrium income is equal to initial spending (spending at income zero) times the multiplier.  The multiplier is 1/(1-mpc) .  In our example, initial spending is 800, and the multiplier is 1/.5 = 2. 

 

The multiplier as an infinite series: 

        Imagine a bag with 100 pennies in it.  The teacher gives the bag to Anna.  The student counts out 20 pennies and puts them on the desk and passes the bag to Maxim.  The 100 pennies represents income, the 20 pennies savings and the 80 pennies consumption.  The next student also saves 20%.  Maxim places .2(80) = 16 and passes on the remaining 64.  

 

Y = 100 + 80 + 64 +…… in an infinite series.

S = 20 +16 +……. also in an infinite series. 

 

Adding up income would be tedious but we know what the limit of savings is as the process

continues.  Eventually, there will be only one penny left in the bag.  Our students will have to split pennies to keep the game going.  At this point, total savings is  99 cents (savings involves taking pennies from a bag of 100).   And the limit of savings is 100. Finally we know savings =  .2 Y so Y = 100/.2 = 500.  Here, the multiplier is 5:  1/(1-mpc) = 1/(1-.8) = 5. 

 

What causes unemployment?

 

        In this simple Keynesian story, the failure of households and businesses to coordinate behavior causes unemployment.  Households save for retirement or to buy a house.  Investment in retirement communities and houses may or may not be equal.  It depends on what businesses think is likely to be demanded and the signals they are getting are not particularly clear.  When you set aside $1000 what do you intend to do with it in the future?  How do businesses know? 

        Classical economists find the claim such a story can be an equilibrium rather irritating and point out several reasons for such circumstances to put pressure on households and businesses to change behavior – which of course implies the situation is not an equilibrium.   For example, they claim the demand for labor is equal to its marginal product (if real wages are on the axis) and the supply of labor is set so that the disutility of work equals the real wage.  Therefore the labor market clears where the disutility of work equals the marginal product of labor.  The only sensible way to define unemployment is to argue that the real wage is above the equilibrium inducing more people to seek work than can find it.  In the diagram, the distance between the yellow and green lines represents unemployment. (Blue is supply of labor and red is the demand for labor).

 

 

 

 

 

 

 

 

 

 

 

Classicals argue this can not last, they claim workers will take wage cuts.  Keynes disagrees.  We can do no better than let him explain.  The excerpt is taken from Chapter 2 of the General Theory. 

 

Though the struggle over money-wages between individuals and groups is often believed to determine the general level of real-wages, it is, in fact, concerned with a different object. Since there is imperfect mobility of labour, and wages do not tend to an exact equality of net advantage in different occupations, any individual or group of individuals, who consent to a reduction of money-wages relatively to others, will suffer a relative reduction in real wages, which is a sufficient justification for them to resist it.

 

The rest of chapter 2 is available at http://csf.colorado.edu/pkt/pktauthors/Berglund.Per/Keynes/GT/Chap02.htm

 

The other way to get the real wage down is through price increases, but with unemployment and unsold goods prices are more likely to fall. 

 

Conclusion:

 

        Unemployment results due to a failure to coordinate household and business decision-making. The unemployment persists because nominal wages are sticky.  Unemployed workers resist wage cuts for fear their relative wage will be permanently reduced. 

        Classicals doubt the coordination problem is severe and point out that there are markets linking savings and investment.  They believe wages are flexible in the long run while Keynes famous reply is that “In the long run we are all dead.”