Why Paul Krugman is right about deficit spending

By Herb Engstrom, Ph.D.

 

Economist Paul Krugman writes that in times of economic doldrums, it is government spending, even deficit spending, that is the solution.  A very simple calculation shows why Krugman is right and Republican orthodoxy is wrong.

 

      With some very simple assumptions–certainly oversimplified but not totally unrealistic assumptions–a calculation involving nothing more than high school algebra will show that government spending, as advocated by Nobel prizewinning economist and New York Times columnist Paul Krugman, is the key to getting a depressed economy moving.  Conversely, tax reductions as championed by all Republicans could well have the opposite effect.

      The first assumption is contrary to conventional wisdom and so requires some explanation.  It is that a very large fraction of any money spent on consumables goes ultimately into people’s pockets as salary.  Conventional wisdom, which you see frequently in the news, is that only a small portion of what the government or a business or a consumer spends goes into wages.  That’s true of direct wages.  As an example, suppose the government wants to improve infrastructure by building a bridge.  A very large fraction of the cost goes into materials: concrete, steel, copper, lights, asphalt, etc., which are not direct wages.  But if you track the money that might go into the purchase of one of those, the steel, for example, you find that those funds go to pay the workers in the steel mill, its managers, its custodians etc.  The steel mill also spends much on materials, iron ore, coal, machinery, and so on.  Money for coal goes into the wages of coal miners, their managers, their taxes, which in part pay the wages of government workers like safety inspectors.  The point is that if you track all the money spent by the government in this series of purchases, you do find that wages represent a very much larger fraction of the total than is commonly cited.

      There is, however, some fraction that does not go directly into wages, at least not directly into the wages of American workers.  Many of those bridge builders, steel workers, miners, and their managers will go to Wal*Mart to buy cheap goods made in China.  Money for imported goods will not directly stimulate the American economy, but even here there is an important positive effect.  That is, China and other foreign vendors to America also buy from America, and that does stimulate the U.S. economy.  It is the trade deficit that adversely affects the American economy, and the trade deficit is a relatively small fraction of the total cost goods and services that we purchase from abroad.

      There is one other drain on the American economy from government spending.  That is the money spent for top level, overpaid executives and other members of the super rich.  These people often invest in various financial instruments like stocks and bonds that do not go even indirectly into wages.  It is well known, for example, that many large banks are sitting on deposits, which they are unwilling to commit to investing.  It’s important to emphasize that not all such financial instruments are deleterious to the economy; the stock market does provide an important source of capital for investment in the productive economy for many companies.

      A second assumption involves taxes.  It is well known that secretaries pay income tax at a higher rate than billionaires and that people whose wages are sufficiently low, pay no income tax at all.  So to simplify the illustration with a specific example, I’ll have to assume an average tax rate covering all taxes–income, sales, utility, whatever.  In the end it does not matter a whole lot what that average rate is as long as it is a reasonable number.

      A third assumption is that there is only one government, not the three consisting of federal, state, and local.  The analysis could apply to any one of these.

      For simplicity and clarity let me begin with a specific numerical example.  Let’s say the government spends $100 for a gardener to mow a park lawn.  And suppose that the tax rate is 10%.  That means that the gardener ultimately gets to spend only $90, since he must repay the government 10 bucks.  Next let us suppose that of the $90 he gets to spend, another 5% goes to people like the Wal*Mart family who put it into our trade deficit or financial instruments that do not stimulate the American economy.  Thus, of the $100 a total of $85 (i.e., 85% of wages) goes into stimulating the American economy.  Actually it’s much more than that, because when the government takes your tax money, it pays its workers and contractors further stimulating the economy.  But to keep the calculation simple, let’s say that 85% goes into stimulating the economy.

      But wait!  The gardener now spends that $85 on groceries.  The grocer has to pay taxes at 10% and another 5% to the indolent rich, so the grocer stimulates the economy with 85% of his $85 or $72.25.  So far the total stimulation of the economy is $85.00 + $72.25 or $157.25, which, you have noticed, is substantially larger than the $100 that the government originally spent.

      The grocer also spends his $72.25 at a restaurant dinner for him and his wife.  The restauranteur gets to stimulate with 85% of that  or $61.41.  You see where this is going.  After many such transactions the original stimulus of $100 is spent to the last penny, which we can express as

 

S = $100×0.85 + $100×0.85×0.85+ $100×0.85×0.85×0.85 + … .

 

      How much is that?  Here’s where high school algebra comes in.  Let N = the original stimulus, $100 in this example, and let r = the fraction of money received by a vendor that is used to further stimulate the economy.  In this example r = 0.85.  Using these symbols we can write S as

 

S = Nr(1 + r + r2 + r3 + r4 + …).

 

As you might remember from high school algebra, the infinite series

 

1 + r + r2 + r3 + r4 + … = 1/(1 – r),

 

so that

 

S = Nr/(1 – r).

 

In our example where N = $100 and r = 0.85, we find S = $566.67.  All this from a government outlay of only $100.

      But it’s better than that.  Remember that our tax rate was 10%.  Numerically, the government recoups $10 on the first transaction, $8.50 on the second, $7.22 on the third, $6.14 on the fourth, and so on.  Let’s call the tax rate t, so that the government recoups a fraction t at every transaction.  Hence the government earns back a total amount, T, where we can see

 

T = Nt(1 + r + r2 + r3 + r4 + …) = Nt/(1 – r).

 

In our example where t = 0.1 we find the government recoups a total T = $66.67, so really the government expenditure of $100 only costs us taxpayers $33.33.  In fact, if all of the government expenditure went into stimulating the economy, which would mean r = 0.90 rather than 0.85, the government would recoup all of its initial expenditure.  That is why the 5%, which goes to the idle rich and to the trade deficit actually depresses, rather than stimulates the economy.

      Bottom line: Paul Krugman is absolutely right; Republicans couldn’t be more wrong.

 

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