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Economics: The Multipliers

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  • Type: Video Tutorial
  • Length: 14:24
  • Media: Video/mp4
  • Use: Watch Online & Download
  • Access Period: Unrestricted
  • Download: MP4 (iPod compatible)
  • Size: 154 MB
  • Posted: 03/29/2010

This lesson is part of the following series:

Economics: Full Course (269 lessons, $198.00)
Economics: The Aggregate Expenditures Model (13 lessons, $26.73)

This economics video lesson will teach you about applications of the Multipliers. Taught by Professor Tomlinson, this lesson was selected from a broader, comprehensive course, Economics. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/economics. The full course covers economic thinking, markets, consumer choice, household behavior, production, costs, perfect competition, market models, resource markets, market failures, market outcomes, macroeconomics, macroeconomic measurements, economic fluctuations, unemployment, inflation, the aggregate expenditures model, banking, spending, saving, investing, aggregate demand and aggregate supply model, monetary policy, fiscal policy, productivity and growth, and international examples.

Steven Tomlinson teaches economics at the Acton School of Business in Austin, Texas. He graduated with highest honors from the University of Oklahoma and earned a Ph.D. in economics at Stanford University. Prof. Tomlinson's academic awards include the prestigious Texas Excellence Teaching Award given by the University of Texas Alumni Association and being named "Outstanding Core Faculty in the MBA Program" several times. He has developed several instructional guides and computerized educational programs for economics.

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Here's a question: How will a change in autonomous spending affect equilibrium output in the economy? That is, suppose you go out, and for no good reason, increase your autonomous consumption spending by $16.00--just on a whim. Maybe the stock market had boomed, maybe your animal spirits move you, and you just go out and buy a compact disc for $16.00. If we follow through the consequences of that choice, what will be the effect on gross domestic product of that purchase? Well, think about it for a moment, you go to the record store and you spend $16.00. Now the guy who runs the record store has $16.00 in income that he didn't have before; he spends part of it and he saves the rest. The part that he spends, maybe on ice cream, becomes the income of the proprietor of the ice cream store. She saves part of it and spends the rest. What she spends becomes the income of someone, maybe at a T-shirt stand. He spends part of it and spends the rest. So your one act of spending sets in motion a process that creates income and motivates spending for a lot of other people.
This is what we call the Multiplier Effect. When there is an increase in autonomous spending, real gross domestic product, equilibrium income increases by much more than the original increase in spending. A small increase in spending can catalyze a large increase in equilibrium income, equilibrium output. Let's see how it works.
Let's go through our example carefully. You go to the record store and you spend $16.00, so your increase in consumption creates an increase in income of $16.00 for the person who owns the record store. So that is going to influence his consumption. And let's suppose--for the sake of making this example really simple--we take a marginal propensity to consume equal to 50 percent. That is, everybody is going to spend one-half of any new income they get. So, the guy who runs the record store gets $16.00 worth of income and let's suppose that he puts half of it immediately into the bank and spends the rest. So what he is going to do? Having put half of this into the bank, he is going to spend half of this amount, or $8.00, let's say at the ice cream store. So he has now increased the income of the ice cream store proprietor by $8.00. (The rest of this went into the bank.) So now that this $8.00 has been spent at the ice cream store, it becomes the income of the ice cream proprietor. She takes this money and thinks, "I just got $8.00. Well, my marginal propensity to consume is 50 percent, so I am going to put half of it into the bank and save it, the other 50 percent I am going to spend." So she goes and buys a T-shirt that costs $4.00 and that $4.00 becomes the income of the guy that runs the T-shirt stand. So he now has $4.00 in income and he thinks to himself, "Well, I better put $2.00 of it into the bank, and the other $2.00 I can spend." So he spends $2.00 and saves $2.00. And the process continues. That becomes someone else's income who saves half, and increases spending by $1.00, which becomes someone else's income and so forth, until finally, we've got down to little increases of income that are so small that they hardly matter.
Well, what has been the total increase in income that resulted from that original expenditure of $16.00? You created $16.00 worth of income for the record salesman, $8.00 for the ice cream salesman, $4.00 for the T-shirt salesman, $2.00 for somebody else, $1.00 for somebody else, one-half, one-quarter, and so forth, until the pieces are so small that you can't even pick them up anymore.
Let's add it all up. $16.00 + $8.00 + $4.00 + $2.00 + $1.00 + +1/4 + 1/8, and so forth, until the pieces are so little that you just can't even handle them anymore, and it adds up to a bar that is exactly twice as big as the original expenditure. That is, the total amount of income that is created if we add up all of these incremental increases of income equal to $16.00 + $8.00 + $4.00 + $2.00 + $1.00, and eventually, if we keep on adding up those smaller and smaller fractions, we are going to get a total of $32.00; that's the sum. Now that is the total amount of gross domestic product increase that resulted from the original expenditure of $16.00.
How does it work? It works because you're spending becomes someone else's income. They are going to spend part of it and save part of it, creating income for someone else. And eventually when you add up of the pieces, this is what you get. Now where does that number come from? Where does that multiplier number come from? There are two ways that we can derive the multiplier. First of all, let me define the multiplier carefully. The multiplier in Keynesian analysis is equal to the change in equilibrium gross domestic product that results from a change in autonomous spending. This change in autonomous spending can be an increase in autonomous consumption, an increase in business investment spending, an increase in government spending, an increase in net export spending; anything that increases autonomously, that is, on its own, that's independent from income. Any increase in autonomous spending gives rise to a multiplier through this process. That is one person's spending becomes another person's income, until you have got a multiple of autonomous spending, created in new gross domestic product.
Well, let's see where that number comes from. And there are really two ways for us to derive the multiplier. Method number one of deriving the multiplier is what we call the geometric sequence. That is, the change in equilibrium income is equal to the change in autonomous spending times one. This is the amount of money you spend at the record store. Sixteen dollars times one, plus the marginal propensity to consume. This is how much the record salesman spends. He put part of his money in savings and he spent one-half, plus margin propensity to consume squared; this is how much the person who owned the ice cream stand spent. She got half of what you spent, because the guy at the record store saved part, and then she spend half of it herself. So the number squared, and then cubed, and so forth, and it keeps adding up forever. Well, a geometric sequence like this has a nice simple expression that is, if you have a formula that is 1 + B^2 + B^3 + B^4, and so forth, forever and ever, if B is a fraction, that eventually converges to this: 1/1 - B. Imagine that B is 1/2, like in our example. One-half, if you subtract it from 1 gives you 1/2, and the reciprocal of 1/2 is 2. That is, we wound up with twice as much as the original change in autonomous spending. So the marginal propensity to consume in this equation is B and if we manipulate this a little bit, we can see that the change in real gross domestic product that results from a change in autonomous spending equal to this multiplier.
So that is one way to do it. And that way will be more fun if you know something about geometric sequences. But, the trick is in knowing that this formula right here eventually converges to this, if you add all of the terms together.
There is an easier way that uses just simple algebra, and that starts with output is equal to C + I; and in our simple model we have two components of aggregate expenditure: consumers and businesses. And also, we know that consumption is equal to A + B x Y. That is, we have a simple linear consumption function with an autonomous component, and with a marginal propensity to consume B--the fraction of each additional dollar that you spend of consumer goods.
Well, substitute this equation up here into this one, and you get Y is equal to A + BY + I; and if you subtract so as to get the Y terms on one side of the equation together, and here we have... let's see this is equal to 1 - B x Y = A + I, and that gives us that Y = 1/1 - B times these two terms taken together--I'll scoot this over so I can get this all on one page--and I have got A + I. And there is your multiplier effect: that output is going to be equal to 1/1 - B x A + I. That is, if A increases, or if l increases--if either of these components of autonomous spending increase--then Y is going to increase by a multiple of that. The coefficient on both of these autonomous components is one over one minus B. So the multiplier is 1/1 - B. Any change in A, any change in I, any change in any of these autonomous components of spending increases Y by a multiple of that amount, and the coefficient is one over one minus the marginal propensity to consume.
Now let's look at how this plays out in our diagram. We have used this diagram before and we can show the effect of an increase in investment spending on equilibrium output. Let's start here, and let's suppose that we have, in this case, a different formula that consumption is equal to 10 plus .8 x Y. This is the consumption function that we have used in our numerical example before. And we saw that if we have consumer spending as our only component of spending, then equilibrium income in that case is equal to 50. So I could go over here and write that on this axis, but I don't want to clutter my diagram. Now let's suppose we add investment spending, so if investment spending is equal to 10, I would have to add on another spending term down here. Here's the investment line and it is going to be equal to 10, and it is autonomous, it doesn't depend on Y, so no matter what your level of GDP is, businesses are planning to spend $10.00 on investment. So let's add 10 onto the consumption function, which shifts it up by this vertical distance. So, here we have our change in investment spending. It has gone from zero to 10 and we calculated last time that our, or we saw from our table in a previous example, that if you increased investment spending from zero to 10 that the equilibrium level of output rose from 50 to 100.
Well, how do you figure that? Here is the change in income down here, and here was the change in investment. The change in investment spending was from zero to 10, so that is only equal to 10. The change in income is from 50 to 100, that's equal to 50. Where do you get that? Well, In this case the multiplier is going to be one over one minus the marginal propensity to consume, which is 8/10. So the multiplier in this case should be the change in output that results from the change in business spending, is equal to 1/1 - 8/10. Well, 8/10 from 1 leaves 2/10. Two-tenths--20 percent--is 1/5 and the reciprocal of 1/5 fifth is equal to 5. So in this particular case, our multiplier is going to equal to 5. Well, look, that is exactly what happened. We increased income by 50 after we increased investment by 10. So the ratio of this change in equilibrium income 50, to the change in investment spending 10, is 5.
How did it happen? It happened because businesses from the original equilibrium decide that they want to buy $10.00 more worth of stuff. Well, there is not $10.00 more worth of stuff for them to buy, so businesses have to increase their production in order to meet this extra demand. And whenever they increase their production by 10, they create $10.00 worth of additional income; which does what? It motivates people to spend more. And how much more do they spend? They spend $10.00 worth of income times 8/10, which is the marginal propensity to consume, they add $8.00 to their total consumption plan. Well, that then creates excess demand for goods so businesses have to produce more stuff. Then people decide to spend more with this new income they got from the increase in production and things keep going until finally output has increased--not just by the original $10.00 to satisfy businesses demand for investment goods--but by a full $50.00 after you take into account the multiplier effect. Businesses created an additional demand of $10.00, but that put income into the workers pockets who went out and spent more, which created more demand and more income, and more demand and more income, until finally the pieces get so small that you can't even pick them up; and that is whenever you have converged to a new equilibrium.
So, that is the way this process works. You have seen it with simple example with my red bars, which is, if we use one-half as our MPC; we wound up with twice as much new income as the original change in autonomous spending. You have seen it in algebra. You have seen that the multiplier is the coefficient on equilibrium output whenever there is a change in autonomous spending. And finally, you have seen it in the diagram when you shift the line up, the new equilibrium point involves a much bigger increase in income, and then we had increase in autonomous spending. The trick here is the marginal propensity to consume that is what the multiplier depends on. When there is an increase in autonomous spending, that creates income, and part of it is going to be spent, part of it saved; but the part that is spent creates income for somebody else which means they are going to spend part of it, and save part of it; which creates income for someone else and so forth. And when all of the dust settles, you wind up with this: a multiplier, and the multiplier tells you the change in equilibrium income that results from a change in autonomous spending.[]
Aggregate Expenditures Model
The Multipliers
Applications of the Multipliers Page [3 of 3]

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