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2017 | OriginalPaper | Chapter

11. Expenditure Multipliers

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Abstract

We extend the mill parable of Chap. 9 to develop some intuition about how expenditure multipliers work, as well as conditions under which thy’re more or less likely to be relevant. This covers both physical inability and simple unwillingness to increase output. We then derive the conventional Keynesian multipliers for changes in expenditure and taxation. The informal version from the mill parable is used to introduce some limitations of multiplier analysis.

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Footnotes
1
Keep in mind that a farmer’s “income” here is how much food she produces, not her revenue. Let’s say she accepts tokens in payment of food but she doesn’t increase her output nor does she decrease her consumption, opting instead to use the tokens to buy the extra food from someone else. (This is the situation of Problem 9.2.) Her income in that case is unchanged (Δ y = 0). Her revenue has increased, but her expenditure has increased an equal amount.
 
2
If you’re familiar with the concept of limits, you can approach the problem that way. What happens as Δ y gets smaller and smaller, heading towards zero? That is, what’s the limit of μ as Δ y → 0? The term Δ c in this case is negative, which means that Δ cΔ y becomes a larger and larger negative number, approaching −. That implies that 1 −Δ cΔ y becomes an ever larger positive number, approaching , and the multiplier in turn is approaching 1∕, which is the same as approaching 0. You can also revert to Eq. 11.1, where there’s no problem with Δ y = 0 and we can directly calculate that μ = 0.
 
Metadata
Title
Expenditure Multipliers
Author
Karl Seeley
Copyright Year
2017
DOI
https://doi.org/10.1007/978-3-319-51757-5_11