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Chapter 5: Problem 177

Prove that the sum of the average propensity to save and the average propensity to consume is always equal to one,

Short Answer

Expert verified
The sum of the average propensity to save and the average propensity to consume is always equal to one. We can prove this by defining APS as \(\frac{S}{Y}\) and APC as \(\frac{C}{Y}\), then adding these fractions together: APS + APC = \(\frac{S}{Y}\) + \(\frac{C}{Y}\). We can rewrite this sum as \(\frac{S + C}{Y}\), and recall that total income (Y) is equal to the sum of total savings (S) and total consumption (C). Thus, we can replace the numerator with Y: \(\frac{Y}{Y}\), which simplifies to APS + APC = 1.

Step by step solution

01

Define APS and APC

We'll first define the formulas for APS and APC. The average propensity to save (APS) is the ratio of total savings (S) to total income (Y), and the average propensity to consume (APC) is the ratio of total consumption (C) to total income (Y). In mathematical terms: APS = \(\frac{S}{Y}\) APC = \(\frac{C}{Y}\)
02

Add APS and APC

Now, let's add APS and APC: APS + APC = \(\frac{S}{Y}\) + \(\frac{C}{Y}\)
03

Find a common denominator

To add these two fractions, we need to find a common denominator, which in this case is Y. So, we rewrite the sum as: APS + APC = \(\frac{S + C}{Y}\)
04

Express the sum in terms of total income

Recall that total income (Y) is the sum of total savings (S) and total consumption (C): Y = S + C
05

Replace the numerator in the fraction

Now, we replace the numerator (S + C) with Y, since they are equal: APS + APC = \(\frac{Y}{Y}\)
06

Simplify the fraction

Lastly, let's simplify this fraction: APS + APC = 1 Therefore, we have proved that the sum of the average propensity to save and the average propensity to consume is always equal to one.

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Most popular questions from this chapter

Keynesian economists claim that investment is the most volatile component of private spending. If this is so, why is the investment function, as shown, drawn as a straight line, rather than as an erratic curve?

Letting \(\mathrm{C}\) be consumption, \(\mathrm{S}\) be savings, and \(\mathrm{Y}\) be disposable income, suppose the consumption schedule is as follows: \(\mathrm{C}=200+(2 / 3) \mathrm{Y}\). a) What would be the formula for the savings schedule? b) When would savings be zero?

Suppose that John's \(\mathrm{MPC}\) is constant at \(4 / 5\). If he had no income at all, he would have to borrow $$\$ 2,000$$ to meet all his expenses. Graph John's consumption function and write it out algebraically. Using the formula for John's consumption function, find his break-even point.

Contrast the Keynesian, or modern, economic theory of saving and investment with the classical economic view.

How does classical economic theory answer the claim that the existence of saving undermines Say's Law, that is, that saving results in under spending, or a deficiency of total demand?
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