Answer to Question #177824 in Macroeconomics for Ahmed

Question

Q#5. Explain why the sum of MPC and MPS equals to 1.

Consider an individual consumption function, which is the standard textbook consumption function, that is, has a y-intercept of autonomous consumption and is linear in the disposable income. Assume that the slope of this consumption function equals 0.7, and that the autonomous consumption equals $20 billion in the aggregate economy.

 

a.   Write down the consumption function for this economy.

b.  What is the marginal propensity to save (MPS) in this example?

c.   Suppose there is an increase in real income of $500 billion in this economy. Given your consumption function, what is the change in consumption given this change in real income?

Answer 1

$$solution$$

A]

$C=a+MPC \\ DI= 20+0.7yd$ , where $DI$ is the individual disposable income, $DI = Y-(T-TR)$.

B] Slope$=MPC$ in the linear consumption function. Therefore:

$MPS = 1-MPC\\MPS = 1-0.7=0.3\\MPS=0.3.$

C]The change in consumption is equal to $350 billion. To see this consider your consumption function :

$C = a + b[(Y – (T – TR)]$ .

The only thing that changes in this equation on the right hand side is $Y.$

The change in $y$ is $\$500 \ billion$ . So, effectively you are calculating:

$\Delta C=.7(\Delta Y)=.7(500)=\$350\ billion.$