Economics: Consumption Functions and Savings Functions? (1 Viewer)

[LoveHateSchool]

Could someone please explain consumption and saving functions +how to calculate them please? My teacher only vaguely explained them in class...

Rep and my admiration as your incentive!

 

[deterministic]

Assume we are in a world where we either spend on consumption goods/services or save.
ie. Total Income (Y) = Total Consumption (C) + Savings (S)

Consider the consumption component (C). There is a fixed component and a variable component which is dependent on our income.
- The fixed component is called autonomous consumption (C0) which represents what we need to consume irrespective of what our income is. This includes food, rent, bills etc. Effectively it is our consumption when our income is 0.
- The variable component depends on our income through our marginal propensity to consume (MPC). MPC is basically the proportion I would spend out of every extra dollar I earn. For simplicity, we assume MPC does not change.

Thus we have:
Consumption (C)= Fixed component + variable component
= autonomous consumption (C0) + MPC * Income (Y)

To derive the savings function, we simply use the first equation at the top (ie. what we didn't spend we shall save) to get:
Saving (S) = Y - C
= Y - C0 - MPC*Y = -C0 + (1-MPC)*Y = -C0 + MPS*Y
Note that MPS represents the marginal propensity to save, and that the proportion we didn't spend of our extra dollar is saved (ie. MPS+MPC=1).

 

[animeiswild]

Consumption:
C=Co+cY
Savings:
S=-Co+sY

Consumption:
Co= autonomous consumption (autonomous:independent of income)
So if C=80+0.8Y
Co=80=autonomous consumption (survival expenditure when Y=0)
c=MPC=0.8
Y=level of income

Saving:
so if C=80+0.8Y
-Co=autonomous saving=-80
s=MPS=(1-0.8)=0.2
Therefore S=-80+0.2Y

MPS+MPC=1

 

[LoveHateSchool]

Thank you to you both!

Just to check I get it, so if the autonomous consumption is essentially when our income is 0, then that would make our autonomous saving always the negative of our autonomous consumption? So if the consumption function is e.g C=20+0.5 Y then our savings function would be S=-20+0.5Y (becaue our income which is MPC + MPS always has to equal one right?)

 

[animeiswild]

Yep, you got it!

 

[LoveHateSchool]

^Thank you so much