Question
Discuss relationship between MPC and MPS.

Answer

The relationship between these two is as under:
  1. If MPC remains constant, MPS would also be constant.
Y C S $\Delta\text{Y}$ $\Delta\text{S}$ $\Delta\text{C}$ MPC MPS
3000 3000 - - - - - -
4000 3800 200 1000 200 800 0.8 0.2
5000 4600 400 1000 200 800 0.8 0.2
6000 5400 600 1000 200 800 0.8 0.2
7000 6200 800 1000 200 800 0.8 0.2
  1. If MPC falls, MPS increases and vice versa.
Y C S $\Delta\text{Y}$ $\Delta\text{S}$ $\Delta\text{C}$ MPC MPS
3000 3000 - - - - - -
4000 3800 200 1000 200 800 0.8 0.2
5000 4550 450 1000 250 750 0.75 0.25
6000 5250 750 1000 300 700 0.7 0.3
7000 5900 1100 1000 350 650 0.65 0.35
$\text{MPC}\downarrow\rightarrow\text{MPS}\uparrow$
  1. MPC + MPS = 1
Proof: We know that income (Y) is either spent on consumption (C) or saved (S), i.e.,
Y = C + S
or $\Delta\text{Y}=\Delta\text{C}+\Delta\text{S}$
By dividing both sides by AY, we get,
$\frac{\Delta\text{Y}}{\Delta\text{Y}}=\frac{\Delta\text{C}}{\Delta\text{Y}}+\frac{\Delta\text{S}}{\Delta\text{Y}}$
1 = MPC + MPS
Numericals:
You Must Know,
  1. $\text{Y}=\text{C}+\text{S}$
  2. $\text{AD}=\text{C}+\text{I}$
  3. $\text{AS}=\text{C}+\text{S}$
  4. $\text{APS}=\frac{\text{C}}{\text{Y}}=1-\text{APS}$
  5. $\text{MPS}=\frac{\Delta\text{C}}{\Delta\text{Y}}=1-\text{MPS}$
  6. $\text{MPS}=\frac{\Delta\text{S}}{\Delta\text{Y}}=1-\text{MPC}$
  7. $\text{C}=\bar{\text{C}}+\text{B}(\text{Y})$
  8. $\text{S}=-\bar{\text{C}}+(1-\text{b})\text{Y}$

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