# MPC and MPS relationship

I have a question from an old assignment that I cant wrap my head around.

Other things remaining the same, if households suddenly decide to save more at each level of income, then the consumption function will:

a) become steeper because the marginal propensity to consume (MPC) falls.
b) become less steep because the marginal propensity to save (MPS) rises.
c) make a parallel shift downward as autonomous consumption expenditure falls.
d) remain unchanged but the savings function will shift downward.


I don't understand why it can't be option B. Since

MPS+MPC = 1


and

C = C₀ + (MPC)Y (Consumption function = Auto. Consumption + MPC(Income))


Given this, if MPS increases - it should mean that MPC decreases and so the slope of the consumption function decreases. Hence, option B. The answer however is C and I don't understand why.

You are correct in stating that if MPS increases, then MPC decreases. But the question doesn't actually say that MPS increases. What it says is that saving increases at each level of income. That's consistent with a scenario such as the following in which MPS does not change while autonomous consumption falls from $$10$$ to $$5$$:
$$\qquad$$Before: $$S = -10 + 0.2Y$$ and $$C = 10 + 0.8Y$$
$$\qquad$$After: $$S = - 5 + 0.2Y$$ and $$C = 5 + 0.8Y$$
In this scenario, consumption falls by $$5$$ at each level of income - a parallel shift of the consumption function as per option C.