Step 1: Recall Keynesian Absolute Income Hypothesis.
According to Keynesβ Absolute Income Hypothesis, consumption mainly depends on current disposable income.
The Keynesian consumption function is
\[
C = a + bY
\]
where
\[
a=\text{autonomous consumption}
\]
\[
b=\text{marginal propensity to consume (MPC)}
\]
\[
Y=\text{income}
\]
Step 2: Define APC and MPC.
Average propensity to consume (APC) is
\[
APC=\frac{C}{Y}
\]
Substituting the consumption function:
\[
APC=\frac{a+bY}{Y}
\]
\[
APC=\frac{a}{Y}+b
\]
Marginal propensity to consume is
\[
MPC=b
\]
Step 3: Analyze behavior as income increases.
As income \(Y\) increases,
\[
\frac{a}{Y}\rightarrow 0
\]
Therefore,
\[
APC \rightarrow b
\]
Since
\[
MPC=b,
\]
we get
\[
APC \rightarrow MPC
\]
Step 4: Analyze the options.
(A) Incorrect, because Keynes assumed MPC remains positive but less than one, not necessarily increasing with income.
(B) Incorrect, because APC generally decreases as income increases.
(C) Incorrect, because APS increases as income increases.
(D) Correct, because APC approaches MPC as income rises.
Step 5: Final conclusion.
Hence, the correct statement is
\[
\boxed{\text{The average propensity to consume approaches the marginal propensity to consume as income increases}}
\]
Therefore, the correct option is (D).