If interest rate increases and consumption in the present increases, is present consumption a normal good?
First, the definitions:


A normal good is one whose demand rises when income rises.
An inferior good is one whose demand falls when income rises.


I will use $c_1$, $c_2$, and $y$ to denote current consumption, future consumption, and (lifetime) income.

Now, if $r$ rises, then as usual there are two effects, the substitution effect (SE) and the income effect (IE). We are given that the Total Effect (TE) is that $c_1$ increases or equivalently, that TE is positive.

Let us write $$TE=SE+IE&gt;0.$$

We now look at each of the two individual effects:

Substitution Effect (SE). You correctly identified the cause of this effect -- "the price of $c_1$ increases". And so, the SE is that the consumer should substitute out of $c_1$ and into $c_2$. That is, the SE unambiguously says that $c_1 \downarrow$. We write $SE&lt;0$.

However, you then made the mistake of concluding that this shows $c_1$ is inferior. But remember that whether a good is inferior or normal depends on responses to changes in income. So, the SE has nothing to do with whether a good is inferior or normal.



Income Effect (IE). We first note that since $$TE=SE+IE&gt;0 \text{ and } SE&lt;0,$$ it must be that $IE&gt;0$.

Here there are two possibilities. I very much suspect the person writing this question overlooked possibility #2 (in which case the answer should be B) and went only with possibility #1 (answer C).


If the consumer is a lender (or saver), then an increase in $r$ implies an increase in $y$. In which case, $IE&gt;0$ if and only if the good is normal. Hence, the answer is C.
However, if the consumer is a borrower,  then an increase in $r$ implies a decrease in $y$. In which case, $IE&gt;0$ if and only if the good is inferior. Hence, the answer is B.