# If interest rate increases and consumption in the present increases, is present consumption a normal good?

I recently wrote an economics quiz and one of the questions was:

Suppose "r" is the interest rate that prevails between the present and the future. If "r" increases and a household chooses to consume more in the present, then:

I answered that since the price of current consumption increases and the consumer consumes more, current consumption must be an inferior good.

However this was marked incorrectly for me and the correct answer was current consumption must be a normal good. I'm unsure of why this would be the correct answer, could somebody explain the reasoning?

Edit: The five options were:

A) it is an irrational decision.

B) consumption in the present must be an inferior good.

C) consumption in the present must be a normal good.

D) consumption in the future must be an inferior good.

E) consumption in the future must be a normal good.

I chose chose B but the correct answer was listed as C.

• What were the available choices? Or was it open-ended? – Kenny LJ Nov 13 '18 at 6:27
• The options are added in the edit – pdid Nov 13 '18 at 6:30
• Have you perhaps omitted any other information? For example, does it state if the consumer is a borrower or a lender? – Kenny LJ Nov 14 '18 at 7:13

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 $$TE=SE+IE>0.$$

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 $$SE<0$$.

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 $$TE=SE+IE>0 \text{ and } SE<0,$$ it must be that $$IE>0$$.

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).

1. If the consumer is a lender (or saver), then an increase in $$r$$ implies an increase in $$y$$. In which case, $$IE>0$$ if and only if the good is normal. Hence, the answer is C.

2. However, if the consumer is a borrower, then an increase in $$r$$ implies a decrease in $$y$$. In which case, $$IE>0$$ if and only if the good is inferior. Hence, the answer is B.

• But a lender can still be better off by reducing his present consumption when rate of interest rises. – DrStrangeLove Nov 14 '18 at 9:02
• @DrStrangeLove: Sure. But how does that relate to anything here? – Kenny LJ Nov 14 '18 at 9:09
• I am sorry I had missed the context of your explanation. – DrStrangeLove Nov 14 '18 at 9:20