**Principle**

Break problems down into smaller parts to gain a better understanding.

The way to break
the problem down may be obvious, or even contained in the question. But sometimes
it is useful to break the problem down in non-obvious ways.

**Tip**

A fairly obvious way of breaking down a
problem into parts is to look step by step at how some cause has some effect.
Example: what impact does reducing taxes on labor income has on wages? Look first
at the impact of the tax reduction on how much workers want to work, and then
look at the impact of the latter change on wages.

When determining how to break down the
problem in non-obvious ways, you may often want to define parts that are independent
of each other. (See the example below).**Example**

You already know
(maybe using the art of caricature) that a reduction of tax rates has two
effects. There is an “income effect”: even if the worker works the same, she
will be richer because she will keep more of her labor income. This may be an
incentive to work less (but you are not sure at this stage). The second effect
is that, in addition to the previous effect, the worker has an incentive to
work more because she will keep a larger proportion of her additional labor
income. This is called the “substitution effect”: it is an incentive to
substitute something by some other thing (here leisure by work) because the relative
price of these two things has changed, but which comes in addition to the
income effect mentioned above.

It would be useful
to separate the substitution effect from the income effect. In order to do it,
break the tax-rate reduction into the two following parts. Consider first a
fiscal reform that would consist of our tax-rate reduction and of a lump-sum
tax calibrated such that the worker pays exactly the same tax as before if she
does not change her work load. This may seem quite artificial, but it is constructed
in order to get a pure substitution effect (since the income stays the same if
the work load stays the same). Second, consider a fiscal reform consisting of
giving back the lump-sum tax discussed above. In this second reform there is no
change of the tax rate: the change of income does not depend on the work load.
Thus, this leads to a pure income effect. And the sum of the two reforms is our
tax-rate reduction.

Think about the
first reform. It is clear that this reform is an incentive to work more, since
the worker will keep more of additional labor income and there is no issue
about increased revenue with the same work load that would make this picture
fuzzy.

Let’s now forget
about the first reform and think about the second reform. Since the sole change
for the worker is that it makes her richer (but without changing her after-tax wage),
it seems obvious that she will want to work less. But you surely can imagine a
case in which she would want to work more. Maybe thanks to the money provided
by the state she can take out a mortgage to buy the house of her dreams if she
works a bit more, whereas she would not have enough incentives to work that bit
more before that reform because it was not worth her while to work more to buy
more small things (your common sense will probably tell you that this is rather
exceptional, but to really understand why we will need the trick in the next
post).

**Exercise**