We aren't talking about national income. We are talking about Gross Domestic Product. For sure, the Expenditure method is one method used to determine GDP, but it is also the most widely used method and it is the one used by the government because accurate data is easier to get.
First of all, statistical agencies usually use
both expenditure and income data to compute GDP. The reason is that both of these quantities must be
exactly equal by definition. Ultimately, you're tracking cash flows and calling them income or expenditure is just a matter of perspective. When you compute both of them, you will never get the exact same value in practice because of measurement errors. The whole point here is that by getting two estimates and forcing them to be equal, you can split the statistical discrepancy equally between both and limit the amount of error you would incur from using either method alone. Moreover, you will usually find an entry for a statistical discrepancy in national accounts. So, whether you talk about income, production or expenditures, you're talking about the same quantity, albeit from different points of view.
All of this is explained here by the BEA:
Box: The Statistical Discrepancy.
As far as how changes in different values affect GDP...it's a formula. Changing values and looking at the resulting changes in GDP is the easiest thing in the world.
Y = C + I + G + (X - M)
Let's use primes to denote other values. It is true that if we take C'=C, I'=I, G'=G, use XN := (X-M) as net exports, we have Y' > Y if XN' > XN, as you explain: if the trade deficit (minus net exports, -XN) falls and
nothing else changes, GDP will rise. The whole problem is, however, that we have spillovers across countries and multiple markets in this environment that you cannot neglect. Not only is it not true that nothing else will change, but it is also the case that the region of the function you are exploring with this trick is not even interesting.
You might have in mind something such as imposing a tariff or some other barrier to entry so that imports might be pushed downward and the domestic product would rise. However, you have to keep in mind that any such measure would impose costs on domestic households and producers. If you target raw materials, intermediate goods or services, you will raise production costs for domestic firms. That is pretty much the definition of what you're doing to curb import in practice. And whether you do this or go after final goods, it will ultimately impact what consumers pay and that will influence their behavior with regards to saving and borrowing. Likewise with firms, depending on how permanent your policy is perceived to be. And, obviously, this will have an impact on foreign firms and their investments as well, not to mention that other countries might want to retaliate in a like manner.
It's by no means obvious that you won't turn out to shoot yourself in the foot. One way to answer this question would be to try it in a few DSGE models and see what happens. It would be especially interesting because those models impose that this accounting identity holds exactly all the time. I personally never looked into this literature on international trade, but your
quick and dirty idea of just looking at the above equation suggests you'd anticipate a change of 1:1: push imports down one dollar, gain one dollar of domestic production. I would be surprised to find anything like it, let alone anything like that if the changes to trade policy are very large.
My comment also underscores a problem with this thread: you're all asking the wrong question. From a practical standpoint, the question is how to modulate trade policy. You don't have a hand on any component of GDP, except perhaps government spending (usually, with a delay).