Why does immigration boost the economy? (or does it not...?) I'm a novice at macroeconomics, and trying to understand the effect of immigration (from developing nations) on the economy of a developed nation. Specifically, I am considering the effect when the nation itself does not have full employment.

So, from what I have read, immigration is a positive thing for the economy in general. The increase in workforce capacity means that production can increase, therefore exports increase, and therefore the economy grows.

However, what if the nation does not have full employment? In this case, there is already a section of society (let's say 5%) which is available to work. This would suggest that there are actually not enough jobs around, and so any immigrants arriving will also not have any jobs. If there had been any jobs for the immigrants to take, then employment wouldn't be at the 5% level. Despite this however, all developed nations have at least some level of unemployment, yet immigration is still beneficial. Why is this?

My suggestions are the following:


Immigrants from developing nations tend to be happier to take on unattractive jobs, which citizens of the developed country may refuse to do. Therefore, whilst the citizens remain unemployed and live off benefits, the immigrants will take on "newly created" jobs which would otherwise not have existed, boosting the economy.
The 5% unemployment rate is actually due to people who are sick / disabled / otherwise unable to work. Therefore, assuming the immigrants are able to work, again there will be new jobs created which would otherwise not have existed.
Higher immigration creates more competition for jobs, causing wages to decrease and allowing companies to pay their employees less. Therefore, the nation's companies make more money, and this causes the economy to grow.


Are any of these correct, or reasonable suggestions? Or are there any other thoughts? Thanks!

Alternatively, is my hypothesis that immigration typically boosts the economy not, in fact, correct?!
You’re right, the migration of workers boost the economy. It’s a stylized fact. It may have political consequences, though, but it is not the part of the analysis of economics. Let’s consider $A$ the set of active labour force of an economy before, and $A'$ after the migration. Then $A$ is the subset of $A'$:
$$A \subseteq A'$$
This notation means that the social planner of the economy is able to optimize on a greater number of workers. We can assume that opening the door for migrant workers is at least as good as it was before migration:
$$A \preceq A'$$
If this condition is not true (e.g. the migrants doesn't want to work), the authorities of the economy won't open borders for migrant workers.

You're considering the effect when the nation itself does not have full employment. This condition is not important. The nation could have 0% unemployment, however, the migrant workers would still get jobs.


  Immigrants from developing nations tend to be happier to take on unattractive jobs, which citizens of the developed country may refuse
  to do.


Absolutely, these people have got different preferences. Here're the utility functions of residents ($r$) and immigrants (i):
$$u_r=C-\alpha_r L$$
$$u_i=C-\alpha_i L$$
where C and L denotes consumption and work. We can conclude that $\alpha_r$ must be higher than $\alpha_i$. The disutility of work is higher in the case of the residents. 


  That means migrant workers are more cost-efficient for firms. Higher immigration creates more competition for jobs, causing wages to
  decrease and allowing companies to pay their employees less.


Therefore, the nation's companies make more money, and this causes the economy to grow. Growth and R&amp;D may also improve by means of brain-drain effect, because there are migrant scientists and white-collar workers, too.


  The 5% unemployment rate is actually due to people who are sick /
  disabled / otherwise unable to work.


By definition it is not correct. In Economics, active workers and job-searchers are on the labour market only.

The main concept of migration being good is the increase of the horizon of labour optimization. See also: Krugman &amp; Obstfeld: International Economics Theory and Policy