How to interpret a regression that includes GDP, GDP per capita, and population While GDP per capita = GDP / population and are obviously related, these three measurements are not perfectly collinear and can be included in OLS just fine. 
However, when interpreting the coefficient of GDP per capita, how does it make sense to say that we "keep GDP and population fixed in order to find the effect caused by GDP per capita"?
 A: They are not perfectly collinear, but they are collinear to a problematic degree:
set.seed(123)
gdp <- exp(rnorm(100))
pop <- rnorm(100, 10000, 2000)
gdppercap <- gdp/pop
dv <- rnorm(100) #For collin, dv doesn't matter
library(perturb)
m1 <- lm(dv~gdp+pop+gdppercap)
summary(m1)
colldiag(m1)

The largest condition index is 21, which isn't outrageous but isn't good. And all the IVs have variance decomposition proportions over 0.75, which is also not good. 
So, you should leave one of the IVs out, both for the logic of the model and for colinearity. 
A: There is not necessarily a problem in terms of getting estimates for each of the components. There is however a problem of interpreting them, as has been outlined above already.
Having said that, usually people include the logarithms of these variables in a regression. This may be more error prone. Since ln(GDP/POP)=ln(GDP)-ln(POP), a specification like 
$y = \alpha + \beta_1 \ln(gdp) + \beta_2 \ln(gdp/pop) + \beta_3 \ln(pop) + \epsilon  $
is equivalent to
$y = \alpha + \beta_1  \ln(gdp) + \beta_2 \ln(gdp) - \beta_2 \ln(pop) + \beta_3 \ln(pop) + \epsilon  $
and hence
$y = \alpha + (\beta_1 + \beta_2) \ln(gdp) + (\beta_3- \beta_2) \ln(pop) + \epsilon$
$\ \   = \alpha + \hat\beta_1 \ln(gdp) + \hat\beta_2 \ln(pop) + \epsilon  $
Here you see that only two parameters are identified $(\hat\beta_1, \hat\beta_2)$. Above, you attempt to estimate three parameters, though. This is a problem!
A: Having all 3 in your model will introduce multicollinearity, which will prevent you from solving the system of equations necessary to produce the estimate coefficients of the least squares regression. 
A: Regressing on GDP or log GDP is usually problematic because they are not stationary. In econometrics we usually regress on differences of log GDP. I hope you know the spurious regression concept.
If you insist on having levels, i.e. GDP, GDP/POP and POP, then the way to interpret your problem is the same as with the model y ~ x1 * x2 in R notation, where x1=GDP/POP and x2 = POP.
