there we saw that real inerest rates went up then planned investment went down if real interest rates went down then planned investment went up what we want to do in this video is take this conclusion and apply it to our Keynsian cross and think about how real interest rates will affect overall planned expenditure and then what that would do in model like the Keynsian cross what that would do to our equilibrium real GDP so just as a reminder, just let's us draw our Keynsian cross or parts of it. So on this axis right over here we have expenditure. This axes right over here we have income and we know for many videos now that in economy is equilibrium when income is equal aggregated real income, aggregated real income is equal to aggregated real expenditures, so circular flow EPD so let's draw or make a line that is all the points where Y is equal to expenditures so 45 degree overhere, so this is actually expenditures at this point over here that should be the same value as what our aggregated income is. Now that's part of the Keynsian cross, the other part is to actually plot planned expenditures relative to this and see where this intersect, what is the equilibrium point of that planned expenditure line and I'll write it here as, I've written it in the past as planned expenditures. We could write it even as expenditures planned like that. And it's eqaul to our aggregate consumption and our aggregate consumption we can write it as a function of disposable income. "Y - t" is disposable income, aggregate income minus aggregate taxes.