A positive investment multiplier does not exist in an open economy simple Keynesian model when the entire amount of investment goods is supplied from import. Examine the validity of this statement.
$$Y= c_0 + c_1 Y + I + G + X - M$$
Assuming a simple Keynesian model.
My understanding about the question could be wrong here. I think the question meant that $$I = i_0 + b_1 Y - b_2 r $$, meaning that the investment is positive function of Income ($Y$) and a negative function interest rate ($r$). But since the entire amount of investment is supplied by imports, therefore the multiplier will not exist because the parameters that investment is dependent on are considered to be exogenous here.
But i am not convinced with my understanding of the question so need a second opinion.
Anything will be much appreciated.