Create a PAE column equal to C + Ip + G + X - IM. At Y equal to 1200, PAE is equal to 1400. Since PAE is greater than output, Y, there is a shortage of output. To determine unintended investment, Iu, consider the following. Since all output is always purchased, by definition, it is true that Y is equal to C + I + G + X - IM where I is actual investment equal to Ip + Iu; that is, I = Ip + Iu, or actual investment is equal to the sum of planned and unplanned investment.

(Unplanned investment is the unintended change in business inventories. ) Therefore, substituting for I, this output identity can be written as Y = C + Ip + Iu + G + X - IM; that is, all output is always purchased. This can be written as Y = PAE + Iu since PAE is equal to C + Ip + G + X - IM. (The definition of Iu is Y - PAE; that is, the unintended change in inventories is always equal to the surplus of output over planned expenditures.)

Since, in this question, PAE is 1400 when Y is 1200, the output surplus, Iu, equal to Y - PAE is equal to -200 indicating there is a shortage of output of 200 to meet demand. Since Iu = -200 not positive 200, there is a shortage of output of 200 rather than a surplus