Differential multiplier effect in the Leontief-Keynes input-output model

"Closing" input-output models, i.e., taking into account the fact that households spend the income they receive from the productive sectors, is an important issue for the development of realistic macroeconomic models. Classical Type II multipliers fail to do that. This is why we consider here what we term the Leontief-Keynes (LK) model by introducing the Keynesian circuit into the Leontief model. We find that LK multipliers are deduced from the Leontief multipliers by adding to them a constant equal to the product of the marginal propensity to consume, the Keynesian multiplier, and the average ordinary output multiplier. With respect to the ordinary Leontief multipliers, the smallest LK multipliers are multiplied by a value greater than k, the greatest LK multipliers are multiplied by a value lower than k, such that the average LK multiplier is exactly multiplied by k. Thus, the macroeconomic Keynesian effect is not applied uniformly among sectors in relative terms: the better placed a sector is, with respect to its Leontief multiplier, the less it benefits from the Keynesian multiplier, and conversely. A numerical example shows that Type II multipliers are nevertheless a particular case of LK multipliers, both coinciding when the "pivot value" for the marginal propensity to consume is chosen.