The marginal propensity to invest (MPI) indicates the extent to which investment expenditures are induced by changes in income or production. If, for example, the MPI is 01, then each dollar of extra income in the economy induces 10 cents of investment expenditures.The marginal propensity to invest is important to the study of Keynesian economics. First, the MPI reflects induced investment. Second, the MPI is the slope of the investment line, which makes it important to the slope of the aggregate expenditures line, as well. Third, the MPI affects the multiplier process and affects the magnitude of the expenditures and tax multipliers.
The MPI Formula
The standard formula for calculating marginal propensity to invest (MPI) is: MPI  =  change in investment change in income 
This formula has a couple of interpretations. First, it quantifies induced investment, that is, how much investment is induced by extra dollar. If income or production changes by $1, then investment changes by the value of the MPI. Income induces the change in investment at a rate measured by the MPI.
 Second, the MPI is actually a measure of the slope of the investment line that plots the relation between investment and income. The measurement of slope is generally given as the "rise" over the "run." For the investment line, the rise is the change in investment and the run is the change in income.
The Slope Of The Line
Investment Line 


The marginal propensity to invest is another term for the slope of the investment line. This can be demonstrated and illustrated using the red investment line, labeled I, in the exhibit to the right. Most notable, the investment line is positively sloped, indicating that greater levels of income generate greater investment expenditures by the business sector.This investment line reflects a plot of the following investment equation:
where: I is investment expenditures and Y is income or production (national income or gross domestic product).In particular, as specified in this investment equation, the slope of this investment line is equal to 0.1. This slope value indicates that each $1 change in income induces a $0.1 change in investment. In general, slope is calculated as the "rise" over the "run," that is, the change in the variable on the vertical axis (investment) divided by the change in the variable on the horizontal axis (production or income).
The change in investment divided by the change in income or production is the specification of the marginal propensity to invest. That is, the slope of the investment line is the marginal propensity to invest. To highlight this point, click the [Slope] button in this exhibit.
Moreover, because the investment line is a straight line, the slope is constant over the entire range of income. This means that the marginal propensity to invest is also constant.
Multiplier
The marginal propensity to invest is important to the multiplier process. The multiplier measures the magnified change in aggregate production (gross domestic product) resulting from a change in an autonomous variable (such as investment expenditures). While the marginal propensity to consume is the most important marginal affecting the multiplier process, the marginal propensity to invest also enters the picture.The basic multiplier process results because a change in production (such as what occurs when autonomous government purchases are used for national defense) generates income, which then induces consumption. However, the resulting consumption is also an expenditure on production, which generates more income, which induces more consumption. This next round of consumption also triggers a change in production, which generates even more income, and which induces even more consumption.
And on it goes, round after round. The end result is a magnified, multiplied change in aggregate production initially triggered by the change autonomous government purchases, but amplified by the change in induced consumption.
The multiplier process with induced consumption is augmented by induced investment. The change in production and income generated by the autonomous change in government purchases induces changes in both consumption AND INVESTMENT. Because both are expenditures on production, both generate more income, which induces more consumption AND INVESTMENT, which generates more income, and which induces even more consumption AND INVESTMENT.
The MPI enters into the process along with the marginal propensity to consume (MPC) because it determines how much investment is induced along with the induced change in consumption with each change in production and income. If the MPI is greater, then the multiplier process is also greater as more investment is induced with each round of activity.
This connection between the multiplier process, the marginal propensity to consume, and the marginal propensity to invest is illustrated in the standard formula for an expenditures multiplier:
expenditures multiplier  =  1 (1  (MPC + MPI)) 
An increase in the marginal propensity to invest reduces the value of the denominator on the righthand side of the equation, which then increases the overall value of the fraction and thus the size of the multiplier.For example, given a marginal propensity to consume of 0.75, a marginal propensity to invest of 0.05 results in a multiplier of 5. In contrast, a larger marginal propensity to invest of 0.15 results in a larger multiplier of 10.
Other Marginals
The marginal propensity to invest is one of several marginals that enters into the study of Keynesian economics. In fact, all induced variables have corresponding marginals that quantify the impact of income changes.Here a few of the more important marginals:
 Marginal Propensity to Consume: The most important marginal in the study of Keynesian economics is the marginal propensity to consume (MPC). This embodies the fundamental psychological law indicating that an increase in income induces changes in consumption. The MPC is the slope of the consumption line and thus forms the foundation of the slope of the aggregate expenditures line. This marginal is also key to the magnitude of the multiplier process.
 Marginal Propensity to Save: The flip side of consumption is saving. The fundamental psychological law indicates that an increase in income induces changes in both consumption and saving. The marginal propensity to save (MPS) quantifies the saving part of this relation. It indicates the change in saving resulting from a change in income. In fact, if the MPC and MPS are calculated based on aftertax disposable income, then the two marginals sum to one: MPI + MPS = 1.
 Marginal Propensity for Government Purchases: Government purchases, like investment, is also induced by income and has a corresponding marginal. The marginal propensity for government purchases (MPG) is the change in government purchases induced by a change in income. The induced change in government purchases is related to the induced change in tax collections, and while it also small compared to investment, but it too affects the slope of the aggregate expenditures line and the size of the multiplier.
 Marginal Propensity to Import: The last of the four aggregate expenditures, net exports (exports minus imports), also has a corresponding marginal. However, the marginal is not for net exports proper, but for the imports part. The marginal propensity to import (MPM) is the change in imports induced by a change in income. The induced change in imports is closely connected to the marginal propensity to invest. That is, a portion of investment expenditures is actually used to purchase imports, which is reflected the marginal propensity to import.
MARGINAL PROPENSITY TO INVEST, AmosWEB Encyclonomic WEB*pedia, http://www.AmosWEB.com, AmosWEB LLC, 20002019. [Accessed: January 16, 2019].