Understanding Negative Marginal Propensity to Consume or Save

Understanding the economic behavior of individuals and households is crucial for economic analysis. Two key concepts used in this analysis are the Marginal Propensity to Consume (MPC) and the Marginal Propensity to Save (MPS). These concepts describe how an additional unit of income is allocated between consumption and savings. Typically, these values range from 0 to 1, reflecting the standard economic assumption that households generally spend more when their income increases. However, what if these measures can be negative? This article elucidates the theoretical and practical implications of a negative MPC or MPS.

Marginal Propensity to Consume (MPC)

The MPC is defined as the change in consumption resulting from a change in income. It is commonly expressed as dC / dY, where C is consumption and Y is income. The typical range for MPC is from 0 to 1:

0 indicates that all additional income is saved, and none is consumed. 1 indicates that all additional income is spent, and none is saved.

A negative MPC would imply that when income increases, consumption decreases. This phenomenon, while not common in standard economic models, can occur in specific scenarios, such as when households are heavily indebted and feel compelled to save more rather than increase their consumption despite income increases.

Marginal Propensity to Save (MPS)

Similar to MPC, the MPS is defined as the change in savings resulting from a change in income and is mathematically expressed as dS / dY. It is typically also within the range from 0 to 1:

0 indicates that all additional income is consumed, and none is saved. 1 indicates that all additional income is saved, and none is consumed.

A negative MPS would mean that households are dissaving, spending more than their income in response to an increase in income. This is unconventional behavior but can occur when households prioritize spending over saving, possibly due to expectations of future income declines.

Accounting Identity: MPC MPS

Since total income (Y) is the sum of consumption (C) and savings (S) (i.e., Y C S), it follows that the sum of MPC and MPS is always equal to 1: MPC MPS 1. Accordingly, it is impossible for both to be negative at the same time. At least one of them must be positive, as this is an accounting identity.

Optimal Intertemporal Consumption

To further understand the concept, we need to delve into the underlying utility function and intertemporal consumption. Consider an economic agent deciding how to consume income across different periods and states of the world. The agent's utility function typically exhibits diminishing marginal utility of consumption within a period. This means that each additional unit of consumption provides less additional satisfaction compared to the previous unit.

Assuming no borrowing frictions, the agent can sell expected future income to increase current consumption. However, if income increases and the agent faces borrowing constraints, the ability to smooth consumption across time and states of the world is constrained. In such situations, the agent may choose to consume more today and less in the future (negative MPC) or save less today and more in the future (negative MPS) to take advantage of high-yield investment opportunities or to avoid excessive leverage.

Examples of Negative MPC and MPS

Let's consider a minimal counterexample to illustrate how negative MPC or MPS can arise. Suppose an agent has access to a technology that provides returns far above the interest rate on savings, but only if they invest with at least a million dollars. Before reaching this threshold, the agent saves as if the opportunity isn't present. However, once the agent's lifetime income exceeds the million-dollar threshold, they may choose to consume all current income to take advantage of the new investment opportunity, leading to a negative MPC. Conversely, if the agent can borrow as a fraction of income and initially borrows at the maximum allowed limit, an increase in income can enable further borrowing, leading to a negative MPS.

Conclusion

While negative MPC and MPS are not typical in standard economic models, they can occur under unusual circumstances, such as when households face significant financial constraints or when they have access to high-yield investment opportunities. These scenarios highlight the importance of considering specific economic contexts when analyzing consumer behavior. Understanding these concepts is crucial for economists, policymakers, and investors to make informed decisions in dynamic and complex economic environments.