Consumption function
The consumption function is a foundational concept in macroeconomics that describes the relationship between aggregate consumer spending and disposable income, positing that consumption rises with income but less than proportionately due to a marginal propensity to consume (MPC) that is positive yet less than one.[1] Introduced by British economist John Maynard Keynes in his seminal 1936 book The General Theory of Employment, Interest, and Money, it underpins Keynesian economics by linking household consumption decisions to overall economic output and demand.[1][2] Typically expressed by the linear equation C = a + bY_d, where C represents total consumption expenditure, a denotes autonomous consumption (spending independent of income, such as on necessities), b is the MPC (the fraction of additional income devoted to consumption), and Y_d is real disposable income, the function highlights how consumption forms a stable but sloped line in graphical representations, with the slope b indicating sensitivity to income changes.[1][2] Keynes emphasized that current income is the primary determinant of consumption, influencing aggregate demand and employment levels in the economy.[1] The MPC is empirically observed to be positive and less than one (typically 0.5–0.9 across various studies).[3] Key assumptions of the basic Keynesian model include a static relationship between income and consumption, with households passively responding to national income levels without forward-looking behaviors or interest rate effects dominating decisions.[1] The model has been refined through extensions such as the life-cycle and permanent income hypotheses, which incorporate lifetime resources and expected income. The consumption function holds significant implications for economic policy, as shifts in the function—upward from factors like rising consumer confidence or falling interest rates, or downward from pessimism or credit constraints—can amplify business cycles through multiplier effects on aggregate demand.[2] Policymakers use it to assess fiscal stimuli, such as tax cuts, which boost disposable income and thus consumption more effectively among lower-income groups with higher MPCs.[2] Despite its simplicity, the framework remains central to modern macroeconomic modeling, informing analyses of recessions, inequality's impact on spending, and the effectiveness of monetary policy in sustaining demand.[1]Theoretical Foundations
Definition and Basic Model
The consumption function describes the relationship between household consumption expenditure (C) and disposable income (Y_d), positing that consumption rises with income but by less than the full amount of the income increase. This concept serves as a foundational element in Keynesian macroeconomics, linking individual spending behavior to broader economic activity.[4] John Maynard Keynes introduced the consumption function in his 1936 work, The General Theory of Employment, Interest, and Money, to model how consumption responds to changes in income and thereby explain fluctuations in economic output. Drawing on what he termed the "fundamental psychological law," Keynes argued that individuals tend to increase consumption as income rises, though the increment in consumption is smaller than the income gain, leading to higher savings at higher income levels.[5] The basic Keynesian model expresses this relationship linearly asC = C_0 + c Y_d,
where C_0 represents autonomous consumption—the level of spending that occurs even when disposable income is zero, often financed through savings, borrowing, or dissaving to meet essential needs—and c is the marginal propensity to consume (MPC), a constant between 0 and 1 indicating the fraction of additional disposable income devoted to consumption. The MPC captures the idea that not all extra income is spent, with the remainder allocated to saving, while autonomous consumption underscores the necessity of baseline expenditures regardless of current earnings. This formulation highlights consumption's dual nature: partly independent of income and partly responsive to it.[6][4]
Key Assumptions and Derivation
The basic consumption function proposed by John Maynard Keynes rests on several core behavioral assumptions about household decision-making. Consumers are assumed to base their consumption expenditures primarily on current disposable income, denoted as Y_d, without significant consideration of future income prospects or accumulated wealth.[7] This short-run focus emphasizes immediate income fluctuations over long-term planning or intertemporal optimization.[6] A central tenet is Keynes's "fundamental psychological law of consumption," which posits that as income rises, individuals increase their consumption, but not by as much as the income increase, reflecting habitual spending patterns and a tendency to save more at higher income levels.[7] This law implies that consumption grows less than proportionally with income, leading to a positive but less-than-unity marginal propensity to consume (MPC).[4] The linear form of the consumption function, C = C_0 + c Y_d, can be derived from the household budget constraint and these assumptions, where C is consumption, C_0 is autonomous consumption (positive spending even at zero disposable income, financed by dissaving or borrowing), and c is the constant MPC with $0 < c < 1. The budget constraint states that disposable income equals consumption plus saving: Y_d = C + S. Assuming saving follows a linear rule S = -C_0 + s Y_d, where s is the marginal propensity to save, and noting that s = 1 - c due to the identity between propensities to consume and save, substitution yields Y_d = C + (-C_0 + (1 - c) Y_d ). Rearranging terms gives C = C_0 + c Y_d.[4] This derivation highlights the role of a constant MPC in producing the linear relationship, consistent with the psychological law's emphasis on stable behavioral responses to income changes.[8] These assumptions have key implications for the relationship between consumption and income. In the consumption-income space, the function appears as a straight line with vertical intercept C_0 and slope c, positioned below the 45-degree line (where C = Y_d), indicating that consumption never fully equals disposable income at equilibrium due to positive saving.[4] The average propensity to consume (APC), defined as \text{APC} = \frac{C}{Y_d} = \frac{C_0}{Y_d} + c, declines as Y_d rises because the autonomous component \frac{C_0}{Y_d} diminishes, approaching the MPC asymptotically at high income levels.[6] In contrast, the MPC remains constant at c = \frac{\partial C}{\partial Y_d}, representing the fixed incremental response of consumption to income changes, while the APC exceeds the MPC at lower incomes but converges toward it over time. This distinction underscores how the assumptions generate a falling APC, aligning with the psychological law's prediction of increasing saving shares as income grows.[4]Major Extensions
Permanent Income Hypothesis
The Permanent Income Hypothesis (PIH), proposed by economist Milton Friedman, posits that individuals base their consumption decisions primarily on their "permanent income," defined as the long-term average expected income, rather than current measured income. This distinction arises because income can be decomposed into a permanent component, representing stable, anticipated earnings, and a transitory component, consisting of temporary fluctuations such as windfalls or unexpected losses. As a result, the marginal propensity to consume (MPC) out of transitory income is low, often near zero, as households tend to save most such income to smooth consumption over time, while the MPC out of permanent income is higher and closer to the average propensity to consume (APC).[9] Mathematically, the hypothesis formulates consumption as a function of permanent income:C = k Y_p
where C is consumption, Y_p is permanent income, and k is the propensity to consume out of permanent income, which Friedman argued is relatively stable and approaches 1 over the long run, aligning with observed stable APCs across income levels. Permanent income itself is estimated using an adaptive expectations model that weights past and current income:
Y_{p,t} = (1 - \lambda) Y_{p,t-1} + \lambda Y_t
here, \lambda (between 0 and 1) serves as an adjustment factor reflecting how quickly households update their estimate of permanent income based on new observations Y_t. This formulation captures the forward-looking nature of consumer behavior without requiring perfect foresight.[9] The theoretical motivation underlying the PIH is rooted in the idea that rational consumers aim to maintain stable consumption patterns that match their lifetime resources, using savings and borrowing to buffer against income volatility. Transitory income, such as bonuses or inheritances, is largely saved rather than spent, preventing sharp consumption swings that would otherwise occur under a strict current-income hypothesis. Friedman developed this framework to resolve empirical puzzles in Keynesian consumption theory, particularly the observation that the APC remains roughly constant over time and across income groups, rather than declining as income rises, which contradicted the absolute income hypothesis.[9] Historically, Friedman introduced the PIH in his seminal 1957 book A Theory of the Consumption Function, building on earlier empirical work like studies of veterans' bonuses to illustrate low MPCs from transitory sources. This extension refined the basic consumption function by emphasizing expectations and income classification, providing a microeconomic foundation for aggregate consumption stability.[9]