Consumption Theories and Hypotheses

Keynes's Conjectures

  • Keynes proposed three conjectures about consumption:

    • Marginal Propensity to Consume (MPC): 0 < MPC < 1. This means that for every dollar increase in income, consumption increases by less than one dollar.

    • Average Propensity to Consume (APC): The APC falls as income rises. APC is defined as APC = \frac{C}{Y}, where C is consumption and Y is income.

    • Income as the Main Determinant: Income is the primary factor determining consumption levels.

The Keynesian Consumption Function

  • The consumption function is represented as C = \overline{C} + MPC \cdot Y, where \overline{C} is autonomous consumption (consumption independent of income).

  • MPC is the slope of the function.

  • As income rises, consumers save a bigger fraction of their income, causing APC to fall.

Early Empirical Successes

  • Early studies showed that households with higher incomes consume more and save more.

  • MPC is greater than 0 and less than 1.

  • Higher-income households save a larger fraction of their income, leading to a decreasing APC as income increases.

  • There is a strong correlation between income and consumption, suggesting that income is a main determinant of consumption.

Problems with the Keynesian Consumption Function

  • Economists predicted that consumption would grow more slowly than income over time based on the Keynesian consumption function. This prediction turned out to be inaccurate.

  • In reality, the APC did not fall as incomes grew, and consumption grew at the same rate as income.

  • Simon Kuznets demonstrated that C/Y (APC) was very stable in long time series data.

The Consumption Puzzle

  • The consumption puzzle arises from the difference between the consumption function derived from cross-sectional household data (falling APC) and long time series data (constant APC).

Irving Fisher and Intertemporal Choice

  • Fisher's model provides the basis for much subsequent work on consumption.

  • It assumes that consumers are forward-looking and make consumption choices for the present and future to maximize lifetime satisfaction.

  • Consumer choices are subject to an intertemporal budget constraint, which measures the total resources available for present and future consumption.

The Basic Two-Period Model

  • The model considers two periods: the present (Period 1) and the future (Period 2).

  • Notation:

    • Y1, Y2 = income in period 1 and period 2, respectively.

    • C1, C2 = consumption in period 1 and period 2, respectively.

    • S = Y1 - C1 = saving in period 1 (S < 0 if the consumer borrows in period 1).

Deriving the Intertemporal Budget Constraint

  • Period 2 budget constraint: C2 = Y2 + (1 + r)S = Y2 + (1 + r)(Y1 - C_1)

  • Rearranging terms: (1 + r)C1 + C2 = Y2 + (1 + r)Y1

  • Divide through by (1 + r) to get: C1 + \frac{C2}{1 + r} = Y1 + \frac{Y2}{1 + r}

The Intertemporal Budget Constraint

  • C1 + \frac{C2}{1 + r} = Y1 + \frac{Y2}{1 + r}

    • The left side represents the present value of lifetime consumption.

    • The right side represents the present value of lifetime income.

  • The budget constraint shows all combinations of C1 and C2 that just exhaust the consumer's resources.

  • The slope of the budget line equals -(1 + r).

Consumer Preferences

  • An indifference curve shows all combinations of C1 and C2 that make the consumer equally happy.

  • Higher indifference curves represent higher levels of happiness.

  • Marginal Rate of Substitution (MRS):

    • The amount of C2 the consumer would be willing to substitute for one unit of C1.

    • The slope of an indifference curve at any point equals the MRS at that point.

Optimization

  • The optimal (C1, C2) is where the budget line just touches the highest indifference curve.

  • At the optimal point, MRS = 1 + r.

How Consumption Responds to Changes in Income

  • An increase in Y1 or Y2 shifts the budget line outward.

  • If both C1 and C2 are normal goods, both increase, regardless of whether the income increase occurs in period 1 or period 2.

Keynes vs. Fisher

  • Keynes:

    • Current consumption depends only on current income.

  • Fisher:

    • Current consumption depends only on the present value of lifetime income.

    • The timing of income is irrelevant because the consumer can borrow or lend between periods.

How Consumption Responds to Changes in Interest Rate (r)

  • An increase in r pivots the budget line around the point (Y1, Y2).

  • Income Effect: If the consumer is a saver, the rise in r makes them better off, which tends to increase consumption in both periods.

  • Substitution Effect: The rise in r increases the opportunity cost of current consumption, which tends to reduce C1 and increase C2.

  • Both effects lead to an increase in C_2.

  • Whether C_1 rises or falls depends on the relative size of the income & substitution effects.

Constraints on Borrowing

  • In Fisher's theory, the timing of income is irrelevant, as consumers can borrow and lend across periods.

  • Borrowing Constraints (Liquidity Constraints): If a consumer faces borrowing constraints, they may not be able to increase current consumption.

  • The borrowing constraint can take the form: C1 = Y1

  • The budget line with a borrowing constraint means consumption in period 1 cannot exceed income in period 1.

  • Consumer Optimization:

    • If the borrowing constraint is not binding, the consumer's optimal C1 is less than Y1.

    • If the borrowing constraint is binding, the best the consumer can do is to consume all of their current income.

The Life-Cycle Hypothesis (LCH)

  • Developed by Franco Modigliani.

  • Fisher's model states that consumption depends on lifetime income, and people try to achieve smooth consumption.

  • The LCH states that income varies systematically over the phases of the consumer's life cycle, and saving allows the consumer to achieve smooth consumption.

The Basic Model of LCH

  • Variables:

    • W = initial wealth

    • Y = annual income until retirement (assumed constant)

    • R = number of years until retirement

    • T = lifetime in years

  • Assumptions:

    • Zero real interest rate (for simplicity)

    • Consumption-smoothing is optimal

  • Lifetime resources = W + RY

Achieving Smooth Consumption in LCH

  • To achieve smooth consumption, the consumer divides their resources equally over time: C = \frac{W + RY}{T}, or C = \alpha W + \beta Y

    • \alpha = \frac{1}{T} is the marginal propensity to consume out of wealth

    • \beta = \frac{R}{T} is the marginal propensity to consume out of income

Implications of the Life-Cycle Hypothesis

  • The LCH can solve the consumption puzzle:

    • The life-cycle consumption function implies APC = \frac{C}{Y} = \alpha \frac{W}{Y} + \beta

    • Across households, income varies more than wealth, so high-income households should have a lower APC than low-income households.

    • Over time, aggregate wealth and income grow together, causing APC to remain stable.

  • The LCH implies that saving varies systematically over a person's lifetime.

The Permanent Income Hypothesis (PIH)

  • Developed by Milton Friedman.

  • Y = Y^P + Y^T

    • Y = current income

    • Y^P = permanent income (average income, which people expect to persist into the future)

    • Y^T = transitory income (temporary deviations from average income)

Consumption and the PIH

  • Consumers use saving & borrowing to smooth consumption in response to transitory changes in income.

  • The PIH consumption function: C = \alpha Y^P, where \alpha is the fraction of permanent income that people consume per year.

Solving the Consumption Puzzle with PIH

  • The PIH implies APC = \frac{C}{Y} = \alpha \frac{Y^P}{Y}

  • If high-income households have higher transitory income than low-income households, APC is lower in high-income households.

  • Over the long run, income variation is primarily due to variation in permanent income, which implies a stable APC.

PIH vs. LCH

  • Both theories suggest that people try to smooth their consumption in the face of changing current income.

  • LCH: Current income changes systematically as people move through their life cycle.

  • PIH: Current income is subject to random, transitory fluctuations.

  • Both can explain the consumption puzzle.

The Random-Walk Hypothesis

  • Developed by Robert Hall.

  • Based on Fisher's model & PIH, in which forward-looking consumers base consumption on expected future income.

  • Hall adds the assumption of rational expectations, that people use all available information to forecast future variables like income.

Implications of the Random-Walk Hypothesis

  • If PIH is correct and consumers have rational expectations, then consumption should follow a random walk: changes in consumption should be unpredictable.

  • Anticipated changes in income or wealth have already been factored into expected permanent income and will not change consumption.

  • Only unanticipated changes in income or wealth that alter expected permanent income will change consumption.

  • Policy changes will affect consumption only if they are unanticipated.

The Psychology of Instant Gratification

  • Theories from Fisher to Hall assume that consumers are rational and act to maximize lifetime utility.

  • Recent studies by David Laibson and others consider the psychology of consumers.

  • Consumers consider themselves to be imperfect decision-makers and recognize the "pull of instant gratification," which explains why people don't save as much as they rationally know they should.

Chapter Summary

  • Keynesian consumption theory:

    • MPC is between 0 and 1.

    • APC falls as income rises.

    • Current income is the main determinant of current consumption.

  • Fisher's theory of intertemporal choice:

    • Consumers choose current & future consumption to maximize lifetime satisfaction subject to an intertemporal budget constraint.

    • Current consumption depends on lifetime income, not current income, provided consumers can borrow & save.

  • Modigliani's life-cycle hypothesis:

    • Income varies systematically over a lifetime.

    • Consumers use saving & borrowing to smooth consumption.

    • Consumption depends on income & wealth.

  • Friedman's permanent-income hypothesis:

    • Consumption depends mainly on permanent income.

    • Consumers use saving & borrowing to smooth consumption in the face of transitory fluctuations in income.

  • Hall's random-walk hypothesis:

    • Combines PIH with rational expectations.

    • Changes in consumption are unpredictable and occur only in response to unanticipated changes in expected permanent income.

  • Laibson and the pull of instant gratification:

    • The desire for instant gratification causes people to save less than they rationally know they should.