Chapter 4: Consumption - Comprehensive Notes

Consumption

Introduction

  • Consumption is the ultimate goal of all production, as stated by Adam Smith.
  • The consumption function is central to Keynesian economics and understanding economic fluctuations.

Keynesian Consumption Function

  • Keynes's theory, presented in "The General Theory" (1936), revolves around the consumption function.
  • Marginal Propensity to Consume (MPC):
    • Definition: The change in consumption resulting from a change in income. It is the amount consumed out of an additional dollar of income. Mathematically expressed as MPC = \frac{\Delta C}{\Delta Y}. Should be noted that
      0 < MPC < 1
    • Keynes's Conjecture: The MPC is between zero and one. Meaning that for every dollar earned, people will consume part of it and save the rest.
  • Average Propensity to Consume (APC):
    • Definition: The ratio of consumption to income. Mathematically expressed as APC = \frac{C}{Y}.
    • Keynes's Claim: The APC falls as income rises.
  • Keynes also posited that income is the primary determinant of consumption, with the interest rate playing a minor role.

Consumption Function Equation

  • Consumption (C) is determined by autonomous consumption and induced consumption which depends on disposable income (Y).
  • Equation: C = \overline{C} + cY where:
    • \overline{C} represents autonomous consumption (consumption independent of income), where \overline{C} > 0.
    • c represents the marginal propensity to consume (MPC), where 0 < c < 1.
  • Graphical Interpretation:
    • \overline{C} determines the intercept on the vertical axis.
    • c is the slope of the consumption function.

Properties of the Consumption Function

  • The consumption function, C = \overline{C} + cY, embodies three key properties according to Keynes:
    1. MPC is between zero and one (0 < c < 1).
    2. APC falls as income rises. As Y increases, \frac{\overline{C}}{Y} decreases, leading to a fall in APC.
    3. Consumption is primarily determined by current income (Y).
  • Interest rate isn't a determinant of consumption in this equation.

Understanding Marginal Propensity to Consume (MPC)

  • Scenario: A shopaholic with an MPC of 0.99 spends $0.99 of every extra dollar earned after tax deductions.
  • The MPC gauges the sensitivity of changes in consumption relative to changes in income.

Early Empirical Findings

  • Households with higher incomes:
    • Consume more (MPC > 0).
    • Save more (MPC < 1).
    • Save a larger fraction of their income, causing the APC to decrease as income increases.
  • Strong correlation between income and consumption: Income appeared to be the main driver of consumption.

Secular Stagnation and the Kuznets Puzzle

  • Secular Stagnation Prediction: Economists predicted a prolonged depression after World War II based on Keynes’s consumption function.
  • The Prediction Failed: The post-war period didn't result in a depression, but the APC didn't fall as income rose, challenging Keynes’s conjecture.
  • Kuznets's Discovery: Simon Kuznets found that the ratio of consumption to income remained stable over time, despite significant income increases, further questioning Keynes's conjecture. He analyzed data back to 1869.

The Consumption Puzzle

  • The constancy of the APC over time contradicted earlier findings.
  • Short-Run vs. Long-Run Consumption Function:
    • Short-Run: Studies of household data and short time-series supported Keynes's conjecture of a falling APC.
    • Long-Run: Long time-series studies indicated that the APC remained fairly constant despite income changes.

Intertemporal Choice Model

  • Developed by Irving Fisher, the model analyzes how rational, forward-looking consumers make choices across different time periods.
  • Key Aspects:
    • Consumer Constraints: The limitations consumers face.
    • Consumer Preferences: The desires and priorities of consumers.
    • Intertemporal Budget Constraint: Measures the total resources available for consumption in different periods.

Consumer's Budget Constraint

  • Interpretation:
    • If the interest rate is zero, total consumption in two periods equals total income in the two periods.
    • With a positive interest rate, future consumption and income are discounted by a factor of \frac{1}{1 + r}.
  • Discounting Rationale: Interest earned on savings makes future income worth less than current income; future consumption costs less due to earned interest.
  • Price of Second-Period Consumption: \frac{1}{1 + r} is the price of second-period consumption in terms of first-period consumption.

Basic Two-Period Model

  • Two Time Periods:
    • Period 1: The present.
    • Period 2: The future.
  • Notation:
    • Y_1 is income in period 1.
    • Y_2 is income in period 2.
    • C_1 is consumption in period 1.
    • C_2 is consumption in period 2.
    • S = Y1 - C1 is saving in period 1 (S < 0 if the consumer borrows).

Deriving the Intertemporal Budget Constraint

  • Period 2 budget constraint:
    Rearrange to put C terms on one side and Y terms on the other
    Divide through by (1+r ):

The Intertemporal Budget Constraint Equation

  • The intertemporal budget constraint is: C1 + \frac{C2}{1+r} = Y1 + \frac{Y2}{1+r}
    • Present Value of Lifetime Consumption: C1 + \frac{C2}{1+r}
    • Present Value of Lifetime Income: Y1 + \frac{Y2}{1+r}

Consumption and Budget Choices

  • Consumer Choices: Combinations of first-period and second-period consumption.
    • Saving: Consuming less than income in the first period and saving the rest.
    • Borrowing: Consuming more than income in the first period and borrowing to cover the difference.
  • Graphical Representation:
    • Horizontal Intercept: Y1 + \frac{Y2}{1+r}
    • Vertical Intercept: (1+r)Y1 + Y2

Budget Constraint and Consumer Resources

  • The budget constraint illustrates all combinations of C1 and C2 that exhaust the consumer’s resources.
  • Intertemporal trade-off: Consumers can choose to consume more or less in either period, but have to operate within the budget constraint.

Slope of the Budget Line

  • The slope of the budget line is -(1+r), representing the trade-off between consumption in the two periods.

Consumer Preferences and Indifference Curves

  • Indifference Curves: Represent consumer preferences regarding consumption in the two periods.
  • Definition: A curve showing combinations of C1 and C2 that provide equal satisfaction.
  • Marginal Rate of Substitution (MRS):
    • The slope of the indifference curve indicates how much C2 a consumer needs to compensate for a 1-unit reduction in C1.
    • Represents the rate at which a consumer is willing to substitute C2 for C1.

Optimal Consumption

  • Consumers maximize satisfaction by choosing the point on the budget constraint that lies on the highest possible indifference curve.
  • Optimum: The indifference curve is tangent to the budget constraint.
  • At the Optimum Point:
    • MRS = 1 + r.

Borrowing Constraints

  • Borrowing Limit: C1 ≤ Y1, indicating that current consumption cannot exceed current income.
  • Impact: Prevents consumers from borrowing to increase current consumption.

Two Consumption Functions

  • Unconstrained Consumers: Consumption in both periods depends on the present value of lifetime income.
  • Constrained Consumers: Consumption depends only on current income due to the borrowing constraint.

Borrowing Constraints Visualization

  • If the consumer's optimal C1 is less than Y1 then the borrowing constraint is not binding.
  • If the borrowing constraint is binding, the consumer cannot borrow and the best they can do is spend all of their first period income in the first period and consume Y_2 in the second period.

Life-Cycle Hypothesis

  • Developed by Franco Modigliani, Ando, and Brumberg in the 1950s.
  • Based on Fisher’s model, it studies the consumption function considering lifetime income.
  • Key Points:
    • Income varies systematically over a person’s life.
    • Saving enables consumers to shift income from high-income to low-income periods.
    • Consumption smoothing is the goal.

Life-Cycle Hypothesis: Basic Model

  • 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.

Life-Cycle Hypothesis: Equations

  • Lifetime Resources: W + RY
  • Consumption Equation:
    • C = \frac{(W + RY)}{T}
    • C = aW + bY
      • a = \frac{1}{T} (marginal propensity to consume out of wealth).
      • b = \frac{R}{T} (marginal propensity to consume out of income).

Implications of the Life-Cycle Hypothesis

  • Explaining the Consumption Puzzle:
    • Implied APC: \frac{C}{Y} = a(\frac{W}{Y}) + b
    • Across households, wealth doesn't vary as much as income, resulting in high-income households having lower APCs than low-income households.
    • Over time, aggregate wealth and income grow together, stabilizing the APC.

Saving Patterns Over a Lifetime

  • The LCH suggests that saving varies systematically over a person’s lifetime.
    • Accumulation during working years, dissaving during retirement.

Permanent Income Hypothesis

  • Proposed by Milton Friedman (1957).
  • Decomposes Current Income (Y) into two components:
    • Permanent Income (Y^P): Average income expected to persist into the future.
    • Transitory Income (Y^T): Temporary deviations from average income.

Consumption and Income

  • Consumers use saving & borrowing to smooth consumption in response to transitory changes in income.
  • The PIH consumption function: C = aY^P
    • Where a is the fraction of permanent income that people consume per year.

PIH and the Consumption Puzzle

  • PIH implies APC = \frac{C}{Y} = a\frac{Y^P}{Y}
  • The APC will be lower in high-income households to the extent that high-income households have higher transitory income than low-income households.
  • Over the long run, income variation is mainly due to variation in permanent income, implying a stable APC.

PIH vs. LCH

  • Both theories emphasize consumption smoothing in the face of changing current income.
  • LCH: Current income changes systematically over the life cycle.
  • PIH: Current income is subject to random, transitory fluctuations.
  • Both can explain the consumption puzzle.

Random Walk Hypothesis

  • Changes in consumption are unpredictable and depend only on new information.
  • Based on the PIH and developed by Robert Hall (1978).

Key Concepts

  • Consumption Smoothing: Basing consumption decisions on expected lifetime income.
  • New Information Drives Changes: Unexpected changes in income lead to changes in consumption.
  • Unpredictability of Consumption: Changes in consumption should be unpredictable and follow a random walk.
  • Equation: Ct = C{t-1} + \epsilon_t
    • Where Ct​ is consumption at time t and \epsilont is a random error term that represents new information.

Implications of the R-W Hypothesis

  • Past income changes do not predict future consumption changes.
  • Temporary government policies have little effect on consumption.
  • Consumption volatility is lower than income volatility.
  • Policy changes affect consumption only if they are unanticipated.

The Psychology of Instant Gratification

  • Consumers aren't fully rational and act to maximize lifetime utility.
  • Consumers are imperfect decision-makers.
  • Instant gratification explains why people don’t save as much as they should.
  • Instant gratification plays a critical role in consumer decision-making and economic consumption theories. It explains why individuals often prioritize immediate rewards over long-term benefits, affecting savings, spending, and investment behaviors.
    • The “pull of instant gratification” explains why people don’t save as much as a perfectly rational lifetime utility maximizer would save.
    • Impulse buying – Choosing to spend on unnecessary items rather than saving.
    • Fast food consumption – Prioritizing convenience over long-term health.
    • Social media addiction – Seeking instant likes and validation rather than engaging in productive activities.

How Instant Gratification Affects Economic Consumption Theories

  • Keynesian Consumption Function:
    • Instant gratification reinforces the idea that people spend most of their income rather than save it.
    • If consumers prioritize immediate spending, then savings rates decline, potentially affecting long-term economic growth.
  • Permanent Income Hypothesis (PIH):
    • Instant gratification disrupts the model, as many people overspend when they earn more rather than save for the future.

Economic Consequences of Instant Gratification

  • Low Savings Rate: Consumers fail to build wealth for emergencies or retirement.
  • Debt Accumulation: Credit card debt rises due to impulsive spending.
  • Boom-Bust Cycles: Overconsumption during economic booms can lead to financial crises.

Time Inconsistency

  • People tend to prefer a smaller, immediate reward over a larger, delayed reward.
  • However, these preferences can change over time, leading to inconsistent choices.
  • Example scenario comparing choices between immediate vs slightly delayed rewards highlights the effects of instant gratification on decision making.