Materials¶
Notebooks¶
The following computational notebooks are companions to the reading assigned in Lecture 03:
The Envelope Condition and the Perfect Foresight CRRA Model: Companion to The Envelope Condition and Perfect Foresight CRRA Model
The Consumption Random Walk and the Permanent Income Hypothesis: Companion to Consumption Random Walk and The Consumption Function
Learning Objectives¶
By the end of this lecture, students will be able to:
Apply the envelope theorem to derive the Euler equation for multiperiod problems
Solve the infinite-horizon perfect foresight CRRA consumption problem and identify the patience conditions (AIC, FHWC, RIC, GIC) required for a well-defined solution
Derive Hall’s random walk result from quadratic utility and explain its testable implications
Compute the marginal propensity to consume out of transitory versus permanent income shocks
Explain why the Keynesian consumption function is incomplete without specifying the income process
Key Concepts¶
Envelope condition: The marginal value of resources equals the marginal utility of consumption, extending the Euler equation beyond two periods
Patience factor: The growth rate of consumption under CRRA utility, determined by the interest rate, discount factor, and risk aversion
Impatience conditions: Restrictions on parameters that ensure human wealth, the PDV of consumption, and the wealth-to-income ratio are all finite
Consumption random walk: Hall’s result that no lagged information predicts consumption changes, providing a model-free test of the Euler equation
Muth’s decomposition: The marginal propensity to consume depends on whether an income shock is transitory or permanent, not on its size