Class Notes Macroeconomics 2

Lecture 1: Consumption

Propensities to consume
● APC: Fraction of current income spent on consumption.
𝐶𝑡
𝐴𝑃𝐶 = 𝑌𝑡
APC is easy to measure, all we need is consumption and current income.

● MPC: Fraction of additional income spent on additional consumption.
∂𝐶𝑡
𝑀𝑃𝐶 = ∂𝑌𝑡
MPC is difficult to measure because we need fluctuations in income (like lotteries) and
consumption fluctuations.
MPC is important for policy making.

Consumption puzzle (definition): APC does not fall when income increases

Consumption straddle
● Rich households / countries consume more than poor households / countries in total
● Rich households / countries have a lower APC than poor households / countries → Cross
Section analysis




○ They spend a lower fraction of their income on consumption
○ For example in Greece, the poorest 20% spends 230% of their income on
consumption, and the richest 20% in Luxembourg spends 50% of their income on
consumption
○ The poorest consume everything, the richest save
● APC seems to be constant when income changes through time → Time series analysis

, ○ Countries become richer but their APC stays approximately constant.

Different theories of consumption
Keynesian
● The MPC is between 0 and 1
○ The extra unit of income devoted to consumption can go from 0 to 1. Does not
specify
● The wealthy have a lower APC than the poor
○ That is, in a cross section analysis, poor households consume a larger fraction of
their income than rich households (or countries)
● Current income is the primary determinant of consumption
○ Future income does not matter!
● Other variables, such as the interest rate, do not play an important role in consumption

𝐶 = 𝐶 + 𝑐𝑌
where
𝐶 is autonomous consumption
𝑐 is the MPC. It represents the consumption that depends on the income




Predictions
● APC (cross section) is decreasing in Y
● APC (time series) is decreasing in Y → WRONG
● MPC is between 0 and 1

Intertemporal choice (Fisher)
● The consumer is rational and forward looking
● The consumers make an intertemporal choice

Intertemporal budget constraint
𝐶1 + 𝑆 = 𝑌1
𝐶2 = 𝑆(1 + 𝑟) + 𝑌2
Combining them, we get
𝐶2 𝑌2
𝐶1 + 1+𝑟
= 𝑌1 + 1+𝑟

,Intertemporal choice
𝐶2 𝑌2
𝓛 = 𝑈(𝐶1, 𝐶2) − λ[𝐶1 + 1+𝑟
− 𝑌1 − 1+𝑟
]


FOC
∂𝑈
[𝐶1] = ∂ 𝐶1
= λ
∂𝑈 λ
[𝐶2] = ∂𝐶2
= 1+𝑟

Combining them, we get the Euler equation
∂𝑈 ∂𝑈
∂ 𝐶1
= (1 + 𝑟) ∂𝐶2

With logarithmic preferences, the Euler equation is
1 1
𝐶1
= β(1 + 𝑟) 𝐶2



Since β(1 + 𝑟) ≃ 1, 𝐶1 ≃ 𝐶2


● If 𝐶𝑡 = 𝐶𝑡+1 = 𝐶𝑡+2 =... = 𝐶𝑡+𝑇 , then MPC is very low. An extra unit of income is smoothed
through T periods. It is equally distributed taking into account its present value.
○ Intertemporal choice gives a low MPC since consumption is approximately equal in
all periods. Therefore, if you receive an extra unit of income, you will try to equally
distribute it in the different periods.

Shocks
↑𝑌
● Income effect: The agent is now richer and will consume more → ↑ 𝐶1 ↑ 𝐶2




Note: MPC between 0 and 1, APC depends on exact preferences
↑𝑟
● Substitution effect: Consuming on 𝑡 = 1 becomes more expensive than consuming on
𝑡 = 2. The agent postpones consumption, as he will get a higher return in the future.
Therefore, ↓ 𝐶1 , ↑ 𝐶2
● Income effect: Depends on the position of the agents.
○ Savers become richer. Thus, ↑ 𝐶1 , ↑ 𝐶2
○ Borrowers become poorer. Therefore ↓ 𝐶1 , ↓ 𝐶2

, Effect of r
● Empirically, the effect of the interest rate on consumption seems small
● Possible explanations
○ Income effects and substitution effects are offsetting
○ Fisher model is not appropriate
○ Borrowing constraints
■ Borrowing constraints restrict the feasible consumption set. 𝐶1 cannot
exceed 𝑌1




Predictions
● APC (cross section) → Does not predict