Consumption function from optimization?
and explain
C1=θ(V1+H1)
V1= Financial wealth (assets, savings)
𝐻1 = Human wealth (lifetime income)
Consumption depends on wealth, NOT just current income.
What is human wealth?
The value today of all the income you will earn over your life.
What is human wealth?
The value today of all the income you will earn over your life.
H1=Y_1^d+Y_2^d/1+r
Y_1^d= Disposable income in period 1
Y_2^d= Disposable income in period 2 (future income).
r= Real interest rate
What is the MPC definition (θ)
How much consumption rises when wealth rises by $1.
0 < θ < 1
People smooth consumption → MPC < 1
Temporary Tax Cuts
Income rises only today.
People know it won’t last → they save part of it.
Small effect on consumption.
Permanent Tax Cuts
Income rises today AND in the future.
People feel permanently richer → big increase in consumption.
Much larger effect.
Intertemporal Elasticity of Substitution (σ)
σ = willingness to shift consumption between today and tomorrow.
If σ is high:
People easily shift consumption when interest rates change.
If σ is low:
People don’t change consumption much.
Ricardian Equivalence
very common
if government cuts taxes today but raises them tomorrow:
Forward-looking consumers save the tax cut to pay future taxes.
→ Consumption does NOT change.
