Topic 4- Don't use, read slides Flashcards
What is the national level of desired consumption (C^d)?
The aggregate quantity of goods and services that households optimally choose to consume, given income and other factors that determine householdsβ economic opportunities
Whoβs consumption decisions do we analyse?
Individual households
How do you calculate the aggregate level of desired consumption?
By adding up the desired consumption of
all households
What is desired national saving?
Level of aggregate saving when consumption is at its desired (optimal) level
How do you calculate desired national saving?
π^π = π β πΆ^π β G
What does the d mean in C^d?
Desired (Optimal)
What is the lifespan of the representative individual divided into?
The current period and the future preiod
What is the budget constraint for the current period?
π^π = π¦ + π β c
where:
a^f = assets in the future period
y= current income
c= current consumption
a= assets
What is the budget constraint of the future period?
π^π = π¦^π + (1 + π)π^f
where:
c^f= future period consumption
y^f= future period income
r= real interest rate
What is the equation for when an individual enhances future consumption from saving?
(1 + r) a^f = (1 + r)(s + a)
where rs is return on savings
We say the individual is a saver
What is dissaving?
When saving is less than zero
When the individual is a borrower, what conditions must be met?
π > π¦ + π β π^π < 0
How much does the future consumption fall below that periodβs income when someone is a borrower?
(1 + π) x absolute value of a^f
What are the conditions for someone to be a lender?
π < π¦ + π β π^π > 0
If π < π¦ β π^π > π, what is the individual?
A saver
If π > π¦ β π^π < a, what is the individual?
A dissaver
What is the no borrowing, no lending case represented by? What needs to be noted here?
π = π¦ + π β π^π = 0
c^f = y^f
Note: the individual is a dissaver as c - y = a > 0
If you consume more in the first period, what happens in the second period?
You canβt consume as much in the second period.
Some of y^f might be required in the current period.
What is one dollar of current consumption traded at for future consumption?
1 + r dollars
What is the price of one dollarβs worth of extra consumption today?
1 + π dollars worth of consumption in the future
Combining the two budget constraints, what is the consolidated budget constraint? Outline the steps.
π^π = π¦^π + (1 + π)(π¦ + π β π)
π^π = π¦^π + (1 + π)(π¦ + π) β (1 + π) c
c + c^f/(1+r) = y + a + y^f/(1+r)
What is the present value of lifetime resources?
y + a + y^f/(1+r) = PVLR = Xbar
What is the present value of lifetime consumption?
c + c^f/(1+r) = PVLC
What is on the axis for the intertemporal budget constraint?
y-axis c^f
x-axis c
What is the vertical intercept of the intertemporal budget constraint?
A(0,c^f): c^f = y^f + (1 + r)(y + a)
What is the horizontal intercept of the intertemporal budget constraint?
B(c,0): c = y^f/(1 + r) + y + a
What is the slope of thei ntertemporal budget constraint?
dc^f/dc = - (1 + r)
What is the constrained optimisation problem for households?
maxπ = π’ (π) + π½π’(π^π)
Such that π^π = π¦^π + (1 + π)(π + π¦ β π)
What is π½ in the constrained optimisation problem?
π½ > 0 is a number reflecting how the individual weighs the current and future consumption.
Alternatively, it is thought to capture the extent to which consumers are patient. If the consumer is very impatient, she places less weight on future utility, thus π½ is lower
What does it mean in the constrained optimisation problem if π½ = 1?
The consumer treats utils received today and in the future equally
What are the assumptions of the household constrained optimisation problem?
π’β²(π) > 0 & π’β²β²(π) < 0
π’β²(π^π) > 0 & π’β²β² (π^π) < 0
How do we make the constrained optimisation problem either to solve?
Substitute away future consumption
What is the maximisation utility function for households (unconstrained optimisation problem)?
maxπ = π’(π) + π½π’(π¦^π + (1 + π)(π + π¦ β π))
