intertemporal choice in the 2 period model Flashcards
what is the keynsian consumption function?
C = c0 +c1*(Y-T) where c0 and c1 are constant parameters, with the marginal prospensity to consume being between 0 and 1, the interest rates are not important nor are future incomes. consumption is a function of disposable income after tax
what did keynes predict about the growth of consumption compared to output?
keynes predicted that C would grow more slowly than Y as individuals would save more as Y increased. it mean that elasticity of consumption with respect to income is postive but less than 1.
what is the empiracle evidence of the keynsian consumption function?
according to the country level data, consumption is close to a constant fraction of GDP -> little evidence that countries consume a lower share of their income as they grow rich
what are the shortcomings of the keynsian consumption function/
inconsistency with aggregated data: it does not seem to be the casr that countries consume a lower fraction of their income as they grow rich
static nature of the model : forward looking decisions of households are not taken into account
why are dynamic consumption savings desicion is crucially important for modern business cycle model?
consumption is a large fraction of aggregate output -:> leading channel of propagation of various macroeconomic shocks
consumption saving response to changes in interest rates is a key element in transmission mechanism of monetary polict
what was irving fishers optimisation problem>
the optomisation problem of a consumer who faces no uncertainty and lives for two perods
what are the assumptions for the two period model?
time is discrete
a large number of identical consumers in the economy
each consumer lives for two periods ( t and t+1) and receives an exogenous income Y in every period
no government so Y = disposable income
all lifetime income should be finally consumed -> no saving in the second period
borrowing/lending is done with a single real interest rate r
what is the representative households budget constraint for the first period?
Ct + S =Yt where if S>0 implies Ct<Yt : the houshold is a saver
if S<0 implies Ct>Yt : the household is a borrower
S=0 implies that Ct=Yt : current consumption exactly equals income of this period
what is the budget constraint of the second period?
Ct+1 =Yt+1 + S + rS = Yt+1 + (1+r)S
what is the final form of the intertemporal budget constraint?
C_t +C_t+1 /(1+r) = Yt + Y_t+1 / 1+r where first section is the present value of lifetime consumption and second is the present value of lifetime income.
what does present value mean?
present value means the value in terms of the consumption goods in period t
what is the final consumption equal to ?
the income in both periods
what are the assumptions for the intertemporal utility function?
current and future consumptions are normal goods
consumers prefer to smooth their consumption over time
monotonicity of preferences: consumers prefer more to less
households are impatient => the same level of consumption provides larger utility if it comes now than if it comes in the next period.
what is the intertemporal utility function?
U(Ct, Ct+1) = u(Ct) + bu(Ct+1)
b<1 is discount factor ( a measure of our impatience)
b=1/1+P <=> where P is a subjective discount rate or rate of time preference
what does the intertemporal indifference curve show?
it shows all combinations of Ct and Ct+1 that provides the same level of utility for the consumer ie make the consumer equally happy
