Present value Q: How much money would have to be saved now, in the present, to obtain $1 at the start of the next period? A: Sm saved now becomes $m(1+r)at the start of next period, so we want the value of m for which m(1+r)=1 That is, m=1/(1+r), the present-value of $1 obtained at the start of next period
Present Value Q: How much money would have to be saved now, in the present, to obtain $1 at the start of the next period? A: $m saved now becomes $m(1+r) at the start of next period, so we want the value of m for which m(1+r) = 1 That is, m = 1/(1+r), the present-value of $1 obtained at the start of next period
Present value The present value of $1 available at the start of the next period is PV 1+r And the present value of $m available at the start of the next period is PV= 1+r
Present Value The present value of $1 available at the start of the next period is And the present value of $m available at the start of the next period is PV r = + 1 1 . PV m r = 1+
The Intertemporal Choice Problem Let m and ma be incomes received in periods 1 and 2. Let C, and c2 be consumptions in periods 1 and 2. Let p, and p2 be the prices of consumption in periods 1 and 2
The Intertemporal Choice Problem Let m1 and m2 be incomes received in periods 1 and 2. Let c1 and c2 be consumptions in periods 1 and 2. Let p1 and p2 be the prices of consumption in periods 1 and 2
The Intertemporal choice Problem The intertemporal choice problem Given incomes m, and m2, and given consumption prices p, and p2, what is the most preferred intertemporal consumption bundle(c1, C2)? For an answer we need to know: the intertemporal budget constraint intertemporal consumption preferences
The Intertemporal Choice Problem The intertemporal choice problem: Given incomes m1 and m2 , and given consumption prices p1 and p2 , what is the most preferred intertemporal consumption bundle (c1 , c2 )? For an answer we need to know: – the intertemporal budget constraint – intertemporal consumption preferences
The Intertemporal budget Constraint To start, let's ignore price effects by supposing that p1=p2=$1
The Intertemporal Budget Constraint To start, let’s ignore price effects by supposing that p1 = p2 = $1