Consumption -Applications Inflation So far, consumption prices were assumed to be 1. Allowing for inflation in the price level is straightforward. The price today is 1 and tomorrow is p2. Tomorrow, the an spend p2c2 P2m2+(1+r)( The inflation rate, T, is the increase in the price level, p2=1+r. Therefore the budget line equation is e=m2+1+r Clt + Where 1+p=(1 +r)/(1+r)-p is the real interest rate. r is the nominal interest rat Rearranging to find P gives p=(r-T)/(1+x)Nr-t. Often the second approximation is used. Consumption-Applicatiorsa Present value Ignoring inflation, how much is a pound tomorrow worth in terms of pounds today? What is its present value? A pound today is worth 1 +r tomorrow(from saving it- its future tale), so the present value of a pound tomorrow is 1/(1+r). Budget sets are when"present value of consumption is at most present value of income Present value can be generalised to many periods. If there were 3 days. the present value of an income ms on day 3 rould be ma/(1+r)2.(If ma were saved on day I it would grow to ma(l +r)on day 2, and m3(1+r)2 on day 3). If there were t periods, the present value(Pv) of an income stream mI ...,mt is: Pv=m+1++a+7+…+a+1P=∑a+7 This is the correct way to value income streams. It is easy to generalise to allow for interest rates that change over time. t can be finite or infinite. This formula will appear again and again- remember itConsumption — Applications 11 Inflation • So far, consumption prices were assumed to be 1. Allowing for inflation in the price level is straightforward. • The price today is 1 and tomorrow is p2. Tomorrow, the consumer can spend p2c2 ≤ p2m2 + (1 + r)(m1 − c1). • The inflation rate, π, is the increase in the price level, p2 = 1 + π. Therefore the budget line equation is: c2 = m2 + 1 + r 1 + π (m1 − c1) ⇐⇒ c1 + c2 1 + ρ = m1 + m2 1 + ρ • Where 1 + ρ = (1 + r)/(1 + π) — ρ is the real interest rate. r is the nominal interest rate. • Rearranging to find ρ gives ρ = (r − π)/(1 + π) ≈ r − π. Often the second approximation is used. Consumption — Applications 12 Present Value • Ignoring inflation, how much is a pound tomorrow worth in terms of pounds today? What is its present value? • A pound today is worth 1 + r tomorrow (from saving it — its future value), so the present value of a pound tomorrow is 1/(1 + r). Budget sets are when “present value of consumption is at most present value of income”. • Present value can be generalised to many periods. If there were 3 days, the present value of an income m3 on day 3 would be m3/(1 + r) 2 . (If m3 were saved on day 1 it would grow to m3(1 + r) on day 2, and m3(1 + r) 2 on day 3). • If there were t periods, the present value (PV ) of an income stream m1, . . . , mt is: PV = m1 + m2 1 + r + m3 (1 + r) 2 + · · · + mt (1 + r) t−1 ⇐⇒ PV = Xt i=1 mi (1 + r) i−1 • This is the correct way to value income streams. It is easy to generalise to allow for interest rates that change over time. t can be finite or infinite. This formula will appear again and again — remember it