(a) (b) Consider the function f(x)=In (1+x). Obtain a Taylor Series Expansion of f(x) around x=0....

 

Transcribed Image Text:

(a) (b) Consider the function f(x)=In (1+x). Obtain a Taylor Series Expansion of f(x) around x=0. Hence explain why it is often said that: In(1+x)=x for small x. Let Pt be the price of a commodity on day t, and let p = ln(P). Using the result of (a), show that the proportional rate of increase in price (provided it is small) can be approximated by the logarithmic change in the price: P-P P Ap, P-Pt-1 (a) (b) Consider the function f(x)=In (1+x). Obtain a Taylor Series Expansion of f(x) around x=0. Hence explain why it is often said that: In(1+x)=x for small x. Let Pt be the price of a commodity on day t, and let p = ln(P). Using the result of (a), show that the proportional rate of increase in price (provided it is small) can be approximated by the logarithmic change in the price: P-P P Ap, P-Pt-1