4. Complete the steps in the derivation of the Fisher equation discussed on slide 19 of lecture 3 by showing that if we 1 + i a Be ' 'th = 1 + . ( ) gin WI 1 + 7:8 r 1 (b) Roplace 1 + with the Taylorseries expansion We 1 1+7re = 1 7re+(7re)2 (71's)3+(7re)4... in the expression in part 4(a) above. (c) Assume that we can ignore any terms involving We or (We)11 for n 2 2 because 71"2 is small. that we are left with the Fisher equation 7" = i 71's. Consider 1 item that costs one US. dollar USD today. I could buy it today, but if I wait a year: 0 My dollar can grow to USD 1.00 x (1 + i) in a bank account. where z' is the nominal interest rate. 0 The number of items (quantity) I expect to have in the future is dollars in account _ USD 1.00 x (1 +i) dollars per item _ USD1.00 x (1 + rte) item = (1 + 1') items where are is expected inflation and r is the real interest rate. 0 If we neglect inc and terms involving (#3)\" for n 2 2 we get the Fisher equation: r=i7re