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Interest  Rates,  Inflation  and  the  Fisher  Equation    Inflation  is  an  increase  in  the  general  price  level.  Expected  inflation  rate  is      

𝑖 =  𝑃! −  𝑃!𝑃!

 

 

 The  Nominal  Interest  Rate,  R  is  in  terms  of  money  and  includes  inflation.  If  you  save  £1  today  then  you  will  receive  £(1+R)  pounds  tomorrow.    Economists  often  say  that  the  Real  Interest  Rate,  r  is  in  terms  of  goods  -­‐  if  you  save   one   unit   of   goods   today   then   you   will   receive   (1   +   r)   units   of   goods  tomorrow  –  which  is  very  unclear  as  banks  don’t  tend  to  let  you  put  you  car  into  a  vault  and  return  it  with  an  extra  steering  wheel  as  interest.  

Nominal  Interest  Rates  vs.  Real  Interest  Rates  The  real  interest  rate  accounts  for  inflation  whereas  the  nominal  interest  rate  does  not.  Here’s  an  example  to  illustrate  the  difference:    Lets  clear  this  up:  Sally   the   Squirrel   has   £100   to   save   for   next   year’s  cold  winter.  A  nut  costs  £4  today  so  she  could  have  purchased  25  nuts  this  year  and  buried  them  away.  But   like  many   squirrels   she   is   somewhat   forgetful.  Instead   she   goes   to   her   bank   -­‐  NutWest   -­‐   and   they  offer   her   a   savings   account   with   40%   interest    (R   =   40%).   Banks   always   offer   rates   in   nominal  terms  as  they  don’t  understand  economics.  Plus  this  way  they  get  to  rob  poor  squirrels  blind.  

Poor   Sally   saves   her   £100   thinking   she’s   going   to  receive  enough  interest  to  buy  an  extra  10  nuts  next  year,   which   would   be   40%   more   nuts.   Poor   Sally  should   have   studied   economics.   Due   to   many  squirrels  unable  to  find  their  buried  nuts  the  price  of  nuts  rises  greatly  over  the  year.  As  nuts  are  the  only  good  in  the  squirrel  economy,  this  is  inflation,  and  the  price  rises  a  whooping  25%  so  that  now  nuts  cost  £5!  

When   Sally   goes   back   to   the   bank   she   receives   her   £100  plus   £40   interest   –   a  40%  return  on  her  money.  However,  when  she  goes  to  spend  this  £140  she  finds  that   it  only  buys  her  28  nuts  at   the  new  price  of  £5  per  nuts.  She   feels  robbed.  The  40%  interest  rate  was  nominal  because   it  did  not  account   for   inflation.   In  

Quick  Maths  If  the  current  price  level  is  £1,  meaning  that  the  average  good  costs  £1,  and  the  expected  price  level  is  £1.10  next  year  the  inflation  is  £".!"!£"

£"= 10%  

     

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terms  of  goods  (as  economists  would  say),  she  was  not  able  to  buy  10  more  nuts,  but  only  3  more  nuts.   So   the  real   interest   rate,   telling  us  what  our  money   can  really  afford   in  terms  of  goods,  and  which  accounts   for   inflation,  was   lower.   In  this   example,   she   could   previous   afford   25   nuts,   now   she   can   afford   28   so  28÷ 25   =  1.12  (r=12%)  

 In  the  real  world,  where  inflation  and  interest  rates  are  much  smaller  than  the  above  example,  then  an  accurate  approximate  for  the  Fisher  Equation  ,  which  describes  the  relationship  between  the  real,  nominal  and  inflation  rates  is.    

 If   inflation   is  positive,  which   it   generally   is,   then   the   real   interest   rate   is   lower  than   the   nominal   interest   rate.   If  we   have  deflation,  meaning   that   the   inflation  rate  is  negative,  then  the  real  interest  rate  will  be  larger.    For  an  exact  mathematical  relationship,  read  on:    The  real  interest  rate  is  the  interest  from  savings  in  terms  of  goods  rather  than  money.  We  must  convert  goods  into  money,  invest  the  money  and  then  convert  back  into  goods  at  the  new  prices.    

Ø One  unit  of  goods  buys  P  units  of  today’s  money  Ø Saving  P  units  of  unit  today  returns  you  𝑃!(1  +  𝑅)  units  of  tomorrow’s  

money.  Ø 𝑃!(1  +  𝑅)  units  of  tomorrow’s  money  will  buy  you  

!!!  goods  tomorrow  

 Therefore    

1 + 𝑟 =𝑃!  ×  (1 + 𝑅)

𝑃!  

 

1 + 𝑟 =(1 + 𝑅)𝑃!

𝑃!

 

 

or  (1+ 𝑟)(1+ 𝑖) = (1+ 𝑅)  

 Note:  the  approximation  works  because  𝑟𝑖  is  negligible  because  both  r  and  i  are  such  small  numbers  and  then  the  1s  cancel  out.    

𝑅   =  𝑟   +  𝑖  

1+ 𝑟 =(1+ 𝑅)(1+ 𝑖)