real vs nominal interest in IS/LM  

• IS model: firms want values in terms of goods
  • dependent on real interest rate
  • Y = C(Y-T) + I(Y,r) + G
• LM model: dependent on nominal interest rate
  • determines opportunity cost of holding money vs holding bonds
  • M/P = Y L(i)
• r ~ i - pe
• nominal interest rate affected directly by monetary policy
• real interest rate affects spending/output
• effects of monetary policy depend on how nominal interest rate translates to real interest rate translates to output

money growth - effects on nominal/real interest rates differ from short to medium run  

• higher money growth >> lower nominal interest rates in short run, higher nominal interest rates in medium run
  • increase money growth >> i must decrease (function L(i) is negatively correlated to M/P), and r must then decrease
  • medium run >> output returns to natural level of output (due to unemployment rate returning to natural rate) >> rate of inflation equal to rate of money growth minus rate of output growth (p = gm-gy)
  • by IS relation, at natural output rate, there's a natural real interest rate >> in medium run, go back to natural rate of output and real interest
  • Yn = C(Yn-T) + I(Yn,rn) + G
  • i = rn + p = rn + (gm-gy) >> nominal interest still increases in medium run since higher money growth = increasing gm
• higher money growth >> lower real interest rates in short run, no effect on real interest rates in medium run (neutrality of money)
  • return to natural rate of output >> return to natural real interest rate
  • i = (gm-gy)
• Fisher hypothesis - in medium run, nominal interest rate increases one for one w/ inflation (assuming permanent nominal money growth)