Stock Markets and Monetary Policies Assuming we're dealing with rational investors, the stock price is equal to the present value of all future dividends(supposedly discounting at the nominal or real interest rates should give the same present value).

Imagine the Central Bank increases the real money supply, from an initial state of equilibrium, and this increase is unexpected by the investors of the stock market.

Now we have the consequences of monetary expansion in the 'physical' economy:


In the short run, the expansion causes the nominal interest rate to decrease and the output to increase. However, in the medium run, the output reverts back to the natural level, and assuming for simplicity that the output growth rate is zero, the nominal interest rate also increases when compared to initial medium run equilibrium.
In the short run, real interest rate decrease. In the medium run it increases to the natural level, and remains equal to initial levels.


In a book I'm reading on macroeconomics, it's stated that since in the short run the output (and dividends) increase, and the nominal interest rate decreases, the stock prices will go up, because the monetary expansion was unexpected. 

My question is: shouldn't the rational investor know that changes in the nominal interest rate are only short term, with the longer term effect being in the opposite direction, and hence it's not clear cut that stocks' price should go up? Or should they always go up? Is it due to expected inflation that counteracts the higher expected nominal interest rate?
I think at the outset you have to make the distinction between the real interest rate and the nominal interest rate. The nominal interest rate is the real interest rate less inflation. Assuming the money supple curve is a vertical line in M-r space, then a shift of the line to the right (as indicated by a monetary expansion) implies a decrease in the nominal interest rate. Some books make the distinction between money demand being dependent on nominal interest rates, but it makes intuitively more sense that money demand be a function of real interest rate rather than nominal. The real interest rate decreases as the nominal return on assets stays constant but the price level increases (increase in inflation as a result of the monetary expansion). Remember that the price of a stock in a perfect world is the net present value of all future dividends, discounted by real interest rate. As this interest rate decreases, we discount stocks less, and hence price increases. This is the intuition behind the inverse relationship between asset prices and interest rates. This however, is a short run effect, so stock prices increase in the short run. When the real interest rate returns to its original level in the medium run, the stock prices decrease again. In short, the fluctuations in stock prices reflect fluctuations in interest rate. (the illustration is simplest for a fixed coupon bond that pays C every period). Basically, it all depends when you examine the price.