How would the risk premium and a simplified taylor rule change the MP curve?
I get it now 

Under traditional monetary policy 
MP Curve is set by the central bank and follow the fisher equation
$$i_t = R_t + \pi_t$$

But traditionally the taylor asks that when the central bank considers monetary policy that they consider short run output and inflationary gap.
$$i_t = R_t + \pi_t+\bar m(\pi_t-\bar \pi)+\bar n \tilde Y_t$$
Where the monetary policy rule is
$$R_t-\bar r = m(\pi_t-\bar \pi)+n \tilde Y_t  $$
Now 
$$R^{CB}_t-\bar r = \bar n \tilde Y \space  where \space \bar n&gt;0  $$ 

and 
$$R_t = R^{CB}_t+\bar p $$

I assume that in the original taylor rule
$$R_t-\bar r = m(\pi_t-\bar \pi)+n \tilde Y_t  $$

Hence in the original taylor rule
$$i_t = R_t + \pi_t+\bar m(\pi_t-\bar \pi)+\bar n \tilde Y_t$$
$$i_t = R_t + \pi_t+R_t-\bar r$$

But in this simplified taylor rule $R^{CB}_t-\bar r=n $
$$R^{CB}_t-\bar r = \bar n \tilde Y  $$

To which i assume also that 
$$R_t-\bar r = \bar n \tilde Y = m(\pi_t-\bar \pi) $$

Hence 
$$i_t = R_t + \pi_t+R_t-\bar r$$
$$i_t = R_t + \pi_t+n \tilde Y $$

If $R_t = R^{CB}_t+\bar p$

$$i_t = R_t + \pi_t+n \tilde Y $$ $$i_t =R^{CB}_t+\bar p + \pi_t+n \tilde Y $$

Hence the $ n \tilde Y $ component of the simplified taylor rule makes the MP curve upward sloping.