*Why* were the Chernobyl control rods tipped with graphite? I understand the graphite tips of the boron control rods displaced water (a moderator) which lead to an increased reaction rate, rise in temperature and steam pressure etc.
Question: why were the control rods tipped with graphite at all? What purpose did that serve? 
 A: "Tipped" is a somewhat simplistic term that has been repeated so often it has become fact.  In fact the use of graphite for part of the control rods is more involved that "tip" might suggest.
The report :

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*INSAG-7  The  Chernobyl  Accident : Updating  of  INSAG-1  A  REPORT  BY  THE INTERNATIONAL  NUCLEAR  SAFETY  ADVISORY  GROUP

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*Link to download page

*ISBN  92-0-104692-8

*Safety report No. 75



goes into some detail on the design of the rods.

2.2.   DESIGN  OF  CONTROL  AND  SAFETY  RODS
The control  rods  and the  safety  rods  of an RBMK reactor  are  inserted  into the reactor  core  from  above,  except  for  24  shortened  rods  which are  inserted  upwards and  which are  used  for  flattening the  power  distribution.  A  graphite  rod  termed  a displacer  is attached  to each  end  of  the length of  absorber  of  each  rod,  except  for twelve  rods that are  used  in automatic control.
The lower displacer  prevents  coolant water  from  entering the  space vacated  as the rod  is withdrawn, thus augmenting the reactivity worth of the rod. The graphite displacer  of each  rod of all RBMK reactors was,  at  the time  of the accident,  connected  to  its rod  via a  'telescope',  with a water filled  space  of  1.25  m  separating  the  displacer  and  the  absorbing  rod  (see  Fig.  1).
The dimensions of rod and displacer  were such that when the rod was fully  extracted the displacer  sat centrally  within the  fuelled region  of the core with  1.25  m of water at either end.  On receipt  of a  scram  signal causing a  fully  withdrawn rod  to fall, the displacement  of  water  from  the  lower part  of  the  channel  as  the  rod  moved  down-wards from  its upper limit stop position  caused a local insertion of positive  reactivity in the lower part of the core. The magnitude of this 'positive scram'  effect  depended on  the  spatial  distribution  of  the  power  density  and  the  operating  regime  of  the reactor.

So the use of graphite had more than one purpose.
A: The graphite displacer improved the efficiency of the cycle by improving the geometry and 'coupling' between the upper and lower active sections of the core when the control rod was fully withdrawn. At the 'full out' position the displacer improves the flux pattern and reduces the amount of heat absorbed by the Control Rod Channel Cooling System. Allowing this space to be full of water would be a 'small' but continuous thermal loss for each withdrawn rod. The displacers would save significant operating cost over the life of the unit. 
