I have booked the New Zealand holiday ( with the Cook Island add on) leaving Heathrow in Nov 25.  I have upgraded all my long haul & Cook island flights to business class but one internal flight remains economy ( from Christchurch to Auckland). Unfortunately there are no business class seats on this flight.  I am concerned regarding my baggage allowances with this one flight I cannot upgrade. 
Could you inform me as to the baggage allowances for these upgrades, will I be able to pay for an extra case on the internal flight and so long as I manage any extra cases myself, is this allowed when using the coaches in NZ?