We study the {\em multicommodity rent-or-buy problem}, a type of      
network design problem with economies of scale.  In this problem,     
capacity on an edge can be {\em rented}, with cost incurred on a      
per-unit of capacity basis, or {\em bought}, which allows unlimited   
use after payment of a large fixed cost.  Given a graph and a set of  
source-sink pairs, we seek a minimum-cost way of installing sufficient
capacity on edges so that a prescribed amount of flow can be sent     
simultaneously from each source to the corresponding sink.  The first 
constant-factor approximation algorithm for this problem was recently 
given by Kumar et al.~(FOCS '02); however, this algorithm and its     
analysis are both quite complicated, and its performance guarantee is 
extremely large.                                                      
                                                                   
In this paper, we give a conceptually simple 12-approximation       
algorithm for this problem.  Our analysis of this algorithm makes   
crucial use of {\em cost sharing}, the task of allocating the cost  
of an object to many users of the object in a ``fair'' manner.  While 
techniques from approximation algorithms have recently yielded new 
progress on cost sharing problems, our work is the first to show the 
converse---that ideas from cost sharing can be fruitfully applied in \
the design and analysis of approximation algorithms.