user28116: If I am a miner, it makes sense for me to broadcast recent blocks since I want my chain to be the longest (see What encourages Bitcoin miners to relay blocks?). 
However, what is my incentive for broadcasting old blocks? Deep blocks are very unlikely to be orphaned, so it seems that I get no gain from relaying them, despite it costing me bandwidth. 

user24925: There is no incentive to serve historical blocks beyond altruism, generally that applies to all facets of participating in the p2p network. Nodes without incoming connections will generally not be requested to send any old blocks, and this is a standard operating mode for people who have disabled listening or are behind restrictive NAT with no ability to hole punch through port 8333. 

user85: Miners have spent money on mining hardware. The value they are able to get out of that mining hardware is tied directly to the price of Bitcoins and the mining difficulty.
If the price goes up, that will incentivize some additional miners and if the price goes down, more people will mine. But this doesn't happen immediately nor does it cancel out perfectly. Miners benefit from an increase in the price of Bitcoins and are harmed by a drop in the price of Bitcoins.
Your incentive for sending old blocks is that the utility of bitcoins drops if it's more difficult for new nodes to join the network. While this effect on the price of bitcoins is slight, the amount of old blocks you need to send is also slight.

28116: <p>If I am a miner, it makes sense for me to broadcast recent blocks since I want my chain to be the longest (see <a href="https://bitcoin.stackexchange.com/questions/9107/what-encourages-bitcoin-miners-to-relay-blocks">What encourages Bitcoin miners to relay blocks?</a>). </p>

<p>However, what is my incentive for broadcasting old blocks? Deep blocks are very unlikely to be orphaned, so it seems that I get no gain from relaying them, despite it costing me bandwidth. </p>
 24925: <p>There is no incentive to serve historical blocks beyond altruism, generally that applies to all facets of participating in the p2p network. Nodes without incoming connections will generally not be requested to send any old blocks, and this is a standard operating mode for people who have disabled listening or are behind restrictive NAT with no ability to hole punch through port 8333. </p>
 85: <p>Miners have spent money on mining hardware. The value they are able to get out of that mining hardware is tied directly to the price of Bitcoins and the mining difficulty.</p>

<p>If the price goes up, that will incentivize some additional miners and if the price goes down, more people will mine. But this doesn't happen immediately nor does it cancel out perfectly. Miners benefit from an increase in the price of Bitcoins and are harmed by a drop in the price of Bitcoins.</p>

<p>Your incentive for sending old blocks is that the utility of bitcoins drops if it's more difficult for new nodes to join the network. While this effect on the price of bitcoins is slight, the amount of old blocks you need to send is also slight.</p>
