When prices for homes rise why might construction companies decide to build more homes

It works like law of supply.

Explanation:

The law of supply tells that as the price of a good rises, the quantity supplied of that good also rises. So to get benefit and make a profit they decided to build new houses. In this way when there will be more price and more buyer then companies make new houses to get profit.

Simply because people are paying more for homes and people who construct them will get more in that period of time if they build during that time since the value of homes is going up.