Why would you think this? If the insurance base is expanded substantially to include many millions more young people, the average cost of care per insured will go down.
Remember, starting in 2014, insurance companies will no longer be allowed to charge higher rates for higher-risk customers. Right now, a disproportionately large percentage of the insured are higher risk (they're the ones who do not choose to be uninsured, because they know they're going to need expensive medical care). After ACA fully kicks in, the proportion of higher-risk insured customers will go down, so the average insured person will be lower risk than currently, and insurance rates will go down to reflect this reduction in average risk.
Actually, in 2014 insurers will still be able to charge higher rates for higher-risk customers. The risk premium within a rate band cannot exceed 300%; IOW the highest premium can be nor more than 4x the lowest premium.
The mandate is expected to bring in millions of more customers, many of whom will be young and healthy. This will work to push average premiums for young, healthy people lower. Some of the people brought in by the mandate will be those who were previously uninsurable. This will work to push average premiums for older, unhealthy people higher. Unfortunately, since the individual risk pool must be aggregated and the small group/employer risk pool must be aggregated or merged into the individual risk pool, PLUS the 300% premium disparity, insurers will not be able to offer young, healthy people the low rates they should be paying nor older, unhealthy people the higher rates they should be paying. The most at-risk individuals will see lower premiums but everyone else will see higher premiums.
Then add in the fact that Essential Health Benefits can no longer be capped and loss costs will increase, pushing all rates higher.
The insurers I've heard from all say average rate increases of 20-25% "at least" come 2014.