I have a lamp with two 100 Watt light bulbs wired in parallel (normal way) . If I change them to two 200 Watt light bulbs but wire them in series. How much longer will they last and what will be the difference in total light output. Thanks.

I would say 2 100 watt bulbs in parallel would be 200 watts, 2 200 watt bulbs in series should be 200 watts, but since the 2 in series are burning at half voltage, bulbs will last much much longer.

If you wire them in series then each bulb will see only half the normal voltage, and so they may not come on at all. If they do come on they will be dim. The current through the bulbs will be equivalent to what you would have with a single 100W bulb (assuming the bulbs act as 2 resistors in series), so that would be the equivalent max light output you could expect. This may work with incandescent bulbs, but certainly would not with fluorescent (including CFLs).

In my experience, incadescent bulbs operating at half voltage put out much less than half the expected light. I do not expect this idea to work.

Putting incandescent bulbs in series will NOT be efficient or give much light.

My son just did a science fair project that looked at light output versus current consumption of regular household light bulbs. If I recall correctly, on average, light output (lumens) was about 50% somewhere around 80% current. (Lower wattage bulbs did slightly better than higher wattage bulbs.) Most would glow a weak orange, (just a few percent of full output lumens) at 50% current which is what you would have with 2 like bulbs in series. Interestingly, good name brand bulbs had the best lumens per watt ratios of all he tested. No generics that we tested came in as efficient. And those "long life" or 130 volt bulbs were horrible energy wasters. We tested a "20,000 hour" bulb which was MUCH better for heating than lighting!