True or false?
The correct answer is false. Had the question said economic efficiency rather than economic welfare the answer would have been true. If the supply curve is vertical, the entire tax burden will be shifted onto suppliers and output will not change because no cost savings result from cutting output. All of producers' total revenue is rent. Of course, the tax must be less than this entire revenue for production to continue---otherwise the good would be taken off the market entirely and an efficiency loss would occur. Whether a tax affects welfare depends on the effect of the tax on the distribution of income---which raises a whole additional set of issues.