Although this gap decreases with A, it is always correct to say that the deadweight loss per dollar tax revenue is greater for the rectangular distribution.
t*, the level of the optimal per unit tax is greater for the rectangular distribution than for the identical distribution, and this gap increases proportionally with A.
d) From (a) and (c) it is clear that the total deadweight loss to society is always much greater under a rectangular distribution than under an identical (homogenous population) distribution.
In the case of heterogeneous customers with a rectangular distribution, the average or median customer is "located" at A/2, and thus has a reservation price of A/2.
In statistical terms, the sale data created what would be termed a rectangular distribution, certainly not a normal distribution in a classical statistical sense.
If the limited amount of sale data available are fit to a probability curve, it is most likely that a rectangular distribution will occur; in actual practice a few small molehills may pop up every so often along the X axis, rather than a smooth normal distribution.