Ed Lazear is an excellent economist.
So as he surely knows, the proposed cuts in (or elimination of) retail taxes on gasoline aren't likely to reduce the price paid by the consumer, except maybe for a brief initial period.
That's because the "equilibrium" price is going to be determined by SUPPLY AND DEMAND.
So unless somebody can show me that cutting the retail tax will increase the supply of gasoline, I must conclude that the final price paid by the consumer will remain pretty much the same.
What WILL change with a tax cut is likely to be the short-run distribution of "profits" (or "rents" -- to use proper economic terminology).
Assuming that refiners are now producing at maximum capacity and that after a tax cut they don't raise the price they charge to retailers, and further assuming that government in its wisdom doesn't impose price controls, then a cut in retail taxes will mostly shift "rents" away from the government(s) and toward the retail merchants. That is, the retail price will remain basically the same and retailers will reap a windfall approximately equal to the government's lost tax revenue.
Complications:
(1) If local, state and/or federal authorities apply retail price controls, so as to force prices down to the former level MINUS the foregone taxes, then shortages and gas lines will appear. This outcome is 100% certain.
(2) Prices may begin to fall a bit after a while, to the extent that retailers and their distributors use some of their new rents/profits to bid petroleum away from foreign users -- since such an action will in fact increase our domestic supplies.
(3) Increased revenues in the hands of retailers may gradually "trickle down" to producers, in the form of higher prices that retailers may be willing to pay for fuel from high cost sources, like the Athabascan tar sands of Canada or capped "stripper" wells in the USA. But this effect is likely to take several years before it produces a noticeable increase in supply.
Bottom line: Taxes and tax cuts affect mainly the distribution of revenues between government and the private sector. Prices at retail are determined by supply and demand.
Now repeat after me: SUPPLY AND DEMAND.
one addition to your excellent post.
Taking profits out of the oil companies simply raises the cost of capital for these companies and thusly reduces future investments. Not allowing for profits in terms of cost of capital is like eating your young.
The best news about a tax cut is it would decrease funding available to the govt.
The second thing: the same supply would cost less. For the same amount of money, you would get more gas, and get more of the energy that gas represents.
You have to continuously starve the government until it is small enough to drown in a bathtup.