Quick and dirty analysis: Greek heating oil tax

Here's a quick and dirty economic analysis of the Greek tax on heating oil, based on the facts as stated in the NY Times article.  By applying some logic and economic intuition to the facts, we can make some informed judgments about the economic efficiency of this tax policy.

The article says that the government "raised the taxes on heating oil by 450 percent."  Taken literally, if the original tax was T0, the new tax is T1 = 5.5T0.  (This is not the same as saying the new tax is 450% of the old tax!)

The original cost of heating "a small apartment" was P0 = C + T0 = $1,300, where C is the pre-tax cost of oil. 
Now the cost of heating the same apartment is "about" P1 = C + 5.5T0 = $1,900. 

So the 450% increase in the tax = $600/small apartment, which implies the original tax was T0 = $600/4.5 = $133 and the new tax is T1 = $733.
The pre-tax cost of oil C = $1,300 - $133 = $1,167/small apartment. 

Now let's estimate the demand elasticity for heating oil:  If the cost of heating rose $600/[($1,300+$1,900)/2] = +37%, and "sales in the last quarter of 2012 plunged 70 percent," then -70%/37% = -1.9.  That looks like a high demand elasticity for the short run, but in this case Greeks had been using a lot of heating oil as diesel fuel because diesel was much more heavily taxed; now the equal taxation of heating oil and diesel eliminates that subsitution.

So here's a crude graph representing the Greek heating oil market.  The article doesn't specify aggregate consumption quantities, but we can graph a consumption index: if last year's oil consumption (when P0 = $1,300) is indexed at 100, this year's consumption index (when P1 = $1,900) equals 30.  (Is this crude enough for you?)   I doubt that Greeks actually reduced heating oil consumption by 70%; less oil is being diverted to the diesel fuel market too.

Since Greece buys its oil in the world market and isn't that big a nation, we'll assume world oil prices are unaffected by changes in Greek consumption.  So the supply schedule is horizontal.

We already estimated the pre-tax cost of heating as C = $1,167/small apartment.  Using our demand elasticity estimate, the old tax of $133 increased the pre-tax price about 11%, which reduced consumption about 1.9 × 11% = 21%. So the old tax had already reduced the consumption index from about 120 to 100.  The tax revenue index was 100×$133 = 13,300, and the deadweight loss index was (20×$133)/2 = 1,330, or 10% of the tax revenue generated.

Now we can estimate the effects of the higher tax.  The new tax revenue index is 30×$733 = 21,990, and the DWL index is (90×$733)/2 = 33,000.  So the 450% increase in the tax rate increased tax revenues only 65% while causing a 24-fold increase in DWL! 

The DWL is now about 50% larger than the tax revenue!  We could do a lot more research and develop a more sophisticated demand analysis with more accurate data, but the basic conclusions would remain the same: this is a truly horrible tax policy!  This DWL isn't just a theoretical abstraction.  Hundreds of thousands of people suffering, and some dying from hypothermia; parks vandalized for firewood; polluted air; the breakdown in cooperation between apartment dwellers to pay for common heat--these are very real costs of bad economic policy!