Let q denote the quantity of heating oil demanded by each household and p denote the dollar price per litre. For the whole nation, Q=6-P. If we change the units of Q to litre instead of millions of litres and denote it with Q, the demand curve could be rewritten as Q=1000000(6-P)
For each householder, since each of the 1 million households has the same demand curve for heating oil, then q=Q/1000000=6-P.
Therefore, the demand function for each household is p=6-_q_ and the demand curve is graphed in next page.
When the price p=$1 per litre, the consumer surplus for each household is 5?5/2=$12.5 p.a. When the price p=$2 per litre, the consumer surplus for each household is 4?4/2=$8 p.a.
Thus, each household would lose $4.5 p.a. of consumer surplus without the government subsidy.
The government has to spend $5 (1?5) on the subsidy for each household per year, so it could cut each familys annual taxes by $5 if the government abandoned the subsidy.
If the government abandoned the subsidy and implemented the tax cut, each family would annually pay $8 (2´4) for the heating oil and get an annual tax cut of $5. In contrast, each family has to pay $5 p.a. for the heating oil if the government subsidise heating oil. Therefore, each family would be better off by $2 per year.
As a result of the government subsidy, the nations annual deadweight loss is 1´1000000/2=$500000. View More »