How does the gasoline tax affect the equilibrium price and quantity?
The gasoline tax artificially raises the price. A common argument is made that gasoline consumption is inelastic so that the demand will be little changed. This is true to a point for household consumption. Many households will simply increase their gasoline expenditures. [The cross impact this would have to their decreased spending on other goods or decreased real savings is important though tangential to your question.] Some households will economize if the price increases enough. In addition, household consumers may travel by air less if the gasoline tax applied to the airlines forces them to increase their price. More importantly, business consumption of gasoline may be very elastic. If transportation costs are a significant portion of costs, an artificial increase to gasoline prices may make some businesses unprofitable and so abort new businesses or cause existing businesses to shut down. So we have interesting opposite impacts. On the one hand, price is driven up artificially by