On January 1st, 2017, the city Philadelphia introduced a $1 tax on soda to raise money for the cityâs public schools while fighting childhood obesity. Suppose that before the tax, the supply and demand of soda are given by (prices are in cents): (inverse) Demand: P = 500 â 3Qd 100 (inverse) Supply: P = 100 + Qs 50 . Assume initially there are no externalities in the market for soda.

A consultant from the mayorâs office criticizes the tax plan. He says that, while the tax raises money for public schools, it does nothing to fight the child obesity epidemic and also points out that instead of getting money from "big soda", the tax in effect is a transfer from Philadelphia residents to the government

What assumptions from earlier in the question would you have to change so that this consultant is correct?

The consultant is partially right.

The quantity consumed is indeed less than before the tax (25% less).

Because of the different elasticities of demand and supply, the tax is absorbed differently by consumers and suppliers.

Of the 100 cents of tax, 75% is contributed by the consumer (pays $2.75 what it was paying $2.00) and 25% is contributed by the supplier (receives $1.75 when he was receiving $2.00). The weight of the tax lies more on the consumer than the supplier.

Explanation:

The demand function is:

The supply function is:

The equilibrium is reached when both demand and supply functions have the same price and quantity:

This is the equilibrium without tax.

When a tax is introduced, the price that consumers pay is equal to the (new) equilibrium price plus the tax.

The demand function changes so as to the quantity demanded at, for example, at P=200, which is Q=100, is now the quantity demanded for P=200-100=100.

That is the same as saying that the demand function goes down in the graph.

The new demand funtion can be calculated as:

The new equilibrium is:

The consultant is partially right.

The quantity consumed is indeed less than before the tax (25% less).

Because of the different elasticities of demand and supply, the tax is absorbed differently by consumers and suppliers.

Of the 100 cents of tax, 75% is contributed by the consumer (pays $2.75 what it was paying $2.00) and 25% is contributed by the supplier (receives $1.75 when he was receiving $2.00). The weight of the tax lies more on the consumer than the supplier.