Question

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?

Answer 1

Step-by-step explanation:

The city Philadelphia introduced

Given Data

Tax on soda in January 1st 2017 =$1

Before the tax:

Demand: P = 500-3Q---------------------------1

Supply : P = 100 + Q-----------------------------2

Calculating the quantity of demand and supply in equilibrium before the tax, we have;

500-3Q = 100 + Q

Solving for Q, we have

Q + 3Q = 500- 100

4Q = 400

Q = 400/4

Q = 100

For the demand,

P = 500-3Q

= 500 - 3 * 100

= 500 -300

P = 200 was the quantity demanded before tax

From equation 2,

P = 100 + Q

P = 100 + 100

P = 200 Quantity supply before tax

Calculating the quantity of demand and supply during the tax and then compare it with the quantity demand and supply before the tax.

Setting the new demand function, we have

P = C - 3Q

when P = 100 and Q =100

C = 100 + 3 *100

= 100 + 300

C = 400

The new quantity of demand and supply in equilibrium becomes;

400-3Q = 100 + Q

400- 100 = Q + 3Q

300 = 4Q

Q = 300/4

Q = 75

For the for the supply,

P = 100 + Q

= 100 + 75

= 175 Quantity supply during the tax

for the demand,

P = 500-3Q

= 500-3*75

= 275 Quantity of demand during the tax

The following assumptions should be changed

1. Increase in tax rate: From the calculation above, the increase in tax rate brought about the increase in demand and decrease supply. That means the consumers which they intend to help with the tax are the ones still paying the tax.

2. The transfer of tax: The same tax raised by the consumer is being transfer from Philadelphia residents to the government. Which means nothing will be done to the childhood obesity epidemic.

For the consultant to be correct, the tax rate should not be raised since it's still the consumer that will suffer for it and the money cannot be used for the epidemic.

Answer 2

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.

Step-by-step explanation:

The demand function is:
`P=500-3Q`

The supply function is:
`P=100+Q`

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

`P_D=P_S\\\\500-3Q=100+Q\\\\4Q=400\\\\Q=100\\\\\\P=100+100=200`

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:

`P=100\\Q=100\\\\P=C-3Q\\\\100=C-3*100\\\\C=400\\\\\\P=400-3Q`

The new equilibrium is:

`400-3Q=100+Q\\\\4Q=300\\\\Q=75\\\\\\P_s=100+75=175\\\\P_d=500-3*75=500-225=275`

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.