Question

You have been hired by the mayor of Philadelphia to provide sage economic advice. The mayor would like to implement a tax on large fountain soda drinks of $0.80 per drink which the buyers will pay when purchasing the drink. At the moment, soda lovers currently consume 1 million fountain drinks per year in the city (i.e. equilibrium quantity). You are given some data on both the demand and supply curves. For every $0.10 increase in the price of the fountain drink, the quantity demanded falls by 60,000. For every $0.10 increase in the price of the fountain drink the quantity that suppliers are willing to sell rises by 20,000. The mayor tells you that the $0.80 will generate a revenue of $800,000 for the city and that the price of fountain drinks will rise by the amount of the tax ($0.80). As usual, the politicians (the mayor in this case) are incorrect. Explain why they are incorrect by doing the following. (The value of the equilibrium price is not given)

a) Explain why it is impossible that the new tax will increase the price the consumer pays by the full amount of the tax (hint: sketching a small supply and demand graph might be helpful)

b) Calculate what the new equilibrium quantity in the market for fountain drinks will be in Philadelphia after the tax is implemented.

c) Calculate the correct increase in the price of the fountain drink at the register for the buyer after the tax.

d) Calculate the correct amount of tax revenue that the city will collect.

Answer 1

Answer(a):

From the above diagram we can see that the Cost per Fountain Drink is measured along the X axes and the Demand for the drink has been measured along the Y axes. OC is the cost per bottle before the tax increase and OA is the demand. Once the tax increases, the cost per bottle increases from OC to OF and the demand for the drink falls from OA to OD. We can see that   The total number of Fountain Soda drink consumption per year = 1 million

After the increase of the per unit $0.80 tax of the Soda drink, the total revenue generated from the tax increase would be                                                  = 1,000,000 x $ 0.80

                                                                                   = $800,000

Now, with every $0.10 increase in the price of the drink, the demand falls by = 60,000

Therefore, with total of $0.80 increase in the price of the drink, the demand will fall by = 60,000 x 8              

                                                                                                                                                             = 480,000

Also, with every $0.10 increase in the price of the drink, the supply increases by = 20,000

Therefore, with total of $0.80 increase in the price of the drink, the supply will increase by = 20,000 x 8              

                                                                                                                                                             = 160,000

Since, the consumers demand is falling by 480,000 quantities, the extra units produced by producers will also remain unsold.

Hence, the total number of Soda drinks which will remain unsold is = 480,000 + 160,000

                                                                                                                         = 640,000

If we estimate the per unit cost of the bottles getting unsold, it will amount to a huge number, thus nullifying the profit to be expectedly earned by the Mayor. With the fall in the demand, the tax increase would therefore be revoked.

Hence, the tax payers would not require paying the complete amount of the tax.

Answer (b) : Since 640,000 bottles will go unsold in Philadelphia now, the new equilibrium unit will be :

                                       = 1,000,000 – 640,000

                                       = 360,000

Answer( c): The correct increase in the price of the fountain drink will be 360,000 x $0.80 = $288,000

Answer (d) : The correct amount of tax revenue that the city will collect will also be $288,000