Question

In East Toodaloo City, the government has decided to collect a tax of $3 per ride from ride-sharing services to reduce traffic congestion and fund mass transit. To keep it simple, assume the market is competitive and all the rides are the same price. Suppose the supply of rides per week is given by QS = 2000p – 6000 and the demand is QD = 42,000 – 4000p. Analyze the effect of the tax by comparing the equilibrium price and quantity without and with the tax in place. Who pays how much of the tax? By how much does the number of rides change? How much revenue does the city collect? How would your answer change if the tax were collected from the riders?

Answer 1

QS = 2000p – 6000

QD = 42,000 – 4000p

Before tax:

At equilibrium point; QD = QS = Q

=> 2000p - 6000 = 42000 - 4000p

=> 2000p + 4000p = 42000 + 6000

=> 6000p = 48000

=> p = (48000 / 6000)

=> p = 8

Equilibrium price (before tax) = 8

and

QD = QS = Q

=>Q = 2000p - 6000

=> Q = 2000(8) - 6000

=> Q = 10,000

Equilibrium quantity (before tax) is 10,000 rides.

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In East Toodaloo City, the government has decided to collect a tax of $3 per ride from ride-sharing services to reduce traffic congestion and fund mass transit.

It will decrease the price received by ride sharing services provider(or seller) by $3 per ride.

New supply after tax: Qs* = 2000(p-3) - 6000

=> Qs* = 2000p - 6000 - 6000

=> Qs* =2000p - 12000

Equilibrium quantity after tax occurs at the intersection point of demand and new supply curve.

=> Qs* = QD = Q

=> 42000 - 4000p = 2000p - 12000

=> 42000 + 12000 = 2000p + 4000p

=> 54000 = 6000p

=> p = (54000 / 6000)

=> p = 9

=>Pconsumer = 9

The price paid by consumer after tax is $9 per ride,

And

QS* = QD = Q

=> Q = 2000p - 12000

=> Q = 2000(9) - 12000

=> Q* = 6000

Equilibrium quantity of rides (after tax) is 6000 rides.

Put Q = 6000 in original supply function to get the price received by rider service provider (seller) after tax.

Q = 2000p - 6000

=> 6000 = 2000p - 6000

=> 2000p = 6000 + 6000

=> 2000p = 12000

=> p = (12000 / 2000)

=> p = 6

=> Pseller = 6

The ride service provider will get a price of $6 per ride after tax.

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Event	Quantity	Price paid by consumer	Price received by seller (service provider)
Before tax	10,000	8	8
After tax	6000	9	6

Check: Tax rate = Price paid by consumer after tax - Price recieved by seller after tax

=> Tax rate = 9 - 6 =3

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Burden of tax on consumer = Price paid by consumer after tax - Price paid by consumer before tax

=> Burden of tax on consumer = 9 - 8

=> Burden of tax on consumer = 1

Consumer is paying $1 out of $3 of tax per ride.

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Burden of tax on seller (service provider) = Price recieved by seller before tax - Price recieved by seller after tax

=> Burden of tax on seller (service provider) = 8 - 6

=> Brurden of tax on seller (service provider) = 2

Seller (service provider) is paying $2 out of $3 of tax per ride.

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Quantity of rides decrease by 4000 (i.e., from 10,000 to 6,000) due to tax

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Government revenue = Tax * Quantity after tax

=> Government revenue = $3 * 6000

=> Government revenue = $18,000

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Answer would not change if the tax were collected from the riders. Because the the how much burden of tax will fall on consumer and buyer depends on the price elasticity of demand and supply. It doesn't matter from which tha tax is collected.