Question

The demand for the Tesla electric automobile is P = 200,000 – 2 Q, where P is in $/car and Q is the number of cars sold per year. Currently, the U.S. government offers incentives to buyers of electric vehicles worth $5000. If the current selling price of the Tesla is $75,000, what is consumer surplus when the subsidy is available? What will be the change in consumer surplus after the incentive has expired?

Answer 1

Given that,

P = 200,000 – 2 Q

Q = number of cars sold per year

P is in $/car

Selling price = $ 75,000

Subsidy = $ 5,000

Equating the demand curve to the price,

200,000 - 2Q = 75,000

2Q = 200,000 - 75,000

2Q = 125,000

Q = 62,500

Without subsidy,

Price = $ 75,000

Quantity demanded = 62,500.

When a subsidy of $ 5,000 is paid then the price paid by buyers will be equal to $ 70,000.

200,000 - 2Q = 70,000

2Q = 130,000

Q* = 65,000

Consumer surplus (without subsidy)
`=(1)/(2) *(200,000-75,000)*62,500`

= 0.5 × 125,000 × 62,500

= $ 3,906,250,000

Consumer surplus(with subsidy) = 0.5 × (200,000 - 70,000) × 65,000

= $ 4,225,000,000

Change in consumer surplus = Consumer surplus(with subsidy) - Consumer surplus (without subsidy)

= 4,225,000,000 - 3,906,250,000

= - $ 318,750,000