Question

5) The demand for the Tesla electric automobile is P = 200,000 – 2.1 Q, where P is in $/car and Q is the number of cars sold per year. The supply of the Tesla in question 3 is P = 20,000 + Q, P is in $/car and Q is the number of cars produced per year. What is Total Surplus in the Tesla market, to the nearest million dollars?

6) The demand for the Tesla electric automobile is P = 200,000 – 2.1 Q, where P is in $/car and Q is the number of cars sold per year. The supply of the Tesla in question 3 is P = 20,000 + Q, P is in $/car and Q is the number of cars produced per year. To promote cleaner transportation, the U.S. government offers an incentive to buyers of electric vehicles, in the form of a $5,000 subsidy per car purchased. What is the actual price received by Tesla, to the nearest dollar?

Answer 1

5. Demand :P= 200000- 2.1 Q

When Q=0 , P=200000

Supply: P=20000+ Q

When Q=0 , P=20000

At equilibrium : Demand = Supply

200000- 2.1Q = 20000+ Q

Q= 58064.5 (Equilibrium quantity)

P= 20000+(58064.5) = 78064.5 (Equilibrium price)

CS = (0.5)(200000-78064.5)(58064.5) = (0.5)(121935.5)(58064.5) =$3540061919.87 = $ 3540.06 millions

PS = (0.5)(78064.5-20000)(58064.5)= (0.5)(58064.5)(58064.5)= $ 1685743080.12= $ 1685.74 millions

TS = $(3540.06 + 1685.74) million = $ 5225.8 million

6. Subsidy = $5000

Demand equation : P= (200000-P)/2.1

After subsidy : Supply equation=(P+5000- 20000) = P-15000

Now, equate demand and supply equation, we get :

(200000-P)/2.1= P-15000

P= $ 74677.4 (Price buyers pay after subsidy)

P= 74677.4 +5000 = $ 79677.4 (Price sellers receive after subsidy)