The Commonwealth government decides to provide a subsidy of 30 for the buyers of bikes. Assume...

The Commonwealth government decides to provide a subsidy of 30 for the buyers of bikes. Assume that the market demand for bikes is given by: p = 300 – 2Q. Assume that the supply curve for bikes is given by p = 30 + Q. Which of the following statements is true?

a. Following the imposition of the subsidy the total price paid to sellers including the subsidy decreases by 10 and the deadweight loss that results from the subsidy is equal to 75.

b. Following the imposition of the subsidy the total price paid to sellers including the subsidy increases by 20 and the deadweight loss that results from the subsidy is equal to 0.

c. Following the imposition of the subsidy the total price paid to sellers including the subsidy increases by 10 and the deadweight loss that results from the subsidy is equal to 150.

d. Following the imposition of the subsidy the total price paid to sellers including the subsidy increases by 20 and the deadweight loss that results from the subsidy is equal to 150.

e. None of the above.

Expert Solution

c. Following the imposition of the subsidy the total price paid to sellers including the subsidy increases by 10 and the deadweight loss that results from the subsidy is equal to 150.

Before subsidy:
At equilibrium: Demand = Supply. So, we get,
300 - 2Q = 30 + Q
So, Q + 2Q = 300 - 30
So, 3Q = 270
So, Q = 270/3 = 90
Q = 90

p = 30 + Q = 30 + 90 = 120
So, p =120

After subsidy: price paid by buyers decrease by 30. So, demand function changes to:
p - 30 = 300 - 2Q
So, p = 300 - 2Q + 30
So, p = 330 - 2Q
Now, at equilibrium, new demand = supply. So, we get,
330 - 2Q = 30 + Q
So, 2Q + Q = 330 - 30
So, 3Q = 300
So, Q = 300/3
So, Qs = 100

Price received by seller, Ps = 30 + Qs = 30 + 100 = 130
Price paid by buyer, Pb = 300 - 2Qs = 300 - 2(100) = 300 - 200 = 100

Change in price received by sellers = Ps - P = 130 - 120 = 10

Deadweight loss = area of triangle = (1/2)*base*height = (1/2)*(Qs - Q)*(Ps-Pb) = (1/2)*(100-90)*(130-100) = (1/2)*10*30 = 150

Rahul Sunny answered 2 years ago

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