Question

8. Suppose that a market is described by the following 

supply and demand equations:

Q^s=1 / 2 p

Q⁰=300-P

a. Solve for the equilibrium price and the equilibrium quantity.

b. Suppose that a tax of $ 30 is placed on buyers. Solve for the new equilibrium. What happens to the price received by sellers, the price paid by buyers, and the quantity sold?

c. The deadweight loss of a tax is the area of the triangle between the supply and demand curves. Solve for deadweight loss. (Recalling that the area of a triangle is 1 / 2 × base x height)

Answer 1

At equilibrium the quantity supplied is equal to quantity demanded. Equate quantity demanded to quantity supplied

QD=Qs

→300 – P= -2

P+P = 300

من انا =P = 300

X 300 نا | نت P ج

P= $ 200 per unit

Equilibrium price = $ 200 per unit

Equilibrium Quantity, Q = 100 units ( = 300 - P)

B. When a tax of $ 30 per unit is placed on the buyers the price paid by is $ 30 higher than the price sellers get. Since tax is imposed on buyer therefore the demand curve will shift to its left. There will be no impact on the sellers as all the tax has to be borne by the buyers.

Price received by sellers = Price paid by buyers - 30

→300 – (P + 30) = -1

​​​​​​

270 = P +-P

P = 270

SP= 270 x .

P= $ 180 per unit

Price paid by buyer = $ 210

Price recieved by seller = $ 180

Quantity = 90 units

Here the supply curve is not perfectly plastic therefore the supplier will be forces to bear the tax. If it might have been perfectly elastic then all the tax might have been borne by the customers.

C. Dead weight loss = (1/2)×(210-180)×(100 -90) = $ 150

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