Question

Consider a competitive market for a good where the demand curve is determined by:

the demand function: P = 5+-1*Qd and the supply curve is determined by the supply function: P = 0.5*Qs.

Where P stands for Price, QD is quantity demanded and QS is quantity supplied.

What is the quantity demanded of the good when the price level is P = $4? Additionally assume a market intervention of the form of per unit $2 tax on the consumption of the good.

How many units of the good are sold in the market at equilibrium considering this market intervention?

How much are consumers going to pay per unit of the good under this market intervention?

How much is the per unit amount that producers will receive as payment under this market intervention?

How much are the tax revenues under this market intervention?

How much is the Dead Weight Loss under this market intervention?

Answer 1

At P=4 quantity demanded , 4=5-Qd this gives Qd=1

Under intervention with $2 per unit of consumption tax demand function will change to (P+2)=5-Qd or Qd=3-P now under Equilibrium Qd=Qs this gives 3-P=2P gives P=$1 and Qd=Qs=2

Consumer is going to pay P+2=1+2=$3

Producer will recieve P=$1

Tax revenue=$2*Q=2*2=$4

Deadweight loss

=1/2*(Tax)*( change in quantity)

Under equilibrium without intervention 5-P=2P gives P=5/3 and Q=2*5/3=10/3 assuming we can break down the unit

Deadweight loss=1/2*2*(10/3-2)=4/3