Consider a market where supply and demand are given by QXS = -14 + PX and QXd = 85 - 2PX. Suppose the government imposes a price floor of $38, and agrees to purchase any and all units consumers do not buy at the floor price of $38 per unit.
a. Determine the cost to the government of buying firms’ unsold units.
b. Compute the lost social welfare (deadweight loss) that stems from the $38 price floor.
To determine the cost to the government of buying firms' unsold units, we first need to find the quantity demanded and supplied at the price floor of $38.
Given that the demand function is: QXd = 85 - 2PX, we can calculate the quantity demanded at a price of $38:
QXd = 85 - 2(38)
QXd = 85 - 76
QXd = 9
So at the price floor of $38, the quantity demanded is 9 units.
Next, we need to find the quantity supplied at the price floor. The supply function is given by: QXS = -14 + PX. By substituting the price of $38 into the equation, we can calculate the quantity supplied:
QXS = -14 + 38
QXS = 24
Therefore, at the price floor of $38, the quantity supplied is 24 units.
Since the government agrees to purchase any and all units consumers do not buy at the price floor, the government will have to buy the difference between the quantity supplied and the quantity demanded:
Units bought by the government = Quantity supplied - Quantity demanded
Units bought by the government = 24 - 9
Units bought by the government = 15
So the cost to the government of buying firms' unsold units is 15 units multiplied by the price floor of $38:
Cost to the government = Units bought by the government * Price floor
Cost to the government = 15 * $38
Cost to the government = $570
Now, moving on to calculating the lost social welfare or deadweight loss caused by the price floor. Deadweight loss occurs when the quantity traded is less than the efficient quantity in a market.
To find the lost social welfare, we need to calculate the difference between the quantity traded under the price floor and the efficient quantity.
The efficient quantity is the quantity where the demand and supply curves intersect. To find it, we set the quantity demanded equal to the quantity supplied:
QXd = QXS
85 - 2PX = -14 + PX
Simplifying the equation, we get:
3PX = 99
PX = 33
So the efficient price is $33. Substituting this into either the supply or demand function, we get the efficient quantity:
QXd = 85 - 2(33)
QXd = 85 - 66
QXd = 19
The quantity traded under the price floor is the quantity demanded at the price floor (9 units). Hence, the deadweight loss is:
Deadweight loss = Efficient quantity - Quantity traded under the price floor
Deadweight loss = 19 - 9
Deadweight loss = 10
Therefore, the lost social welfare (deadweight loss) that stems from the $38 price floor is 10 units.