Final answer:
To calculate the resulting deadweight loss, determine the new equilibrium quantity and price after the price ceiling is imposed, compare the new consumer surplus and producer surplus with the original at the equilibrium price of $214. The resulting deadweight loss due to the price ceiling is 16359.2.
Step-by-step explanation:
To calculate the deadweight loss due to the imposition of a price ceiling, we need to understand how the market operates without any intervention. The market reaches its equilibrium where the supply equals the demand. First, we find the equilibrium quantity and price without the price ceiling.
Step 1: Finding Equilibrium Quantity and Price
Set the demand curve equal to the supply curve to find the equilibrium:
Demand curve: P = 1000 - 5Q
Supply curve: P = 5Q
Equating both:
1000 - 5Q = 5Q
1000 = 10Q
Q = 1000 / 10 Q = 100
This is the equilibrium quantity (Q).
Now to find the equilibrium price (P), we substitute Q into either the demand or the supply curve.
Using the supply curve: P = 5Q P = 5 * 100 P = 500
The equilibrium price (P) is 500.
Step 2: Finding Quantity Demanded and Quantity Supplied at the Price Ceiling
Now we impose a price ceiling of 214. A price ceiling means that the price cannot go above this level.
We need to determine the quantity demanded and supplied at this price.
For quantity demanded (Qd) at P = 214 using the demand curve:
1000 - 5Qd = 214
786 = 5Qd
Qd = 786 / 5
Qd = 157.2
For quantity supplied (Qs) at P = 214 using the supply curve:
5Qs = 214
Qs = 214 / 5
Qs = 42.8
At the price ceiling, the quantity demanded (Qd) is 157.2 and the quantity supplied (Qs) is 42.8.
Step 3: Calculating Deadweight Loss
The deadweight loss is created due to the difference between the quantity demanded and quantity supplied at the price ceiling level. This creates a shortfall in the market, which results in an inefficient outcome.
Using the concept of the area of a triangle to calculate the deadweight loss:
Area of the triangle = 0.5 * base * height
The base of the triangle is the difference between quantity demanded and quantity supplied at the price ceiling:
Base = |Qd - Qs|
Base = |157.2 - 42.8|
Base = 114.4
The height of the triangle is the difference between the equilibrium price and the price ceiling:
Height = Pe - Pc
Height = 500 - 214
Height = 286
Now, we calculate the deadweight loss:
Deadweight Loss = 0.5 * base * height
Deadweight Loss = 0.5 * 114.4 * 286
Deadweight Loss = 57.2 * 286
Deadweight Loss = 16359.2
The resulting deadweight loss due to the price ceiling is 16359.2.