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Suppose demand curve is given by P=1000-5Q and the supply curve is given by P=5Q. If the government imposes a price ceiling of 214 , calculate the resulting deadweight loss.

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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.

User Asher Stern
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