In: Economics
The market for orange juice in North Dakota has a demand function of Q = 120 – 0.4P and a supply function of Q = 0.4P – 20. Imagine the government sets the price to $125. What is the dead weight loss?
Equilibrium is achieved where demand and supply both are equal
So the first step is to find equilibrium price and quantity and show on a graph
Demand
Q = 120 - 0.4P
Supply
Q = 0.4P – 20
Equating both demand and supply
120 - 0.4P = 0.4P – 20
0.8P = 140
P = 175
To find the equilibrium quantity we will use this price in any of the above two equations.
Q = 0.4P - 20
Q = 0.4(175) - 20
Q = 70 - 20
Q = 50
So the equilibrium price is $175 but the government has now set the price at $125 hence the graph will look like this
The blue region is the deadweight loss due to the new price by the government.
At $125, quantity supply is
Q = 0.4P – 20
Q = 0.4(125) – 20
Q = 50 - 20
Q = 30
At 30 units, demand is
Q = 120 - 0.4P
30 = 120 - 0.4P
P = 225
The deadweight will be equal to the area of the blue triangle
Deadweight Loss = Area of blue triangle
Deadweight Loss = 1/2 x base x height
Deadweight Loss = 1/2 x 100 x 20
Deadweight Loss = 1000
Hence the deadweight loss is $1000