The market for orange juice in
The market for orange juice in North Dakota has a demandfunction 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 deadweight loss?
Answer:
Equilibrium is achieved where demand and supply both areequal
So the first step is to find equilibrium price and quantity andshow 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 anyof 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 setthe price at $125 hence the graph will look like this
The blue region is the deadweight loss due to the new price bythe 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 bluetriangle
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
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