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The market for orange juice in North Dakota has a demand function of Q = 120...

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?

Solutions

Expert Solution

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

Rahul Sunny answered 1 year ago

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