# 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?

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

Hence the deadweight loss is \$1000

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