Consider the demand curve for beer: Q= 120 –2P. If the supply curve for beer is P=12+Q and the government imposes a per-unit tax of $1 on producers of beer, the deadweight loss that results is equal to:[Round your answer to 2 decimal places when needed.]
Question
Consider the demand curve for beer: Q= 120 –2P. If the supply curve for beer is P=12+Q and the government imposes a per-unit tax of $1 on producers of beer, the deadweight loss that results is equal to:[Round your answer to 2 decimal places when needed.]
Solution
To find the deadweight loss, we first need to find the new equilibrium price and quantity after the tax is imposed.
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Adjust the supply curve for the tax. The new supply curve is P = 12 + Q + 1 (the tax). Simplify this to P = 13 + Q.
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Set the demand curve equal to the new supply curve to find the new equilibrium quantity: 120 - 2P = 13 + Q Simplify this to Q = 107 - 2P
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Set this equal to the original demand curve to find the new equilibrium price: 107 - 2P = 120 - 2P Solving for P, we find that P = 6.5
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Substitute P = 6.5 into either the demand or supply equation to find the new equilibrium quantity. Using the demand equation, we find that Q = 120 - 2(6.5) = 107
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The deadweight loss is the area of the triangle formed by the original supply curve, the new supply curve, and the demand curve at the new equilibrium quantity. The base of the triangle is the difference in quantity (120 - 107 = 13) and the height is the tax ($1).
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The formula for the area of a triangle is 1/2 * base * height, so the deadweight loss is 1/2 * 13 * 1 = $6.5
So, the deadweight loss from the tax is $6.5.
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