Consider a market with a demand curve of P = 16–2q and a supply curve of P = 2q. If the government levies a tax on consumers of $4 per unit, what is the resulting DWL? [Round your answer to two decimal places when needed]
Question
Consider a market with a demand curve of P = 16–2q and a supply curve of P = 2q. If the government levies a tax on consumers of $4 per unit, what is the resulting DWL? [Round your answer to two decimal places when needed]
Solution
To find the Deadweight Loss (DWL) due to the tax, we first need to find the quantity demanded and supplied before and after the tax.
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Set the demand and supply curves equal to each other to find the equilibrium price and quantity without the tax:
16 - 2q = 2q 4q = 16 q = 4
So, the equilibrium quantity (q) is 4 units and the equilibrium price (P) is 2*4 = $8.
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Now, let's consider the tax. The tax shifts the demand curve down by the amount of the tax. So, the new demand curve is P = 16 - 2q - 4 = 12 - 2q.
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Set the new demand curve equal to the supply curve to find the new equilibrium:
12 - 2q = 2q 4q = 12 q = 3
So, the new equilibrium quantity (q) is 3 units and the new equilibrium price (P) is 2*3 = $6.
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The DWL is the area of the triangle formed by the original and new quantity and the amount of the tax. The base of the triangle is the difference in quantity (4 - 3 = 1 unit) and the height is the amount of the tax ($4).
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So, the DWL = 0.5 * base * height = 0.5 * 1 * 4 = $2.
Therefore, the Deadweight Loss due to the tax is $2.
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