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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 $11 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 $11 on producers of beer, the deadweight loss that results is equal to:

[Round your answer to 2 decimal places when needed.]

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Solution

To find the deadweight loss, we first need to find the new equilibrium price and quantity after the tax is imposed.

  1. Adjust the supply curve for the tax. The new supply curve is P = 12 + Q + 11 (the tax). Simplify this to P = Q + 23.

  2. Set the demand curve equal to the new supply curve to find the new equilibrium quantity.

    120 - 2P = Q + 23 Simplify this to 97 = 3P So, P = 32.33 (rounded to 2 decimal places)

  3. Substitute P = 32.33 into the demand curve to find the new equilibrium quantity.

    Q = 120 - 2(32.33) = 55.34 (rounded to 2 decimal places)

  4. Find the old equilibrium without the tax. Set the original supply curve equal to the demand curve.

    120 - 2P = 12 + Q Simplify this to 108 = 3P So, P = 36

    Substitute P = 36 into the demand curve to find the old equilibrium quantity.

    Q = 120 - 2(36) = 48

  5. The deadweight loss is the area of the triangle formed by the old and new supply and demand curves. It's calculated as 0.5 * base * height.

    The base is the difference in quantities (55.34 - 48) = 7.34 The height is the difference in prices (36 - 32.33) = 3.67

    So, the deadweight loss is 0.5 * 7.34 * 3.67 = 13.46 (rounded to 2 decimal places).

This problem has been solved

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