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Problem on deadweight loss

Assume that the domestic demand for television sets is explained by Q = 40,000 − 180P and that the supply is provided by Q = 20P. When televisions can be freely imported at a price of $160, then how many televisions would be generated in the domestic market? By how much domestic producer excess and deadweight losses modify when the government establishes a $20 tariff per television set? What when the tariff was $70?

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Whenever televisions can be freely imported at a price of PW = $160, the domestic producers will generate 20(160) = 3200 television sets. The Domestic demand is 40,000 – 180*160 = 11,200 units.

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Whenever the import duty of $20 is mentioned, the efficient price of importing televisions is $180. At such price, domestic firms will supply 20(180) = 3600 televisions, and demand will be 40,000 – 180(180) = 7600. The domestic producer surplus will raise by region C = (180 – 160)(3200) + 0.5(180 – 160)(3600 – 3200) = 68,000. The tariff makes a deadweight equivalent to region F + K = 0.5(180 – 160)(3600 – 3200) + 0.5(180 – 160)(11,200 – 7600) = 40,000.

The import duty of $70 increases the efficient import price to $230. You can observe from the graph that this is above the equilibrium price of $200 which would prevail in the domestic market devoid of any foreign trade.  Therefore, imposing such a big import duty is equivalent to banning trade in this industry together. The latest price will be $200 and the quantity demanded 4000. Associative to the free trade equilibrium, producer excess would now raise by area B + C = 0.5(200)(4000) – 0.5(160)(3200) = 144,000. The $70 import tariff makes a deadweight loss equivalent to region F + G + J + K = 0.5(200 – 160)(11,200 – 3200) = 160,000.

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