Compute the lost social welfare, Macroeconomics

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Consider a market where supply and demand are given by QXS = -18 + PX and QXd = 90 - 2PX. Suppose the government imposes a price floor of $41, and agrees to purchase any and all units consumers do not buy at the floor price of $41 per unit.

a. Determine the cost to the government of buying firms' unsold units.

b. Compute the lost social welfare (deadweight loss) that stems from the $41 price floor.

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