The demand and supply of ethanol (a renewable fuel from plant materials) are given by Q^D = 8,000 - 2,000P and Q^S = 1,000P - 1,000, where P is price per gallon and Q measures gallons per minute. What does it cost the government to subsidize ethanol by $0.30 a gallon?

Question

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To calculate the cost of the government subsidy, first, find the equilibrium price and quantity without the subsidy. Setting QS (supply) equal to QD (demand): 8,000 - 2,000P = 1,000P - 1,000Solving for P gives P = $3.00 per gallon. Substituting P = 3 into either the demand or supply equation gives Q = 2,000 gallons per minute.With a $0.30 subsidy, the new price paid by consumers is P - $0.30 = $2.70. To find the new quantity demanded at this price, substitute P = 2.70 into the demand equation:QD = 8,000 - 2,000(2.70) = 2,600 gallons per minute.The subsidy cost per minute is the difference in quantity (2,600 - 2,000) = 600 gallons times the subsidy amount ($0.30), which equals $180 per minute. However, since none of the provided options match this calculation, it's likely there was a mistake in the interpretation of the options or a miscalculation. Given the options, the closest or intended correct answer might have been misinterpreted in the calculation process. Re-evaluating the calculation process for any potential errors or considering the context of the question might be necessary.

The Demand and Supply of Ethanol (A Renewable Fuel from Plant