Kate's Great Crete (KGC)is a local monopolist of ready-mix concrete.Its annual demand function is Q = 20,000 - 400P,where P is the price,in dollars,of a cubic yard of concrete and Q is the number of cubic yards sold per year.What is the difference between price and marginal revenue when KGC sells 5,000 cubic years of concrete per year?

Question

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The correct answer is A.The marginal revenue is the change in total revenue divided by the change in quantity. The total revenue is equal to price times quantity, so the marginal revenue is equal to the derivative of total revenue with respect to quantity. The total revenue is:TR = P * Q = (20,000 - 400P) * QThe marginal revenue is:MR = dTR/dQ = 20,000 - 800PWhen KGC sells 5,000 cubic yards of concrete per year, the price is:P = (20,000 - 400Q)/Q = (20,000 - 400 * 5,000)/5,000 = $100The marginal revenue is:MR = 20,000 - 800P = 20,000 - 800 * $100 = $87.50The difference between price and marginal revenue is:P - MR = $100 - $87.50 = $12.50

Kate's Great Crete (KGC)is a Local Monopolist of Ready-Mix Concrete