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1. Total revenue is defined as T R(Q) = Q × P (Q). Marginal revenue is the R(Q) derivative of total revenue, M R(Q) = dTdQ . a. Show that marginal revenue is always less than or equal to demand. b. Show that when a demand curve is a line, then the slope of the marginal revenue curve is two times the slope of the demand curve. 2. Show that the area between marginal revenue and marginal cost curves (from zero to the output level) equals variable profits, where variable profits are defined as profits plus fixed costs. 1