The inverse Demand curve for a normal good X is given by: Px = 90 - 3Q 15 points

Question

The inverse Demand curve for a normal good X is given by: Px = 90 - 3Q 15 points A. calculate point price elasticity of demand at P = $30 B. What is the total revenue (TR) function? C. What is the marginal revenue (MR) function? D. At what price TR is maximized and what is TR at that point? Explain your answer.

Explanation / Answer

a) price elasticity of demand = rate of change of price of X with respect to Quantity Q demand =>price elasticity of demand at P = $30 => = dP*Q /dQ* P P= 90- 3Q = 30 => Q= 20 = -3 * 20 / 30 = -2 b) Total revenue = Px * Q = price of x * Quantity Q demanded = Px * Q = (90-3Q)Q = 90 Q - 30 Q^2 c) marginal revenue (MR) function = rate of change in revenue wih respect to Q MR = d(TR) / dQ = 90 -60 Q d) maximized when d(TR) =0 hence 90-60 Q= 0 Q= 1.5 Px = 90- 3 *1.5

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