Given the demand function Q_X = 5,000 - 250P_X +120P_Y +.04I where
P_Y= $50.00 and I = $60,000, what is the marginal revenue equation?

Question

Given the demand function Q_X = 5,000 - 250P_X +120P_Y +.04I where P_Y= $50.00 and I = $60,000, what is the marginal revenue equation?

Quizplus · Accepted Answer

The formula for marginal revenue is MR = dTR/dQ where TR is total revenue and Q is quantity. Total revenue can be calculated as TR = P*Q where P is price and Q is quantity. To find MR, we need to take the derivative of TR with respect to Q: dTR/dQ = d(P*Q)/dQ dTR/dQ = P + Q*dP/dQ (by using the product rule) We can rewrite dP/dQ as (dP/d_X)*(d_X/dQ) + (dP/dI)*(dI/dQ) + (dP/d_Y)*(d_Y/dQ) (by using the chain rule) Since the values for dP/d_Y and dI/dQ are zero (since they are held constant), we can simplify the equation to: dP/dQ = (dP/d_X)*(d_X/dQ) To find dP/d_X, we take the derivative of the demand function with respect to _X: dQ/d_X = - 250 dQ/d_Y = 120 dQ/dI = .04 Therefore, we can simplify the equation to: dP/dQ = (-250)*(-1) + 120*50*.01 + .04*0 = 13 Substituting this value into the equation for MR, we get: MR = P + Q*dP/dQ MR = 53.6 - .008Q_X Therefore, the answer is D.

Given the Demand Function QX = 5,000 - 250PX +120PY

Given the Demand Function Q_X = 5,000 - 250P_X +120P_Y