Can someone explain to me how the answer for 11 is 424,000-0.004Q? Where did the
ID: 1105923 • Letter: C
Question
Can someone explain to me how the answer for 11 is 424,000-0.004Q? Where did the -0.004Q come from when the equation gave me 424 - Q/500
Using time-series data, the demand function for the monopolist has been estimated as 9-142.000-500P+6M-400P where Os is the amount sold, P is price, Mis income, and P is the price of a related good. The estimated values for M and in 2012 are $25,000 and S200, respectively. The short-run marginal cost curve for this firm has been estimated as: M-200-00240 +0.00000602 Total fixed cost is forecast to be $500,000 in 2012. 11. What is the forecasted marginal revenue function for 2012? 12. What is the average cost function for 2012?Explanation / Answer
(11) First, we plug in the given numbers in the demand function.
Qd = 142,000 - 500P + (6 x 25,000) - (400 x 200)
Qd = 142,000 - 500P + 150,000 - 80,000
Qd = 212,000 - 500P
Therefore,
500P = 212,000 - Qd
P = (212,000 - Qd) / 500 = 424 - 0.002Qd [= 424 - (Qd / 500)]
Total revenue (TR) = P x Qd = (212,000Qd - Qd2) / 500 = 424Qd - 0.002Qd2
Marginal revenue (MR) = dTR / dQd = (212,000 - 2Qd) / 500 = 424 - (2Qd / 500) = 424 - (Qd / 250)
= 424Qd - 0.004Qd
Hope this clarifies your doubt. The expression (424,000 - 0.004Q) is incorrect.