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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.