Question

The firm's long-run total cost is given by LTC = 5,000Q - 100Q^2 + Q^3 and its long-run marginal cost is given by LMC = 5,000 - 200Q + 3Q^2. At what output level does the firm experience diseconomies of scale?

I don't understand how it goes from this " 5000 - 100Q + Q² " to this equation "-100 + 2Q = 0"

Answer 1

LTC = LATC 5000 d - lood²+ a3 LTC o - 5000 0-100 0²7 83 LATC - Sooo - loo 0 + 0²

The long run average total cost, LATC es minimum when LATC = LMC. LMC= 5000 - 2000+ 302 So, LATC= Lmc 50oo-lood to2 = 5000- 2000 + 3 0 5000 - 100 ot. d² - Sooot doo 0-30² = 0 cos looo - 202 = 0 d (100 - 20) = 0 10o-20=0 20 a los To=50 At Q = 50 units, LATC is minimum. for a 50 units, LATL is increasing 6 at output level, d> 50 units, the from experiences diseconomies of scale.