Raymond B. answered • 03/16/20
Math, microeconomics or criminal justice
Total Cost divided by Quantity = TC/Q = AC = 5Q +10 +50/Q = Average Cost
Take the derivative and set = 0 to get Q at minimum average cost
5 -50/Q2 = 0
5Q2 = 50
Q2 = 10
Q = sqr10 = 3.16 = output at the minimum average cost
plug that into 5Q +10 + 50/Q = 5(3.16) + 10 + 50/3.16 = 15.8 + 10 + 15.82 = 41.62 = minimum AC
To find Marginal Cost take the derivative of the Total Cost function with respect to quantity
dTC/dQ = MC = 10Q + 10 = Marginal Cost
plug it in the AC minimizing Q=3.16
MC =10Q+10=10(3.16)+10 =41.6 = MC = minimum AC
The AC curve is U shaped, with its minimum point intersected by the upward sloping MC curve
But all this is just half the problem, as you need the Demand function, to find the profit maximizing output level.
Still, with perfect competition, economic profit will be driven down to zero, as new firms enter attracted by the economic profit, and price will be driven down to the average cost minimum point. The firm will view demand as a horizontal line intersecting the AC curve at its minimum point.
Marginal Revenue will equal Marginal Cost at the profit maximizing output level. With a flat horizontal demand curve, the MR curve is also horizontal and the same as the Demand curve. The market demand curve is not horizontal, but the individual firm's demand curve will be horizontal at the market price level
It helps to know calculus and how to take a derivative
