Question

Suppose a competitive firm has as its total cost function: TC=26+3q2 T C = 26 + 3 q 2 Suppose the firm's output can be sold (in integer units) at $61 per unit. Using calculus and formulas (don't just build a table in a spreadsheet as in the previous lesson), how many integer units should the firm produce to maximize profit? Please specify your answer as an integer. In the case of equal profit from rounding up and down for a non-integer initial solution quantity, proceed with the higher quantity.

Answer 1

A profit maximizing perfectly competitive firm produces at the point where market price = MC.

Given that, Price = $61

TC = 26 + 3q²

Or, MC = d(TC)/dq = 0 + 6q = 6q

Therefore setting price = MC we get,

6q = 61

Or, q = (61/6) = 10.16667

Answer: 10 units