Question

Assume A Firm Operating Under a short run production period with a total cost function given as TC=200+5Q+2Q^2.Then What Must be the out put size to minimize average cost of production and show if cost of production is increasing or decreasing at this point.

Answer 1

The output size to minimize average cost of production is Q = 10.

The average cost of production is AC = (200 + 5Q + 2Q^2)/Q = 20 + 5 + 2Q.

At Q = 10, AC = 20 + 5 + 20 = 45.

The cost of production is decreasing at this point, since the derivative of AC with respect to Q is dAC/dQ = 2Q - 5, which is negative at Q = 10.