Question

2. Use the relative extrema to answer the following questions:

2.1.- If cf = 25000 is a fixed cost function, demonstrate that the average fixed cost function is decreasing for q> 0; therefore, when the production q grows by one unit, the unitary portion of the fixed cost is reduced.

2.2.- If c = 3q - 3q² + q^3. is a cost function, when is the marginal cost decreasing?

Answer 1

2.1) FC = 25000 so AFC = FC/q = 25000/q. dAFC/dq = -25000/q^2, q being a non negative number. Hence AFC is a decreasing function as dAFC/dq < 0. For every one unit of output increased, unitary portion of the fixed cost is reduced.

2.2. Marginal cost decreases before it reaches its minimum. Find dMC/dq. Here MC = dC/dq = 3 - 6q + 3q^2. Now dMC/dq = -6 + 6q

Hence the minimum value is determined where -6 + 6q = 0 or q = 1. Between q = 0 and 1, MC is decreasing.