Question

A perfectly competitive firm's average fixed cost function is AFC = 30/Q, its average variable cost function is AVC = 6 + 0.1Q, and its marginal cost function is MC = 6 + 0.2Q. The firm optimizes by producing the level of output that maximizes profit or minimizes loss. If the market price of the good is P = $4, then the firm will:

Answer 1

The perfectly competitive firm will optimize its profit or minimize its loss by producing the level of output where the price or marginal revenue (MR) is equal to marginal cost (MC). In this case, the market price (P) is given as $4.

The perfectly competitive firm will optimize its profit or minimize its loss by producing the level of output where the price or marginal revenue (MR) is equal to marginal cost (MC). In this case, the market price (P) is given as $4. From the given information, we can calculate the quantity of output at which MR equals MC:

1. First, calculate the derivative of the average variable cost (AVC) function to find marginal cost (MC):
   
   MC = d(AVC)/dQ = 0.1
2. Set MC equal to 0.2Q + 6 and solve for Q:
   
   0.1Q = 0.2Q + 6
   
   0.1Q - 0.2Q = 6
   
   -0.1Q = 6
   
   Q = -6/0.1
   
   Q = -60
3. Since the quantity of output cannot be negative, we disregard the negative value and set Q = 60.

So, the firm will produce 60 units of output to optimize its profit or minimize its loss.