The mathematical notation for the following economic conditions are:
Shut-down point: AVC > P
Economic loss but continue to produce: AVC < P < ATC
Profit maximizing-loss minimizing: MC = MR < ATC
The shut-down point occurs when the price is less than the average variable cost (AVC), which means that the firm is better off shutting down production in the short run. The economic loss but continue to produce occurs when the price is between the average variable cost (AVC) and the average total cost (ATC), which means that the firm is making losses but still producing in the short run. The profit maximizing-loss minimizing condition occurs when the marginal cost (MC) is equal to the marginal revenue (MR) and both are less than the average total cost (ATC), which means that the firm is maximizing profits while minimizing losses.
In summary, the mathematical notation for the economic conditions of shut-down point, economic loss but continue to produce, and profit maximizing-loss minimizing are important concepts in microeconomics that help firms make decisions about production and pricing in the short run.