Decreasing-Cost Industry
An industry who's long run production curves is negatively sloped is considered a "decreasing-cost industry". The drop in production prices usually is due to the fact that when the industry expands due to a demand increase, production becomes cheaper and thus supply increases as well. These shifts create a new P* and Q* (equilibrium price and quantity). It's important that the shift in supply be greater than the shift in demand, otherwise the industry would be considered an "increasing-cost industry".
The long run supply curve is sloping down, showing that this industry is a decreasing-cost industry
The long run supply curve is sloping down, showing that this industry is a decreasing-cost industry

It may seem counter-intuitive that when more firms enter an industry the production in that industry gets cheaper, but think about economies of scale. Let's say the industry we are talking about is car production. Steel is needed to make cars, but if only one firm is producing a small number of cars (that they could sell for high prices) the steel will be pretty difficult to produce because only a small amount is needed. As more firms start making cars the need for steel rises, steel making firms grow and experience economies of scale, causing the steel to be cheaper, which in turn shifts the car industries supply curve to the right because it becomes cheaper to produce cars.

True or False: If an industry's supply increases due to an increase in demand it must be a "decreasing-cost industry".

This site has a really good graphical representation of this concept.

The clothing industry is a decreasing-cost industry. As the industry has expanded, the size of the corporations has grown so large that they are able to set up and control sweat shops that they wouldn't have been able to set up had they been a small industry. This causes the price of production to drop, allowing for a shift in supply that is essential to decreasing cost industries.

AnswerDecreasing-Cost Industry
An industry who's long run production curves is negatively sloped is considered a "decreasing-cost industry". The drop in production prices usually is due to the fact that when the industry expands due to a demand increase, production becomes cheaper and thus supply increases as well. These shifts create a new P* and Q* (equilibrium price and quantity). It's important that the shift in supply be greater than the shift in demand, otherwise the industry would be considered an "increasing-cost industry".

Answer: False, while those are the conditions needed for a decreasing cost industry, the same conditions are needed for an increasing cost industry. The way to tell them apart is that a decreasing cost industry's supply shift will be more drastic than the demand shift while the opposite is true with increasing-cost industries.