Final answer:
The correct statement is that the long-run supply curve for a purely competitive increasing-cost industry will be upsloping. In an increasing-cost industry, as production expands, so do costs, necessitating higher prices for increased output.
Step-by-step explanation:
The question pertains to the long-run supply curve in different types of industries within perfectly competitive markets. Specifically, the question is about the correct characteristics of the long-run supply curve for increasing-cost and decreasing-cost industries. According to the given information, in an increasing-cost industry, the long-run supply curve (LRS) is upward sloping which indicates that as the industry's output expands, the costs of production also increase, leading to higher prices necessary to supply a greater amount of output. Conversely, the LRS for a decreasing-cost industry is downward sloping, reflecting lower costs of production over time as output expands, which allows for more output to be supplied at lower prices.
Given these details, the correct statement among the options provided is: a. the long-run supply curve for a purely competitive increasing-cost industry will be upsloping. This is consistent with the information outlined about how the LRS behaves in an increasing-cost industry.