In a purely competitive industry:

a. there will be no economic profits in either the short run or the long run.
b. economic profits may persist in the long run if consumer demand is strong and stable.
c. there may be economic profits in the short run, but not in the long run.
d. there may be economic profits in the long run, but not in the short run.

C. There may be economic profits in the short run, but not in the long run.

Explanation:

Perfect Competition is a market structure with very large no of buyers & sellers, transacting homogeneous products, at same price (firms 'price taker') & inelastic demand, with free entry & exit into industry.

Economic profit is the profit earned above normal profit - covering revenues over explicit & implicit costs, necessary to continue business operations.

Free entry & exit into Perfect Competition Industry makes them earn only normal profits - no super normal (economic) profit , abnormal loss in long run

Short Run Economic Profits : Induces new firms entry and supply increases, reducing the industry & firms' price. This reduces their profit & resumes back the normal profits.

Similarly - Short Run Abnormal Losses : Induce existing firms exit,  will reduce supply, increase price & profit, resume back to normal profits.

a.

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