Show that 
is bounded. Show all your work.
Definitions:
Marginal Revenue
The additional income received from selling one more unit of a good or service, crucial for decision-making in output levels.
Marginal Cost
The price of creating one more unit of a product or service.
Purely Competitive Market
A market structure with many buyers and sellers, where all firms sell identical products and no single buyer or seller can influence the market price.
Economic Profit
The discrepancy between a firm's gross income and its total expenses, factoring in both clear and unclear costs.
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