Consider a monopolist facing the demand function: $=$

and a cost function: $()=+.$

Profit Maximization under Monopoly: Solve for the profit$-$maximizing price, quantity, and profit for the monopolist.$$

Welfare Analysis under Monopoly: Calculate the consumer surplus, producer surplus, and total surplus at the monopoly equilibrium.$$

Perfect Competition Outcomes: Assume the same demand and cost structure in a perfectly competitive market.$$

Determine the equilibrium price, quantity,$$