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# A perfectly competitive market exists for wheat. The

A perfectly competitive market exists for wheat. The inverse demand is P = 100?Q where P is the price of wheat and Q is the total quantity of wheat. The private total cost for the unregulated market to produce a quantity of Q is 50+80Q +0.5Q 2 . The production of wheat creates some pollution where the total externality cost is EC = Q 2 .

Task 1: Solve for the free market competitive equilibrium of wheat.

Task 2: Solve for the socially optimal level of wheat. Illustrate it in the graph.

Task 3: Derive the Pigouvian tax (per unit of output of wheat) that results in the social optimum.

Task 4: One big company, WheatsRUs, buys out all the farmers of wheat and becomes a monopolist. Using the same demand and cost information, solve for the quantity and price under the unregulated monopolist.

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