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Nonlinear Price Discrimination : Consider a monopolist that faces an inverse demand curve given by P(Q) = 450 3Q and has a cost function given

Nonlinear Price Discrimination: Consider a monopolist that faces an inverse demand curve given by

P(Q) = 450 3Q and has a cost function given by C(Q) = 2Q2 + 5Q.

Uniform Pricing Model

Suppose the monopolist is unable to price discriminate and must charge the same price to all consumers.

Part 1

What is the Profit-maximizing quantity: ? (Round to two decimal places and use the rounded value in Part 2 below.)

Part 2 - Calculate the producer surplus of this market under the uniform pricing model.

What is the Producer surplus: ? (Round answer to two decimal places.)

Nonuniform Pricing Model

Suppose the monopolist can engage in second degree price discrimination by using two blocks in a declining-block pricing scheme. It charges a high price, P1, on the first Q1 units (the first block) and a lower price, P2, on the next Q2 - Q1 units(the secondblock).

Part 3Calculate the profit-maximizing values for Q1

What is the quantity sold in the first block (Q1) ? (Round your answer to two decimal places and use the rounded value in part 4 and 5).

Part 4 Calculate the profit-maximizing values for Q2.

What is the total quantity sold(Q2) ? (Round your answer to two decimal places.)

Part 5 Calculate the producer surplus of this market under the non-uniform pricing model.

What is the producer surplus ? (Round your answer to two decimal places.)

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