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IO Economic Problem

Need help to solve the following problem:

Consider a monopolist that must choose both price (or quantity) and quality for its product. It faces a demand P = Z(θ − Q), where P is the price of the good, Z is an index of quality, θ > 0 is a parameter and Q is the quantity of output. Assume that the marginal cost of quantity is zero and that the cost of production of quality is D(Z) = αZ2
1) Compute the quantity, the quality and the price of output in equilibrium. Explain.
2) Does the monopolist produce too high or too low quality? Explain.
3) Demonstrate your answer to question 2) analytically. Explain.
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