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Consider a private value auction where each bidder believes that valuations are uniformly distributed between $10 and $50. Michael knows his own valuation is $20.

Consider a private value auction where each bidder believes that valuations are uniformly distributed between $10 and $50. Michael knows his own valuation is $20. Determine Michael's optimal bid in:

a. a second-price sealed bid auction with 2 bidders.

b. a first-price sealed-bid auction with 2 bidders.

c. a Dutch auction with 2 bidders.

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