You are one of five risk-neutral bidders participating in an independent private values auction. Each bidder perceives that all other bidders' valuations for the item are evenly distributed between $30,000 and $70,000. For each of the following auction types, determine your optimal bidding strategy if you value the item at $45,000.

a. First-price, sealed-bid auction.

• Bid $30,000.
• Bid $45,000.
• Bid $70,000.
• Bid $42,000.

b. Dutch auction.

• Let the auctioneer continue to lower the price until it reaches $70,000, and then yell "Mine!".
• Let the auctioneer continue to lower the price until it reaches $42,000, and then yell "Mine!".
• Let the auctioneer continue to lower the price until it reaches $45,000, and then yell "Mine!".
• Let the auctioneer continue to lower the price until it reaches $30,000, and then yell "Mine!".

c. Second-price, sealed-bid auction.

• Bid $42,000.
• Bid $45,000.
• Bid $30,000.
• Bid $70,000.

d. English auction.

• Remain active until the price exceeds $42,000, and then drop out.
• Remain active until the price exceeds $30,000, and then drop out.
• Remain active until the price exceeds $70,000, and then drop out.
• Remain active until the price exceeds $45,000, and then drop out.