An auction website is listing a vintage handbag.No bidder could inspect the bag in person prior to submitting a bid.Instead, bidders only know the probability of getting a real vs. the probability of getting a fake:

Probability(real) = 50%

Probability(fake) = 50%

The auction will be a sealed bidsecond priceauction (Vickrey auction).Bidders know about the 50/50 probabilities of getting a real or fake handbag.Bidders do not know about the preferences of any of the other bidders when they make their own bids.

A.Liz likes the handbag.If real it would be worth $300 to her.If fake it only would be worth $100 to her.Her utility function is risk averse and is: U(Product received) = Square root of $ value of product received

B. Betty really likes the handbag.If real it would be worth $500 to her.If a fake would be worth $150 value.Her utility function is risk averse and is:U(Product Received) = ln($ value of product received)

C. Mary also would like this handbag, but as much as the others.If real it is worth $250 to her.If a fake, it only would be worth $50 to her.Her utility function is risk neutral:U(Product received) = $ value of the product.

Answer questions 1-3):

1.What will be each of the three separate bids from each of the three bidders (Liz, Betty and Mary), for this sealed bid second price auction?Show your work to show how you reached each bid.Identify each bidder's certainty equivalent.

2. Which one of these three people places the highest bid, thus winning the auction?Note that these three people do not know about each other.How much does the auction winner pay for the handbag?

3. Draw the utility function for the auction winner only.Identify probability results, the expected value, and the certainty equivalent on the utility diagram.