[Optimal reserve price] For this exercise we will use the same dataset (SPA_data.csv) from question 3 in PS 8. Recall that the data are from 100 SPA with 2 bidders and no reserve price.

(a) As a benchmark, calculate the average revenue across the 100 auctions in the dataset.

We now want to figure out what would have been the reserve price in these SPA that would have maximized the sellers expected revenue.

(b) If the seller had set a reserve price in these auctions, would you expect the bidders to have bid differently?

(c) Compute the average revenue had the seller set a reserve price of 1 in all of the 100 auctions. Comment. Hint: Remember that in a SPA, if both bids are above the reserve price, then the winner pays the second highest bid. If only one bid is above the reserve price, then the winner pays the reserve price. Finally, if both bids are below the reserve price, then there is no transaction.

(d) Repeat 2c for reserve prices equal to 2, 3, ..., and 10

(e) Would you recommend the seller to set a reserve price in future auctions? If so, at what level?

(f) To investigate the effect of the reserve prices on efficiency, compute the fraction of successful transactions (across the 100 auctions) for each of the reserve prices 0, 1, 2, ..., and 10. Plot the results and comment.