[h1952]

Auction: n bidders, with values drawn from uniform on a,b (not from (0, c)) .
Show revenue equivalence of first price and second price.

what I have: second price: optimal strategy Bid = Value. Second highest bid from n draws on a uniform (a,b) = a + (b-a) (n+1 - 2)/(n+1) (k = 2).
= a + (b-a) (n-1)/(n+1)


First price: optimal strategy B = (n-1/n)V. First highest from n draws on a uniform ((n-1)/n * a , (n-1)/n * b) = (a*, b*) = a* + (b*-a*) (n+1-1)/(n+1) = (n-1)/n a + ((n-1)/n) (a+ (b-a) n / n+1 = a - a/n + (b-a) (n-1)/(n+1).

These are not the same because a/n is not zero. What am I doing wrong here?