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A bond investor values AAA bonds at $5,000 each and values AA bonds at $1,500 each

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A bond investor values AAA bonds at $5,000 each and values AA bonds at $1,500 each.  Sellers of AAA bonds value them at $2,500 and sellers of AA value them at $500.  If the investor cannot observe the bonds type prior to purchase, but believes that 40% are AAA, then the maximum price the investor will pay is ____ and ____ will trade.