Changes

If Anthony sells only three widgets at $9, then that is four less than what a competitive market would sell. The social cost is the sum of (P-MC) over each of the withheld units, noting that the social cost for each withheld unit is different because the unit goes unsold at a different P.  

If Anthony sells only three widgets at $9, then that is four less than what a competitive market would sell. The social cost is the sum of (P-MC) over each of the withheld units, noting that the social cost for each withheld unit is different because the unit goes unsold at a different P.  

'''We assume that society would have purchased the unit up until just below the higher price.''' When the price went from $5 to $6, one unit went unsold and the loss to society was very nearly (P-MC=$6-$5=$1).  Likewise, another unit went unsold at $7 (P-MC=$2), another unit went unsold at $8 and another unit went unsold at $9. That total social cost is very nearly $1 + $2 + $3 + $4 = $10.  

'''We assume that society would have purchased the unit as its price increased until just below the price at which the unit goes unsold and is withdrawn from the market.''' Thus when the price went from $5 to $6, we assume society would have purchased the unit at a price of $5.999.  But at $6, one unit went unsold and the loss to society was very nearly (P-MC=$6-$5=$1).  Likewise, another unit went unsold at $7 (P-MC=$2), another unit went unsold at $8 and another unit went unsold at $9. That total social cost is very nearly $1 + $2 + $3 + $4 = $10.  

If Anthony instead maximized his profits by selling more output, then the social loss is less.  If Anthony sold four units at $8, then the social cost is very nearly $1 + $2 + $3 = $6.  The "very nearly" is so close to the number that we drop the "very nearly" and simply provide the number as the estimated social cost.

If Anthony instead maximized his profits by selling more output, then the social loss is less.  If Anthony sold four units at $8, then the social cost is very nearly $1 + $2 + $3 = $6.  The "very nearly" is so close to the number that we drop the "very nearly" and simply provide the number as the estimated social cost.