Changes

8. Suppose Anthony owns a company having marginal costs of $5 for all his units.  If he sells only one, then he reaps $11; selling two fetches a price of $10 piece; selling 3 attains a price of $9; selling four reaps $8; Q=5 would have P=$7; Q=6 has P=$6, etc.  A competitive firm would have the same cost and demand numbers.  What does Anthony sell at, and what is the social cost of his monopoly?

8. Suppose Anthony owns a company having marginal costs of $5 for all his units.  If he sells only one, then he reaps $11; selling two fetches a price of $10 piece; selling 3 attains a price of $9; selling four reaps $8; Q=5 would have P=$7; Q=6 has P=$6, etc.  A competitive firm would have the same cost and demand numbers.  What does Anthony sell at, and what is the social cost of his monopoly?

'''If Anthony's company has monopoly and a marginal cost of $5 per widget, then using the described demand curve, his company should sell three widgets at $9 apiece. This will give Anthony's company a profit of $12. By increasing his production to four widgets, Anthony would not increase his profits at all, and consequently will not produce the fourth widget.  Instead of spending his time producing a fourth widget that has a marginal profit of $0, Anthony should go on vacation, or spend his time in some productive manner. ...'''  (thanks to Eric J. for that answer) 

'''If Anthony's company has monopoly and a marginal cost of $5 per widget, then using the described demand curve, his company should sell three widgets at $9 apiece or 4 widgets at $8 apiece. Either approach will give Anthony's company a profit of $12.

'''The answer to the second half of the problem is as follows.  From the Lecture, “For a monopoly, its social cost is defined as Price minus marginal cost (P-MC) summed over all of the output not sold by the monopoly that would have been sold in a competitive industry.”  If Anthony sells only four widgets, then that is four less than what a competitive market would sell. But look at the demand curve.  You can’t just multiply Q=4 times the P-MC of $9-$5.  Instead, you have to sum the (P-MC) over each of the withheld units, because each one has a different P. One would have sold at $6 (P-MC=$6-$5=$1), one at $7 (P-MC=$2), one at $8 and one at $9. That total is $1 + $2 + $3 + $4 = $10 social cost. If Anthony sold 5 units at $8, then the social cost is $1 + $2 + $3 = $6.'''

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 at slightly less than the higher price, such $6 minus an infinitesimal amount. When the price went from $5 to $6, one unit went unsold and the loss to society was '''almost''' (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 '''almost''' $1 + $2 + $3 + $4 = $10.  

 

If instead Anthony sold 4 units at $8, then the social cost is '''almost''' $1 + $2 + $3 = $6.  The "almost" is so close to the number that we drop the "almost" and simply provide the number as the estimated social cost.'''

'''Honors''': 9. Estimates are not very accurate about homeschooling, but some guess that 1 out of every 25 students is homeschooled.  At what level or fraction would homeschooling end the public school monopoly?  Discuss.

'''Honors''': 9. Estimates are not very accurate about homeschooling, but some guess that 1 out of every 25 students is homeschooled.  At what level or fraction would homeschooling end the public school monopoly?  Discuss.