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.