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| − | Question: 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? | + | Question: 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, Q=7 has P=$5, 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? |
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| | 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. | | 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. |
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| − | If Anthony sells only four widgets, 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, 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. |
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| | + | '''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. |
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| | + | 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. |