Changes

Monopolies are established by operation of law, by licensing of professionals, by control of valuable resources, by large economies of scale, and by government-granted patents and copyrights that prevent selling substitutes.

Monopolies are established by operation of law, by licensing of professionals, by control of valuable resources, by large economies of scale, and by government-granted patents and copyrights that prevent selling substitutes.

'''6. Suppose Katie likes to paint for money or even for free, but will not pay extra to paint.  Suppose also that the monthly demand for her paintings is P = $500 - 50Q.  How many paintings does she create each month?'''

'''6. Suppose Katie likes to paint for money or even for free, but will not pay extra to paint.  Suppose also that the monthly demand for her paintings is P = $500 – 50Q.  How many paintings does she create each month?'''

She paints 5 a month.  We find this by determining what Q is when P=0, and taking half of that in order to find where MR=0.

She paints 5 a month.  We find this by determining what Q is when P=0, and taking half of that in order to find where MR=0.

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 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.

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.

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.

Marginal Revenue = (change in revenue) divided by (change in sales) = (change in PxQ) divided by (change in Q)

Marginal Revenue = (change in revenue) divided by (change in sales) = (change in PxQ) divided by (change in Q)

The [[Economics_Lecture_Eight|lecture]] says that "You will need this for several homework problems: when the demand curve is a straight line, the curve for the marginal revenue of a monopoly intersects the x-axis at exactly half the quantity of the demand curve."

The [[Economics Lecture Eight|lecture]] says that "You will need this for several homework problems: when the demand curve is a straight line, the curve for the marginal revenue of a monopoly intersects the x-axis at exactly half the quantity of the demand curve."

The intersection of the x-axis is where MR = 0, which is what we seek here.  That occurs at exactly half the quantity of the demand curve, which is Q= 80/2 = 40.  Plugging that back into the demand equation yields P = $50.

The intersection of the x-axis is where MR = 0, which is what we seek here.  That occurs at exactly half the quantity of the demand curve, which is Q= 80/2 = 40.  Plugging that back into the demand equation yields P = $50.

[[Category:Economics lectures]]

[[Category:Economics lectures]]

{{DEFAULTSORT: Economics Model Answers 08}}

{{DEFAULTSORT:Economics Model Answers 08}}