Question 8.4

1. Use the accompanying total revenue schedule of Emerald, Inc., a monopoly producer of 10-carat emeralds, to calculate the answers to parts a–d. Then answer part e.

Quantity of
emeralds demanded		 Total
revenue
1 $100
2 186
3 252
4 280
5 250

  1. The demand schedule

    The price at each output level is found by dividing the total revenue by the number of emeralds produced; for example, the price when 3 emeralds are produced is $252/3 = $84. The price at the various output levels is then used to construct the demand schedule in the accompanying table.

  2. The marginal revenue schedule

    The marginal revenue schedule is found by calculating the change in total revenue as output increases by one unit. For example, the marginal revenue generated by increasing output from 2 to 3 emeralds is ($252 − $186) = $66.

  3. The quantity effect component of marginal revenue per output level

    The quantity effect component of marginal revenue is the additional revenue generated by selling one more unit of the good at the market price. For example, as shown in the accompanying table, at 3 emeralds, the market price is $84; so when going from 2 to 3 emeralds, the quantity effect is equal to $84.

  4. The price effect component of marginal revenue per output level

    The price effect component of marginal revenue is the decline in total revenue caused by the fall in price when one more unit is sold. For example, as shown in the table, when only 2 emeralds are sold, each emerald sells at a price of $93. However, when Emerald, Inc. sells an additional emerald, the price must fall by $9 to $84. So the price effect component in going from 2 to 3 emeralds is (−$9) × 2 = −$18. That’s because 2 emeralds can only be sold at a price of $84 when 3 emeralds in total are sold, although they could have been sold at a price of $93 when only 2 in total were sold.

    Quantity of
    emeralds
    demanded    		 Price
    of
    emerald    		 Marginal
    revenue    		 Quantity
    effect
    component    		 Price effect
    component
    1 $100
    $86 $93 −$7
    2 93
    66 84 −18
    3 84
    28 70 −42
    4 70
    −30 50 −80
    5 50

  5. What additional information is needed to determine Emerald, Inc.’s profit-maximizing output?

    In order to determine Emerald, Inc.’s profit-maximizing output level, you must know its marginal cost at each output level. Its profit-maximizing output level is the one at which marginal revenue is equal to marginal cost.