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In class one, the MC of producing the good is \$2 per unit. The MR curve for class one buyers is MR = 10
– 2Q. Setting MR = MC for this class of buyer we get 10 – 2Q = 2 or Q = 4 units. Class one should get 4
units of the total output of 7 units allocated to the buyers in this class: that implies that class two will get
the remaining three units (we will check that in just a bit). What price will class one pay? Substitute Q = 4
into the demand curve for this class: P = 10 – Q = 10 – 4 = \$6 per unit. That implies that TR from class
one will be \$24. TC for this level of production for class one will be (\$2 per unit)(4 units) = \$8. Profit
from class one will be \$16.
In class two, the MC of producing the good is \$2 per unit. The MR curve for class two buyers is MR = 5 -
Q. Setting MR = MC for this class of buyer we get 5 - Q = 2 or Q = 3 units. Class two should get 3 units
of the total output of 7 units allocated to the buyers in this class: note that Qtotal = Q1 + Q2 where Q1 is
the amount of the good provided to class one and Q2 is the amount of the good provided to class two.
What price will class two pay? Substitute Q = 3 into the demand curve for this class: P = 5 – (1/2)Q = 5 –
(1/2)(3) = \$3.50 per unit. That implies that TR from class two will be \$10.50. TC for this level of
production for class two will be (\$2 per unit)(3 units) = \$6. Profit from class two will be \$4.50.
Total profit from the two classes of buyers will equal \$16 + \$4.50 or \$20.50.
Since total profit from third degree price discrimination is greater than total profit from selling the good at
a single price we can conclude that third degree price discrimination is worthwhile to this monopolist.
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