There is an economy that has 500 consumers with each with identical demands for
ID: 1165498 • Letter: T
Question
There is an economy that has 500 consumers with each with identical demands for a good ?? = ?10???? + 100 where P is the market price of the good and qc is the quantity demanded of 1 consumer at that price. Currently there are 35 identical firms producing the good in a perfectly competitive market each of whom has a marginal cost ???? = ???? 5 + 10 where qf is the quantity produced by 1 firm. You can assume there are constant returns to scale at all output levels. Decimal quantities and prices are possible
Show that the monopoly outcome has a lower total of consumer and producer surplus.
Explanation / Answer
Perfect competitive outcomes=
P = MC
100 - 10Q = 5Q +10
Q = 90/15
= 6
P = 100 - 10*6
= 40
CS = .5(60) (6)
= 180
PS = 0.5 ( 40 -10)(6)
= 0.5 (30)(10)
= 150
TS = 180 + 150
= 330
Monopoly Case:
MR = MC
P = 100 - 10Q
TR = 100Q - 10Q^2
MR = 100 - 20Q
MR= MC
100 - 20Q = 5Q + 10
90 = 25Q
Q = 3.6
P = 100 - 10(3.6)
= 64
CS = 0.5 (36) (3.6)
= 64.8
PS = 0.5 ( 64 -10) *3.6
= 0.5 ( 54)(3.6)
= 97.2
TS = 161.7
Hence proved that monopoly outcome has a lower total of consumer and producer surplus.
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