question archive A monopolist has the following cost function: C(q)=800+8q+6q2C(q)=800+8q+6q2
A monopolist has the following cost function: C(q)=800+8q+6q2C(q)=800+8q+6q2
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A monopolist has the following cost function: C(q)=800+8q+6q2C(q)=800+8q+6q2. It faces the following demand from consumers: P=200−2QP=200−2Q. There is another firm, with the same cost function, that may consider entering the industry. If it does, the equilibrium price will be determined according to Cournot competition.
(a) How much should the monopolist optimally produce in order to deter entry by the potential entrant?
(b) How much would the monopolist produce if there were no threat of entry?
(c) Compared to a situation of a monopoly with no threat of entry, how much better off are consumers when there is the potential for entry, even if it does not actually occur?
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a).
To deter the potential entry, the firm should charge a price equal to marginal cost:
P=MC=∂c(Q)∂Q:8+12Q∴8+12Q=200−2QQ=13.71P=200−2(13.71)P=$172.58P=MC=∂c(Q)∂Q:8+12Q∴8+12Q=200−2QQ=13.71P=200−2(13.71)P=$172.58
The firm should produce 13.71 units to deter entry.
b).
If there's no threat of entry, the firm should maximize profit by producing at a point where marginal revenue is equal to marginal cost:
MR=MC8+12Q=200−(2×2)QQ=12P=$176MR=MC8+12Q=200−(2×2)QQ=12P=$176
It should produce 12 units.
c).
The welfare change of the consumers can be determined by calculating the consumer surplus under threat of entry and with no threat of entry:
Consumer surplus under threat of entry:
CS=12(200−172.58)13.71=$187.96CS=12(200−172.58)13.71=$187.96
Consumer surplus with no threat of entry:
CS=12(200−176)12=$144
