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nakungth nakungth
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4 years ago
On the planet Economus, the demand for Kryptonite is:
QD = 24.08 - 0.06P  P = 401  - 16 QD.  There are four producers of Kryptonite on the planet who have formed a Kryptonite Cartel.  The resulting marginal revenue function for the cartel is:
MR(Q) = 401  - 33 Q.  The marginal costs for producing Kryptonite for the 4 different producers are:
   MC1 ( q1) = q1,
   MC2 ( q2) = 1.5 q2,
   MC3 ( q3) = 2 q3,
   MC4 ( q4) = 2.5 q4.
Determine the Cartel profit maximization output levels of each producer.  If producer #2 cheats and produces 50% more than their collusive output level, determine their new revenue level.
Textbook 

Microeconomics


Edition: 8th
Author:
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Answer verified by a subject expert
CanihCanih
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Posts: 462
4 years ago
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More questions for this book are available here
Note that Q = q1 + q2 + q3 + q4.  To maximize Cartel profits, marginal costs will be equated across producers.  These two facts imply: MCC =  Q.  The profit maximizing Cartel output level sets marginal revenue equal to marginal cost.  This is: 401  - 33 Q =  Q  Q = 11.9.  Marginal costs are 4.636.  This implies the Cartel profit maximization production levels for each producer are:
   {   
The market price for Kryptonite at these production levels is $203 per unit.  If producer #2 produces 4.637 units instead, the market price for Kryptonite falls to $177.233.  Total revenue for the second producer rises from $627.47 to $821.83.  That is, producer #2 raises its own total revenue by 31% if it cheats.
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wrote...
3 years ago
A+ answer, ty
wrote...
A month ago
Thx
wrote...
A month ago
TNX
wrote...
4 weeks ago Edited: 4 weeks ago, Andrew Pudan
Thank you so much
Post Merge: 4 weeks ago

For reference: I only said "Thank you so much" (alongside the other amazing industrial economics students above me) because the website forced me to. The answer is just a semi-broken copy+paste from the default answer sheet and doesn't explain from what mysterious hole the (apparently obvious) MCC=(30/77)Q came from.
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