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Hallo, nog eenmaal u hulp nodig.
Question:
Suppose that the 20 firms in the market form a cartel. Objective of the cartel is to maximize total sum of profits of its members.
Q represents total output of the cartel, production is split equally among the 20 firms q = Q/20.
Show that the objective function of the cartel is equal to the objective of a monopolist, who maximizes profits, and has profits equal to:
Profit Cartel = pQ - C(Q) with C(Q) = 1/64Q^2 + 2,5Q + 100.
(Information from previous questions: c(q) = 5/16q^2 + 2,5q + 5. ... Mkt Demand Qd=210-18p , Supply Qs = 32p-80.)
Het antwoord heb ik van iemand gekregen:
We can derive the C(Q) formula for the cartel from the c(q) function of a producer by:
c(q) = 5/16Q^2 + 2,5Q + 5
Cost in the cartel is one monopolist so one Cost function with:
C (Q/20) = 5/16(Q/20)^2 + 2,5 (Q/20) + 5
= C (Q/20) = 1/1280Q^2 + 0.125Q + 5
Then we are squaring both sides by 20 again and the result will be the C(Q) Function of cartel:
C (Q) = 1/64Q^2 + 2,5Q + 100
Rekenkundig ziet het er goed uit, maar ik moet de reden weten, in woorden, hoe ik deze vraag met antwoord moet uitleggen? Waarom doe je die /20 en dan ineens x20 alles.
Dank
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