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# Cartels and profit maximizing outputs

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Company A and Company B are soft drink companies operating in the same country for two decades. The market demand curve for their soft drinks is given by Q = 119 - 0.5P. Company A's short-run and marginal costs are given by STC = 3q2 + 48q + 572 and SMC = 6q + 48. Company B's short run total and marginal costs are given by STC = 6q2 + 18q + 849 and SMC = 12q + 18.

a. If Company A and Company B form a cartel to market soft drinks, calculate the cartels profit maximizing price quanity combination.

b. Calculate the profit maximizing output produced by each firm.

c. Calculate the profits earned by each firm and the cartel.

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#### Solution Preview

a. If Company A and Company B form a cartel to market soft drinks, calculate the cartels profit maximizing price quantity combination.
<br>
<br>The market demand is Q=119-0.5p or p=238-2Q
<br>The total revenue is TR=Q*p= Q(238-2Q)=238Q-2Q^2
<br>Then marginal revenue is MR= dTR/dQ=238-4Q
<br>While Q=qa+qb, we know MR= 238-4(qa+qb)
<br>Both ...

#### Solution Summary

Calculate the profits earned by each firm and the cartel.

\$2.49