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# GDF 262 - P = 16 – 2(2 – 1/3 q1 – 2(2 – 1/3 q1 –...

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Q 262 Three firms with C 1 = (2/3) q 12 and C 2 = 4q 2 and C 3 = 4q 3 face market demand Q = 8 – 0.5P . Calculate equilibrium price and quantities supplied assuming these firms follow the Stackelberg model with firm 1 as leader. What would happen if these firms formed a stable cartel? Q = 8 – 0.5P P = 16 – 2Q Firm 1 Firm 2 Firm 3 C1 = 2/3 q^2 C2 = 4q C3 = 4q MC = 4/3 q Mc = 4 Mc = 4 BRF 2 P = 16 – 2(q1+q2+q3) P = 16 – 2q1 – 2q2 – 2q3 MR = 16 – 2q1 – 2q3 – 4q2 Note: for MR we will treat the q2 as a variable and rest as a constant. So your q2 will double slope and your constant will remain the same. MC2 = MR2 16 – 2q1 – 2q3 – 4q2 = 4 q2 = 3 – ½ q1 – ½ q3 BRF3 MC3 = MR3 q3 = 3 – ½ q1 – ½ q2 Sub BRF 3 to BRF 2 q2 = 3 – ½ q1 – ½ (3 – ½ q1 – ½ q2) rearrange and simplify q2 = 2 – 1/3 q1 so that means that q3 = 2 – 1/3 q1 Now that we have our BRF in terms of one variable (q1) we can solve for our BRF 1 (leader firm) P = 16 – 2q2 – 2q3 – 2q1 sub q2 and q3

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Unformatted text preview: P = 16 – 2(2 – 1/3 q1) – 2(2 – 1/3 q1) – 2q1 P = 8 – 2/3 q1 MR = 8 – 4/3 q Set MC = MR 4/3 q = 8 – 4/3 q q1 = 3 q2 = q3 = 1 Q(aggregated) = (3+1+1) = 5 P = 16 – 2(5) = \$6 Profit firm 1 = (3*6) – 2/3 (3)^2 = \$12 Profit firm 2,3 = (1*6) – 4(1) = \$2 Stable Cartel For stable cartel, 3 firms act as one big monopolist and will allocate the quantity produced based on their MC productions. So equate your MC1 = MC2 = MC3 MC1 = 4/3q MC2 = 4 MC3 = 4 Since firm 1 is based on a variable marginal cost and firm 2 and firm 3 are based on a constant cost, we can’t aggregate the MC’s Therefore, 4/3 q1 = 4 = 4 solving for q1 q1 = 3 Therefore firm one will produce the first 3 units of output since it will be cheaper to produce in firm 1 and the rest of Q will be produced in firm 2 and firm 3. Then the demand function will be one for the whole industry P = 16 – 2Q Which means that the MR = 16 – 4Q MC1 3 MC 2 = MC3 4...
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GDF 262 - P = 16 – 2(2 – 1/3 q1 – 2(2 – 1/3 q1 –...

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