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There are two firms competing in the market for Airplanes -Boeing and Airbus. 4. 120-p. Boeing has lower Marginal Costs of Th
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The total quantity would be Q = q^A + q^B , and the inverse demand curve would be p = 120 - Q , and the market residual demand would be p = 120 - q^A - q^B .

(a) Boeing's residual demand would be q^B = 120 - p - q^A .

(b) Boeing's MR would be as MR_B = \frac{\partial (TR_B)}{\partial q^B} = \frac{\partial }{\partial q^B}(pq^B) or MR_B = \frac{\partial }{\partial q^B}(120q^B - q^A q^B - (q^B)^2) or MR_B = 120 - q^A - 2q^B .

(c) Boeing's RF would be where its MR is equal to the MC, ie MC_B = MR_B or 20 = 120 - q^A - 2q^B or 2q^B = 100 - q^A or q^B = 50 - 0.5 q^A .

(d) Airbus's residual demand would be q^A = 120 - p - q^B .

(e) Airbus's MR would be as MR_A = \frac{\partial (TR_A)}{\partial q^A} = \frac{\partial }{\partial q^A}(pq^A) or MR_A = \frac{\partial }{\partial q^A}(120q^A - (q^A)^2 - q^A q^B) or MR_A = 120 - 2q^A - q^B .

(f) Airbus's RF would be where its MR is equal to the MC, ie MC_A = MR_A or 40 = 120 - 2q^A - q^B or 2q^A = 80 - q^B or q^A = 40 - 0.5 q^B .

(g) The quantities produced by each firm would be where their reaction functions intersect. Solving for the RF's, putting the RF of Airbus in Boeing, we have q^B = 50 - 0.5 (40 - 0.5 q^B) or q^B = 50 - 20 + 0.25 q^B or (1 - 0.25)q^B = 30 or q^B = 40 , and since q^A = 40 - 0.5 q^B , we have q^A = 40 - 0.5 *40 or q^A = 20 . These are the required quantities produced by the firms.

(h) Boeing produces greater quantities than Airbus since Boeing have lower marginal cost than Airbus.

(i) The total quantity sold in the market would be Q = 20 + 40 or Q = 60 . At this quantity, the market price would be p = 120 - Q or p = 120 - 60 or p = 60 dollars.

(j) The marginal cost of Boeing is MC_B = 20 or \frac{\mathrm {d} }{\mathrm {d} q^B}(TC_B) = 20 or TC_B = \int 20 \mathrm{d} q^B or TC_B = 20 q^B + FC_B , and since fixed cost is zero, we have TC_B = 20 q^B . The profit of Boeing would be \pi_B = TR_B - TC_B or \pi_B = pq^B - 20q^B or \pi_B = 60*40 - 20*40 = 2400 - 800 = 1600 dollars.

The marginal cost of Boeing is MC_A = 40 or \frac{\mathrm {d} }{\mathrm {d} q^A}(TC_A) = 20 or TC_A = \int 40 \mathrm{d} q^A or TC_A = 40 q^A + FC_A , and since fixed cost is zero, we have TC_B = 40 q^A . The profit of Boeing would be \pi_A = TR_A - TC_A or \pi_A = pq^A - 40q^A or \pi_A = 60*20 - 40*20 = 1200 - 800 = 400 dollars.

The market profit would be \pi = \pi_A + \pi_B or \pi = 400 + 1600 = 2000 dollars.

(k) Supposing that the market price is fixed at $35. In that case, Boeing's MR would be MR_B = 35q^B , and the optimal output would be where MR_B = MR_B or 20 = 35q^B or q^B = 4/7 . Similarly, Airbus's MR would be MR_A = 35q^A , and the optimal output would be where MR_A = MR_A or 40 = 35q^A or q^A = 8/7 . In case the price is not fixed, it would be reestablished to the equilibrium price found before as market price. But, if the price is fixed at $35, then the quantity produced would be q^B = 4/7 and q^A = 8/7 .

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Answer #1

The total quantity would be Q = q^A + q^B , and the inverse demand curve would be p = 120 - Q , and the market residual demand would be p = 120 - q^A - q^B .

(a) Boeing's residual demand would be q^B = 120 - p - q^A .

(b) Boeing's MR would be as MR_B = \frac{\partial (TR_B)}{\partial q^B} = \frac{\partial }{\partial q^B}(pq^B) or MR_B = \frac{\partial }{\partial q^B}(120q^B - q^A q^B - (q^B)^2) or MR_B = 120 - q^A - 2q^B .

(c) Boeing's RF would be where its MR is equal to the MC, ie MC_B = MR_B or 20 = 120 - q^A - 2q^B or 2q^B = 100 - q^A or q^B = 50 - 0.5 q^A .

(d) Airbus's residual demand would be q^A = 120 - p - q^B .

(e) Airbus's MR would be as MR_A = \frac{\partial (TR_A)}{\partial q^A} = \frac{\partial }{\partial q^A}(pq^A) or MR_A = \frac{\partial }{\partial q^A}(120q^A - (q^A)^2 - q^A q^B) or MR_A = 120 - 2q^A - q^B .

(f) Airbus's RF would be where its MR is equal to the MC, ie MC_A = MR_A or 40 = 120 - 2q^A - q^B or 2q^A = 80 - q^B or q^A = 40 - 0.5 q^B .

(g) The quantities produced by each firm would be where their reaction functions intersect. Solving for the RF's, putting the RF of Airbus in Boeing, we have q^B = 50 - 0.5 (40 - 0.5 q^B) or q^B = 50 - 20 + 0.25 q^B or (1 - 0.25)q^B = 30 or q^B = 40 , and since q^A = 40 - 0.5 q^B , we have q^A = 40 - 0.5 *40 or q^A = 20 . These are the required quantities produced by the firms.

(h) Boeing produces greater quantities than Airbus since Boeing have lower marginal cost than Airbus.

(i) The total quantity sold in the market would be Q = 20 + 40 or Q = 60 . At this quantity, the market price would be p = 120 - Q or p = 120 - 60 or p = 60 dollars.

(j) The marginal cost of Boeing is MC_B = 20 or \frac{\mathrm {d} }{\mathrm {d} q^B}(TC_B) = 20 or TC_B = \int 20 \mathrm{d} q^B or TC_B = 20 q^B + FC_B , and since fixed cost is zero, we have TC_B = 20 q^B . The profit of Boeing would be \pi_B = TR_B - TC_B or \pi_B = pq^B - 20q^B or \pi_B = 60*40 - 20*40 = 2400 - 800 = 1600 dollars.

The marginal cost of Boeing is MC_A = 40 or \frac{\mathrm {d} }{\mathrm {d} q^A}(TC_A) = 20 or TC_A = \int 40 \mathrm{d} q^A or TC_A = 40 q^A + FC_A , and since fixed cost is zero, we have TC_B = 40 q^A . The profit of Boeing would be \pi_A = TR_A - TC_A or \pi_A = pq^A - 40q^A or \pi_A = 60*20 - 40*20 = 1200 - 800 = 400 dollars.

The market profit would be \pi = \pi_A + \pi_B or \pi = 400 + 1600 = 2000 dollars.

(k) Supposing that the market price is fixed at $35. In that case, Boeing's MR would be MR_B = 35q^B , and the optimal output would be where MR_B = MR_B or 20 = 35q^B or q^B = 4/7 . Similarly, Airbus's MR would be MR_A = 35q^A , and the optimal output would be where MR_A = MR_A or 40 = 35q^A or q^A = 8/7 . In case the price is not fixed, it would be reestablished to the equilibrium price found before as market price. But, if the price is fixed at $35, then the quantity produced would be q^B = 4/7 and q^A = 8/7 .

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