Question

Airbus and Boeing are duopolists that engaged in price competition and produces heterogeneous goods. If Airbus faces the demand curve Q1= 48 - 2P1 +3P2, Boeing faces the demand curve Q2 =48 -2P2 + 3P1, and both firms face zero marginal cost. Determine Airbus reaction curve?

Answer #1

The demand curve of Airbus is Q_{1} = 48 -
2P_{1} + 3P_{2}

To find the reaction curve of Airbus, the following steps are used:

Step 1: Find the total revenue (TR) function of Airbus.

TR_{1} = P_{1} * Q_{1} = P_{1} *
(48 - 2P_{1} + 3P_{2}) = 48P_{1} -
2P_{1}^{2} + 3P_{1}P_{2}

Step 2: Find the derivative of TR_{1} function with
respect to P_{1}.

dTR_{1}/dP_{1} = 48 - 4P_{1} +
3P_{2}

Step 3: Since marginal costs are zero, equate
dTR_{1}/dP_{1} to zero.

dTR_{1}/dP_{1} = 0

48 - 4P_{1} + 3P_{2} = 0

4P_{1} = 48 + 3P_{2}

P_{1} = (48/4) + (3/4)P_{2}

P_{1} = 12 + 0.75P_{2}

**Thus, the reaction curve of Airbus is P _{1} = 12
+ 0.75P_{2}**

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