Answer:
(A). It is a tough commitment.
(B). when the value of f is less or equal to 198.
Explanation:
So, we are given from the question above that;
=> there is reduction in the marginal cost of production from $20 to $15.
=> Also, the fixed cost of undertaking this process innovation is f > 0.
Recall that the demand functions is given as;
Qx = 80 – 2Px + Py. ------------------(**).
Qy = 80 – 2Py + Px a).---------------------(***).
Hence, if we Differentiate πx with respect to Ax we will have that;
(Px - 15) × (-2) + ( 80 - 2Px + Py) = 0. ----------------------------------------------------------(1).
=> 110 + Py = 4 × Px.
Solving for Py and Px using the Bertrand equilibrium gives;
Px = 37.3 and Py = 39.3.
If we slot in the values of Py and Px above into the demand function in equation (**) and (***) we will have;
Qx = 44.7 and Qy = 38.7.
Before innovation = (40 - 20) × 40. = 800
Then, (39.3 - 20) × 38.7 = 747.3 is the after innovation.
(37.3 - 15) × 44.7 - f.
=> 997.5 - f (after innovation).
The values of f would it makes sense for firm x to make this commitment when;
after innovation > before innovation.
997.5 - f > 800.
=>f is less or equal to 198.
