Question

Now suppose firm x undertakes a process innovation that reduces its marginal cost of production from $20 to $15. the fixed cost of undertaking this process innovation is f > 0. is this a tough commitment or a soft commitment? why? for what values of f would it makes sense for firm x to make this commitment?

Answer 1

(A). It is a tough commitment.

(B). when the value of f is less or equal to 198.

Step-by-step 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.