Question

The demand and cost function for a company is estimated to be as follows: P = 100-8Q; TC = 50+80Q-10Q 2 + 0.6Q 3. Suppose the company lacks confidence in the accuracy of cost estimates expressed in a cubic equation and simply wants to use a linear approximation. Suggest a linear representation of this cubic equation.

Answer 1

A linear function is of the form $a+bx$

Hence, to simplify a cubic function, we leave out the squared and cubic terms and the linear function becomes $50+80Q$

There will be no significant difference, the revenue maximizing price would remain the same but the profit maximizing price increases to $90