Question

Problem 3. A profit function (Q) jQ +k is to be used to reect the following assumptions If nothing is produced, the profit will be negative (because of fixed costs The maximum profit occurs at a positive output level What parameter restrictions are called for?

Answer 1

For the profit being negative at no output, the profit function should take a value less than one when Q is zero. So, here, if Q=0, the value the profit function takes will be k which to fulfill this condition must be zero. SO, k<1.

Second, the maximum profit occurs at the point where the second derivative of the profit function is negative. Here, the first derivative of the profit function is: 2hQ+j

The second derivate of the above profit function will be 2h. In order for this to be negative, h must be less than 0 or negative.

So, the two parameters restrictions to hold for the above condition must be:

k<0 and h<0