Profit maximization

Question

The table bellow shows the relationship between total cost and output for a firm in a perfectly competitive market.

The firm sells its product for €7 per unit.

I was told to answer the following question: if the firm seeks to maximize profit at which level of output should it operate?

I’m aware that profit reaches its maximum where marginal cost equals marginal revenue. I also know that, for a perfectly competitive firm, marginal revenue is equal to price.

Thus, MC=MR=7

So I came up with this:

The optimal solution lies between 100 and 200, but can I actually find out the exact level of output where profit is maximized?

Answer 1

How can I actually find out the exact level of output where profit is maximized?

You could find it by using your table to build a graph and interpolating the quantity that matches the maximum profit.

Note: At this price of 7 Euro your firm should exit the market, as it is under in every point in this table, the minimal loss is -900 either for 100 or 200 units of its product, thus the answer to your question is units = 150.

It will profit if it continues to grow, as its Average Total Cost is decreasing and the firm still benefits from economies of scale.

You could calculate the profitable point by extrapolation.

Answer 2

If you are supposed to give an answer solely based on the data provided, then I suggest that you do not extrapolate a new quantity.

Your reasoning to solve the problem is correct, and I believe that the answer should be 100. Indeed, if the profit is already maximized (or in this case the loss minimized), then the rational firm has no interest in increasing its output any further. Thus it should stop at 100.