Question

The organic apple market is perfectly competitive, with apples currently selling at $22 per case. A study commissioned by the organic apple association shows that the short-run total cost of production for a typical producer is TC = 8,000 + 0.02q2, where q is the number of cases sold per year. Calculate the short-run profit maximizing quantity (number of cases) for the typical producer.

Answer 1

In perfect competition, the short run profit maximising number of cases is the number of cases for which the marginal cost is equal to the selling price of $22.

We have the total cost function, which is

TC = 8000 + 0.02q²

Differentiating the total cost function, we get marginal cost. So, the marginal cost function is

MC = 0 + 0.04q

MC = 0.04q

Now, equating the marginal cost to the selling price, we get,

0.04q = 22

q = 550.

So, the short run profit maximising output is 550 cases of apples for the typical producer.

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