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The market for olive oil is highly competitive with thousands of producers competing against each other. These producers have virtually no control over prices and they have to take the prices determined by the market as given when making their production decisions.
Suppose that currently the market demand and supply for olive oil are characterized by the following equations:
p = 10 - 0.5Qd (price-demand)
p = 1 + 1.5 Qs (price-supply),
where the quantities Qd and Qs are measured in millions of liters.
Blue Olive is one of the olive oil producers competing in this market. Suppose that Blue Olive's production cost as a function of quantity is given by:
C(Q) = 5 + 0.5Q + 0.1 Q2, where Q is measured in thousands of liters.
Question:
What is Blue Olive's optimal production level, given the current market conditions?
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