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The city council is deciding how to spend its money. They can either spend their money on more sports complexes, or more administration buildings. They determine that their demand for sports complexes is:

$$S = \frac{p_A(I - \frac{1}{8}I^2)}{p_S}$$

Where $p_A$ is the price of an administration building, $p_S$ is the price of a sports complex, and $I$ is the city council's budget, measured in millions of dollars.

If the price of an administration building is $4$ million dollars and the price of a sports complex is $8$ million dollars, what is the budget level at which sports complexes change from being a normal good to being an inferior good?

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