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The equations of the utility function with red indifference curves are:

Cobb–Douglas, . This utility represents standard textbook preferences that are strictly monotone and strictly convex, which formalize the idea of unlimited wants; for example, shoes and purses or cars and watches.

Perfect Complements, . The preferences are monotone and convex for commodities that are consumed in fixed ratios; for example, sugar and coffee.

Perfect Substitutes, . The preferences are strictly monotone and strictly convex for commodities that can be perfectly substituted in consumption; for example, coffee and tea, if you like both.

Bliss Point, . The preferences have a satiation (or bliss) point; for example, sandwiches and sodas for lunch.

To obtain the equations of the utility functions with blue indifference curves, replace by .