The special case is when the (constant) MRS equals the price ratio (for example, both goods have the same price, and same coefficients in the utility function). In this case, any combination of the two goods is a solution to the consumer problem.

Utility maximization of substitutes

The first order condition:

where .

Inserting to the budget constraint:

It is easily verified that the demand for the two goods decrease with their own price. Moreover, it is easily verified that

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