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I proceeded this way, there are three goods x, y and z so that the budget constraint is P1x+P2y+P3z=m
With x and y being perfect complements the agent will always choose equal amounts of both no matter what the prices are.
So the utility function and budget constraint can be written as either U(x,z) = (x^a)*z^a, (P1+P2)x+P3z=m or U(y,z) = (y^a)*z^a, (P1+P2)y+P3z=m. Now you can solve either of these set of equations.
