Mos amplifier region of operation
Let's momentarily assume that the output voltage remains constant. Increasing \$V_{in}\$ will also cause \$v_{GS1}\$ to increase. And this increase in \$v_{GS}\$ will cause M1 to conduct more current - provided it still has a \$V_{DS} &gt; 0\$.

This ultimately shifts the balance of the "fight over the output voltage" in favor of M1. More current will go from VDD to OUT compared to the current sunk by M2 from OUT to GND. The net result is that the output voltage goes up until \$v_{GS1}\$ is small enough again to match the current sunk by M2.