I can't understand the logic with power = voltage * current
If the device in question actually draws 2000W fixed, then you are correct. 

For example, if I have a 48V switching supply connected to a 1.152\$\Omega\$ resistor, the input current will increase as the input voltage decreases to maintain the same output power. 

However most devices do not behave that way. The current will decrease as the voltage decreases, and the power will decrease even faster than the current (with the square of the voltage for a resistor, somewhat less for most heaters because the resistance drops with decreasing temperature). 

If I have a 220V heater rated at 2000W it will be about 24.2 ohms. If it stays 24.2 ohms, on 180V it will draw 180/24.2 = 7.44A and dissipate about 1339W (P = I * V). You can also calculate it from \$P = (\frac{180VAC}{220VAC})^2 \cdot 2000W\$ = 1339W.