Q. Why GDP is determined only by aggregate demand?

Note that we haven't said anything about the aggregate supply so far. In order to justify why GDP is determined only by aggregate demand we have to explain why supply aggregate Y_S plays no role and why Y_S always would be exactly equal to Y_D (that is essential for the goods market to be in equilibrium).

We can explain why Y_S = Y* by analysing what would have happened if firms didn't supply this quantity.

1. Imagine that firms supplied and also produced a larger quantity so that Y > Y*. 

2. From the figure above, Y_D< Y and firms can't sell everything they produce. 

3. Unplanned stock investments will increase by Y - Y_D when companies are forced to put unsold products in stock. 

4. Then firms will want to lower their supply. Reduction will continue until Y_S = Y*.

5. If, conversely they supply and produce too little, Y < Y* and then Y_d> Y. Stocks will now be decreased and firms will want to increase the supply.

Please note that Keynesian model always presumes quantity adjustment to get back to equilibrium. There are no price adjustments in the Keynesian model.