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Remember that labor demand provides us profit-maximizing quantity of L for a given real wage. If W/P is given (as it's in cross model), we can find profit-maximizing quantity of L from the graph. We signify this by LOPT. If firms use LOPT amount of labor, they would produce YOPT = f (LOPT, K) where f is production function and K amount of capital (exogenous).
Figure: Profit-maximizing quantity of L and Y
A significant assumption in cross model is that YOPT is always larger than YD -aggregate demand isn't enough for the amount that firms would like to supply at given real wage. This assumption has a very significant consequence. Albeit producing YOPT would maximize profits, firms won't produce this level because of the lack of demand. They will only produce YD and we see why it's aggregate demand that is significant in the cross model. Again, note how Keynesian cross model works with quantity adjustments in place of price adjustments as in the classical model. We signify the level of output produced by firms by Y*.
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