The real balance effect provides two interesting insights into the slope of the AD curve.
Firstly, it suggested that, because the supply of money needed to buy real output in the economy is fixed in the short run, a rise in the price level (say P to P2), means that the existing quantity of money in circulation cannot purchase as much output as at the old price level, so 'real' expenditure falls, from Y to Y2. Hence the AD curve slopes downwards.
The second implication of this is that the total amount spent in the economy by households, firms and the government, must, in the short run, remain constant, so P x Y will be constant at all price levels. Hence, the slope of the AD curve is a rectangular hyperbola.
However, there is a long running debate in economics about the slope of the AD curve. Many economists, including Paul Krugman, argue that the real balance effect may be small during a recession, and that the AD curve may become vertical. This relates to the situation of the 'liquidity trap' discussed by Keynes in the 1930s. In basic terms, in a recession interest rates will fall towards zero, and at or near zero changes in the money supply will have little if no effect on AD, and hence output.
This has a recent debate about the wisdom of pumping more money into the economy as a quick solution to the 'credit crisis'.