circulation is small enough to be ignored. This allows us to treat V as constant and solve the first and third equations (the 'first postulate' and the quantity theory) together, leaving the second equation to determine the interest rate from the result. We then find that the level of employment is given by the formula . The graph shows the numerator and denominator of the left-hand side as blue and green curves; their ratio – the pink curve – will be a decreasing function of N even if we don't assume diminishing marginal returns. The level of employment N̂ is given by the horizontal position at which the pink curve has a value of , and this is evidently a decreasing function of W. Chapter 3: The principle of effective demand The theoretical system we have described is developed over chapters 4–18, and is anticipated by a chapter which interprets Keynesian unemployment in terms of 'aggregate demand'. The aggregate supply Z is the total value of output when N workers are employed, written functionally as φ(N). The aggregate demand D is manufacturers' expected proceeds, written as f(N). In equilibrium Z=D. D can be decomposed as D1+D2 where D1 is the propensity to consume, which may be written C(Y) or χ(N). D2 is explained as 'the volume of investment', and the equilibrium condition determining the level of employment is that D1+D2 should equal Z as functions of N. D2 can be identified with I (r). The meaning of this is that in equilibrium the total demand for goods must equal total income. Total demand for goods is the sum of demand for consumption goods and demand for investment goods. Hence Y = C(Y) + S(Y) = C(Y) + I (r); and this equation determines a unique value of Y given r. Samuelson's Keynesian cross is a graphical representation of the Chapter 3 argument. Dynamic aspects of Keynes's theory Chapter 5: Expectation as determining output and employment Chapter 5 makes some common-sense observations on the role of expectation in economics. Short-term expectations govern the level of production chosen by an entrepreneur while long-term expectations govern decisions to adjust the level of capitalisation. Keynes describes the process by which the level of employment adapts to a change in long-term expectations and remarks that: The level of employment at any time depends... not merely on the existing state of expectation but on the states