"Classical" is a term used to describe economic doctrine before Keynes.  Classical economists were mainly interested in understanding long-term changes in national economies, rather than the short-term fluctuations that the Keynesian income-expenditure describes.  No classical economist actually wrote down this model -- rather, it's an effort by recent textbook writers to encapsulate Classical views in a simple mathematical form that can be compared to the income-expenditure model.  The following treatment is adapted from Mankiw's Macroeconomics.

Here is our model:

 Y = C + I + G    (equilibrium condition, in which total output equals the demand for it)
 C = C(Y - T)    (consumption function -- C is function of disposable income)
 I = I(r)     (investment function -- r is the interest rate, and investment rises as r falls, falls as r rises.  This is bcause firms that want to undertake cpital investment have to finance it by borrowing from the bank.)
 G = some fixed amount     (government expenditure is exogenous)
 T = some fixed amount    (taxes are exogenous)
 Y = some fixed amount   (output is fixed at full employment)

Here is a specific numerical example of this model, of the kind we will work with in class:

Y = C + I + G
Y = 1,000
G = 250
T = 200
C = 100 + .5(Y - T)
I = 500 - 25r

1. Figure out C, I, and personal S, and make up a flow picture.  Figure out equilibrium r.

2. Now balance the budget by raising T.  Figure out C, I, and personal S, and make up a flow picture.  Figure out equilibrium r.

3. Instead of balancing the budget, spend like crazy and double G.  Figure out C, I, and personal S, and make up a flow picture.  Figure out equilibrium r.

4. Try something else.  Starting again with the assumptions in (1), lower both G and T to 100. Figure out C, I, and personal S, and make up a flow picture.  Figure out equilibrium r.

5. How about this.  Starting with the assumptions in (1), change the investment function to I = 750 - 25r (imagine that businesses suddenly want to buy more machines).  Figure out C, I, and personal S, and make up a flow picture.  Figure out equilibrium r.

6. And finally try this.  Suppose that the marginal propensity to consume rose from .5 to .75 so that the new consumption function is C = 100 + .75(Y - T).  Work out the results.
 
 

How/why things change in thsi model: the interest rate adjusts to equilibrate the flow of national savings with the flow of investment.

Key features: There is always full employment in this model, by assumption.  The interest rate is the great equilibrator -- if people
decide to spend less and save more (lowering C) r will fall to raise I, so that AD will never be insufficient.  In other words output is not
demand-constrained.  This is a model in which you will get complete crowding-out of investment by any increase in government spending.  There also is no point in doing macro policy to raise employment in this model.