The Simple Keynesian Model

The Simple Keynesian Model, also known as the Keynesian cross, is too simple for many purposes, but it does have a couple of advantages.  First, it illustrates an important point:  the economy can be in equilibrium at less than full employment.  Second, the structure is simple enough to facilitate a first attempt at analysis by students.

EconModel

The EconModel presentation allows you to study this model graphically and numerically.  You can trace out the effects of changes in investment and government spending.

Analysis

The EconModel presentation analyzes the effects of changes in:

Autonomous Investment

Government Spending

Interest Rates

The General Model

An Accounting Identity

The demand for output can be decomposed as Y = C + I + G.

Consumption and Saving

Economic behavior.  Consumption is a function of income.  C = f(Y).

Investment

I is autonomous for now.  Could go either way.

Government Spending and Taxes

G is exogenous.

A Simple Linear Consumption Function

Suppose C = a + b (Y - T ), where T is an exogenous lump sum tax and a and b are parameters.  (b is known as the marginal propensity to consume.)

Equilibrium

We can solve for Y both graphically (see below) and algebraically.

The solution for equilibrium output is

Y =  (1-b)-1 ( a + I + G - bT ).

The Multiplier

The change in Y for a given change in G is known as the multiplier.  For lump-sum taxes, the multiplier for G is (1-b)-1.  That is, G is multiplied by (1-b)-1 to determine Y.

Suppose C = a + b (Y - T ), where T = t Y is a percentage income tax and a, b, and t are parameters.  The solution for equilibrium output is

Y =  (1-b+t)-1 ( a + I + G ).

Increasing the tax rate t decreases Y.

and (1-b+t)-1 percentage taxes.  lower in the second case.

An Example:  Inventory Cycles

[do math here because it is not below]

inventory cycles

Another Advanced Model:  An IS Curve

An advanced element of the EconModel presentation constructs an IS Curve.  If investment is a function of the interest rate I = I(R), then changing R traces out an IS curve.

While this analysis does construct an IS Curve, the IS/LM derivation has the advantage that putting the interest rate on an axis focuses attention on the role of the interest rate in determining investment.  In that presentation, the latter effect is depicted as the slope of a curve rather than as the shift in a curve.

How does this fit with a complete Keynesian model?

For the sake of completeness, the Simple Keynesian Model in an IS/MP World page shows how the Simple Keynesian Model can be seen as a special case of a full-blown Keynesian model.