Keynesian theory/Tutorials

The Keynesian model

Let:-
    M = the money supply
    P = the price level
    y = the national income
     l = the income elasticity of demand for money
     L = the interest elasticity of demand for money
    s =  savings and S =  the marginal propensity to save
    i =  savings and I =  the interest elasticity of investment
    n = the numbers employed in the labour market
    Y =  labour productivity
    W = the money wage

then:-

The demand for money

M = lPy + L(r)   ------------------------ (1)

The consumption function

s = S(y)   -------------------------------- (2)

The production function

y = Y(n)  ---------------------------------- (3)

The labour market

dy/dn = W/P  ----------------------------- (4)

Investment

i = I(r)  ------------------------------------- (5)

Savings

s = i  ---------------------------------------- (6)

Sticky wages

W =W_o,  ------------------------------------ (7)

- and the "multiplier" is 1/S - the reciprocal of the marginal propensity to save