The multiplier-accelerator model. Initial points The model is a synthesis of the Kahn-Keynes multiplier and the “accelerator” theory of investment 1.
P. Samuelson. “Interaction Between the Multiplier Analysis and the Principle of Acceleration,” Review of Economic Statistics (May 1939).
aSherman & Kolk claim this is a reasonable figure since estimates show that GDP is typically equal to 1/3 the value of the capital stock.
If the economy is in equilibrium,
Then output supplied (Y) is equal to aggregate demand (AD). Assuming a closed economy without government, we have:
Yt = Ct + It
1We assume that C depends on lagged, rather than current, income. Also note that for our simplified economy, Y = YD.
To get a homogenous equation, we ignore the constant
To get a standardized form, let A = c + . Also, Let B = . Thus we can write:
Note for the mathematically inclined: equation (5) is a 2nd order (homogenous) difference equation.
Assumptions: (1) Y is $996 in period 1 and $1000 in period 2; (2) C = 96 + .9Yt - 1; and (3) = 1
Assumptions: (1) Y is $996 in period 1 and $1000 in period 2; (2) C = 996 + .9Yt -- 1; and (3) = B = 1
B < 1 and A2 > 4B
B > 1 and A2 > 4B