Write out a general Kenesian Economic System of equations for a closed economy.?

Question

Write out a general Kenesian Economic System of equations for a closed economy.?

Answer 1

One simple version of a closed economy Keynesian System may be like this:

(1) Production Function: Y = F( N, K) where Y is Output (value added), N is employment of labor and K is capital stock.

(2) Demand for Labor: dY/dN= w where w is wage rate and d stands for differentiation i;e. dY/dN is the marginal productivity of capital

(3) Supply of Labor: N=N(w), subject w>wo wo is the minimum wage below which wages may not fall - downward stickiness.

(4) Saving Function: S=s*(Y-T) where S stands for saving, T STANDS FOR TAXES and s is the saving  fraction out of income.

(5) Investment function: I= I(Y, r) where I stands for Investment and r stand for the rate of interest

(6) Demand for Money: Md= kPY + L(r) where k is the coefficient of transactions demand for money as proportion of Money Income, P is the Price level and L stands for Liquidity preference function (speculative demand for money)

(7) Investment equal Change in Capital Stock:  DK= I where DK stands for change in capital stock

(8) Labor Market equilibrium: dY/dN = w = w'(N) where w'(N) is the inverse of the Labor supply function giving the the supply of labor at different wage rate subject to w> or equal to wo.

(9) Saving Investment equilibrium: S = I

(10) Money Market equilibrium Md= Mo where Mo is an exhogeneously fixed quantity of Money Supply.

(11) Income Expenditure Identity: Y = C + G+ S, where G stands for Goverment Expenditure and implies S= Y- (C+G).

The system can be reduced to a  fewer set of equations:one for money market equlibrium, one for saving-investment market equilibrium, the income-expenditure Identity and labour market equlibrium to solve for the variables Y, r, w, P.

Answer 2

Y = C + I + G

   = C0 + c(Y-T) + I0 - br + G0

Where Y = Output, C = Consumption, I = Investment, G = Government Spending,

Given by C = C0 + c(Y-T), where C0 =  Autonomous consumption, c = marginal propensity to consume, T = Lump Sum Tax; I = I0 - br, where I0 = Autonomous Investment, b = sensitivity of interest rate to income, r = interest rate; G = G0, where G0 = Autonomous Government Spending.

Rearranging,

Y = [C0 + I0 + G0 - (br + cT)]/(1-c)

Note, 1/(1-c) is the Keynesian multiplier.