A.Government in the Solow growth model
1.Why is the equilibrium condition now sp + sg = I?
We work with following assumptions:
1. Closed economy with national income accounts identity Y = C + I + G
2. All savings are invested
Before the introduction of tax all of the consumer's savings represent the total Investment. The introduction of tax reduces the net income of the private sector and flows to the government. What is not spent by the government will be saved and is therefore part of the investment. Gov-ernment and consumer savings represent now the total investment. Replacing taxes with gov-ernment consumption and government savings leads to the new equation for output which con-sists of private consumption, private savings, government consumption and government sav-ings. Consumption is the total of private consumption and government consumption. Replacing the basic equation with the calculated figures leads us to the result of i=sg+sp.
Below are the equations shown for this solution.
FormulasFigures as an example
y = c + I
y = cp + tax + sp
tax = cg + sg
y = cp + cg + sg + sp
c = cp + cg
cp + cg + i = cp + cg + sg + sp
i = sg + sp10'000 = 7'000 + 3'000
10'000 = 5'000 + 3'000 + 2'000
3'000 = 2'000 + 1'000
10'000 = 5'000 + 1'000 + 1'000 + 3'000
7'000 = 5'000 + 2'000
5'000 + 2'000 + 3'000 = 5'000 + 2'000 + 1'000 + 2'000
3'000 = 1'000 + 2'000
Shown in the diagram below is that taxes reduce private consumption and savings, making them government consumption and government savings. Total investments are made up of private savings and government savings.
Output total / Investment total
Intuitively, all that...