I have some questions about Macroeconomics I want some profe

I have some questions about Macroeconomics. I want some professional tutors help me solve them.Please give me detailed solutions ( and good handwriting). Thank you!

Solution

The Solow Growth Model

The Solow Growth Model is a model of capital accumulation in a pure production economy: there are no prices because we are strictly interested in output = real income. Everyone works all the time, so there is no labor/leisure choice. In fact, there is no choice at all: the consumer always saves a fixed portion of income, always works, and owns the firm so collects all “wage” income and profit in the form of all output. We will not need to model the “consumer”.

We assume all people work all the time and we assume they save, hence invest, a fixed portion of their income. There is no government, hence no taxation nor subsidies; this is a closed economy, so there is no trade. Since there are no prices there is no need for money: there are no financial markets, etc.

This model, then, is a model that captures the pure impact savings = investment has on the long run standard of living = per capita income. Since we allow for population growth, this model may be called the Blue Lagoon Model (i.e. as opposed to Robinson Crusoe, two people can reproduce).

Ingredients: Consumers and Firms. All consumers own the firms, so consumers receive all output, and therefore all profit and rent.

Aggregates: Output = Real Income = Yt in period t.

Capital Stock = Kt;

Population Size = Nt = Labor Supply (since everyone works all the time).

Consumption = Ct;

Savings = St;

Investment = I.t.

Per Capita: Output = Real Income = yt = Yt /Nt in period t.

Capital Stock = kt = Kt/Nt ;

Consumption = ct = Ct/Nt;

Savings = st = St/Nt;

Investment = i.t = It/Nt;