Solow Growth Model

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I love data. I love financial data, I love economic data. I created this blog as a temporary house (holding area) for my thoughts as I make sense of the works of others and interpret them in my own words. 

I also look forward to questions and contributions from people who have more than decent knowledge about the topics I research on.

Let's dig in right away.

I have been trying to understand the Solow Growth Model of Economic Growth. My ultimate goal for this study is to analyze the effect the stock market has on economic growth in Nigeria. In the course of this research I asked these questions;

What is an economy?

What are the indicators of an healthy economy?

What is the true reflection of economic growth?

What is the stock market?

What is the relationship between the stock market and the economy and what metrics in the economy does the stock market directly affect?

What is the effect of the stock market in other developing economies?

Are they similar to the effects in Nigeria?

What is the effect of the stock market in developed economies?

Are they similar to Nigeria?

What methods will I use to show the relationship between the stock market and economic growth?

In my search for answers I stumbled upon a research paper that talked about the Solow Growth Model as a metric for economic growth.

SOLOW GROWTH MODEL

The model describes how long-run economic growth is affected by a nation's savings, population growth and technological changes.

The standard Solow model basically predicts that in the long-run, economies converge to the steady state equilibrium.

ASSUMPTIONS OF THE MODEL

1. Savings equal investment 

2. Labor and Capital are substitutable for each other

3. Capital depreciates at a constant rate

4. Population grows at a constant rate

5. There are diminishing returns to an individual output

6. Full employment of labor

7. Constant returns to scale

8. No technological progress

Set-up of the Model

Supply side: Production function (assumes constant returns to scale) Y = F (K, L)

where Y is the output, K is the Capital stock and L is the labor (in per worker)

(For convenience, we express all quantities on a per worker basis)

dividing through by L, we have;

Y/L = F(K/L , L/L) =F(K/L , 1)

let y = Y/L , k = K/L , f(k) = F(K/L , 1)

so, y = f(k) that is output per worker is a function of capital per worker

Demand side: (on per worker basis also) output comes from consumption and investment 

y = c + i

c is consumption function, i is the investment 

c = (1 - s) y

NOTE: Marginal Propensity to Consume (MPC) = 1 - s 

MPC is the fraction of income spent on goods, s = saving rate

so i = sy; i.e amount of savings per worker equals investment per worker

Analyzing depreciation, d,

dk is the amount of capital that depreciates each year

so that changes in depreciation Δk = i - dk

Δk = sf(k) - dk

Steady state: The long run equilibrium of the economy

Capital per worker (K/L) is constant

Output per worker (Y/L) is constant

Consumption per worker is constant

Steady state of capital per occurs when Δk = 0

NOTE: With the per worker quantities constant, the total output, total consumption and total capital will increase at the rate of population growth. (that is output can increase with the rate of population growth but output per worker is unchanged.)

Approaching steady state: Capital is subject to diminishing returns. 

Increases in capital per worker increase output per worker at a diminishing rate 

The amount of depreciation increases at a linear rate with increases in capital per worker.

Scenario 1; If investment > depreciation, the capital stock grows and output increases next year.

Eventually, capital and output will rise until the economy reaches the steady state, where capital per worker is unchanged.

Scenario 2; If investment < depreciation, the capital stock shrinks and output decreases next year.

Eventually, capital and output will fall until the economy reaches the steady state, where capital per worker is unchanged.