Chapter 5: The Solow Growth Model

ECON

What is the solows growth model?

the Solows Growth model is a model that extends the production model by allowing capital to accumulate over time.

• in this model capital is no longer fixed and it changes with savings and depreciation

• in short this model shows how capital accumulation can be an engine of long term growth

What aspect of the formula is solows differnet in compared to the previous model?

whats different is that variables change over time, so we add a “t” subscript

what is this formula? and its variables? 

This formula shows that output can be used for consumption or investments( all outputs must be consumed today or invested for the future) 

• C_t: = consumption 

• I_t = investments 

These variables are called resource constrants 

• we also assume ther is no imports or exports.

What is this formula? and its variables 

This is capital accumulation and it shows use that goods invested for the future determines how the capital stock evolves. 

K_t+1= next years capital 

K_t = this years Capital 

I_t = this years investments 

đ = depreciation rate (usually 7-10% per year)

whats the intuition of the Capital accumulation formula? 

Capital tmr = what we keep from today + new investments - what wears out 

whats the intuition of the change in capital stock formula?(looking at I)

if we increase I_t this yr, the change in K_t-1 will go up. the oppoiste will happen if we dont invest.

What is the capital accumulation formula? 

K_t+1= next years capital 

K_t = this years Capital 

I_t = this years investments 

đ = depreciation rate (usually 7-10% per year)

What is the change in capital stock formula?

What is the Labour force, model set up? 

It the amount of labour in the economy that is given exogenously at a constant level

• we hold labour fixed for now so we can focus on capital accumulation

What are the variables in model setup: investment

I_t = investment for period t

Y_t = Output for period t 

s-bar = the fraction of output invested 

I_t = s-(bar)Y_t

S_t = total savings → S_t = I_t = s(-bar)Y_t 

what does this formula say? 

This formula tells us that consumption is the share of output not invested. basically ts ask where our investment came from

whats happening here? (context gross national savings rate by county) 

1. Canada: we can see 1/5 of total income is saved for canada 

2. US: 18% of total income is saved, most likley due to the spending and materialistic culture 

3. China: Really high ravings rate bevcause chinas culture they do not spend much and rather put it in saving 

4. Greece: o the lower side and it is due to its debt crisis

5. Lebanon: it has a -6% rating, meaning they are dis saving. they save less then they borrow from other countries 

What may be a reason for why people save?

1. interest rate increases 

2. education, healthcare so they dont have to save for emergency pension system

Important slide you can skip 

Define solows model variables in per capiat terms…