Solow Growth Model - Solving for Steady State




Solutions
Part A - Growth Rates & Time to Double (Rule of 70)
Part B - Returns to Scale - Constant or Not?
Part C - Solow Growth Model - Solving for Steady State
Part D - Plugging in Numbers
Part E - Using the Solow Model and Diagram


(c)   See page 102, particularly page 105 (of Jones Macro Econ Crisis Update Ed)
(d) is below

 
The incantation of a steady state is the following:
“A steady state is a value,
, such that This implies that "  
   where ().

Take the two equations above, and establish the steady state.

Equation One – the Capital Accumulation Equation  (aka, the Law of Motion of Capital)
       
       
       
        ,    this is our equation (1)

Equation Two – The production function
        
  
           
   

    
     ,    this is our equation (2)

Now – combine (1)  & (2), and solve for Capital
    
    
    
    
    
    

    

You can see that the steady state level of capital (
) depends on all the stuff in the right-hand-side:
          the savings rate.          If
         , the depreciation rate,   If




(d) we are just plugging numbers in

        

                

(assuming I didn’t make a maths mistake along the way)







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