A Short Note On The Solution Procedure Of Barro And Sala-I-Martin For Restoring Constancy Conditions
The so-called AK models (and models that reduce to AK models without generating transitional dynamics) give rise to a very special property that is called constancy conditions. These conditions impose fix ratios among quantities of the model from the start. Hence, knowing one of the initial values of stock variables becomes sufficient to derive time paths of other variables, given constancy conditions. One source of upsetting these conditions is physical shocks. When a shock disturbs these conditions, preserving intertemporal maximization requires restoring them, preferably immediately. This can be done only by employing a temporary maximization problem, in general. Barro and Sala-i-Martin (1995, pp.172-9) offer a solution procedure based on the idea that the abundant variable has to be kept constant while the scarce variable is let to grow till the condition is satisfied. This note contributes to the discussion in two ways. First, it shows that the solution procedure suggested by Barro and Sala-i-Martin (1995) contains flaws. Second, it shows the right solution procedure that restores constancy conditions.
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