This is the knife edge model everything ok if the

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This is the “knife-edge” model. Everything ok if the economy is on the SSBG, but any deviation from it, will send it into explosive instability Adaptive expectations formally: Y * t = λY t - 1 + (1 - λ ) Y * t - 1 or Y * t - Y t - 1 = (1 - λ )( Y * t - 1 - Y t - 1 ) And together with the multiplier-accelerator equation, Y t = v s ( Y * t - Y t - 1 ), they give: Y t ( s v ) + Y t - 1 (1 - λ )(1 - s v ) - Y t - 2 (1 - λ ) = 0 This is a second order linear difference equation. It cannot generate both growth and cycles. Linear difference equations cannot generate both growth and cycles. Model must be rendered non-linear? This was done at the time, with the easiest way of relying upon floors and ceilings; that is, more or less arbitrary upper/lower bound constraints in the cumulative process (e.g. Hicks 1950). 4
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Non-linear difference equations can, and have, also be used. But, these are not subject to ready solutions (algorithms), suffering not only from tractability issues, but also from multiple equilibria (an additional inconvenience). For example, Goodwin growth with cycles models (bringing less arbitrary non-linearities to floors/ceilings)... But, simplest solution predominantly taken: treat SR and LR as independent from each other . Further developments dealt with the simplistic assumptions of the HD model by both rejecting them and, in doing so, tempering the possibility of instability. It is adaptive expectations that lead to such instability (as optimism leads to undershooting expectations relative to actual outcome which repeats itself indef- initely). Do they make sense? Intro of Rational Expectations (New Classical Economics) Investment function: does not account for a number of factors (e.g. costs of investment or pace of installation) that would dampen the momentum. Saving function: S = sY and consequently the Keynesian consumption function as a fixed proportion of current income. But, if consumers optimise over their lifetime utility (PIH) this would dampen the effect of the multiplier No price mechanism No money All five elements became standards in the macroeconomics toolkit Domar’s also allowed for capacity utilisation and a connection between the short and the long runs, though the process of moving inputs from old machines into newer more productive ones. And identified a problem in that process that may lead to less than full capacity utilisation. 5
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