Golden RuleQ 1. In the context of growth theory, which allocations areclearly bad allocations?Q 2. What are the observable implications of these bad alloca-tions?The literature on the Golden Rule adopts a weak notion of whatconstitutes a bad allocation. Specifically, a feasible allocation isbad if there is another feasible allocation that at all d ates allowsfor a greater amount of aggregate consumption.1Golden Rule Steady State: kGRIf one could live in any steady state of the Solow model, thenwhich steady state would that be? Arguably, the one with thelargest party! The size of the party is measured by aggregatesteady state consumption.max F (k, 1) − k[(1 + n)(1 + g) − (1 − δ)]⇒ Fk(k, 1) − [(1 + n)(1 + g) − (1 − δ)] = 0⇒ Fk(kGR, 1) = [(1 + n)(1 + g) − (1 − δ)]2Geometry:The previous slide tells one that the Golden Rulesteady state capital-labor ratio is precisely the ratiok where the marginal product of capital equals theslope of the line determining steady sta te investment.This result will be expressed geometrically on the nextslide.3Figure 1: Solow Model—Steady State 0 kk(d+n+g+ng) y= F(k,1)i= s F (k ,1 )k*i* y* Figure 2: Solow Model—Golden Steady State 0 k*k(d+n+g+ng) y=F(k,1) k*max k* g i* g y* gQ1: In the context of growth theory, which allocations are clearlybad allocations?Answer: Any steady state k above the Golden Rule steady state isa BAD allocation. This is because in any such steady state thereis something feasible to do which will INCREASE consumptionin each future date.Steady states below the Golden Rule are not BAD allocations bythis criteria.4Q2: Observable Implications of these bad allocations?Fk(kGR, 1) = [(1 + n)(1 + g) − (1 − δ)] - Golden RuleFk(k, 1) < [(1 + n)(1 + g) − (1 − δ)] - Above Golden Rule1+Fk(k, 1) − δ<(1 + n)(1 + g)kFk(k, 1) <k(δ + n + g + ng)51+Fk(k, 1) − δ<(1 + n)(1 + g)LHS: 1 + real interest rateRHS: 1 + growth rate of GDP in steady statekFk(k, 1) <k(δ + n + g + ng)LHS payment to capitalRHS is steady state investment6Abel, Mankiw, Summers and Zeckhauser:They pushed a more sophisticated version of this line of argumentin both theoretical and empirical directions.Empirically: They conclude that it is best to look at the impli-cations coming from comparing investment and the p ayment tocapital. They looked at data from the US and other advancedcountries to determine whether or not investment always exceedsthe payment to capital. It does not!70.20.30.4tion of GNPUS Data 1929‐ 8500.11920 1930 1940 1950 1960 1970 1980 1990FractYearInvestment/Y Payment to