Suppose that the economy under study has the following characteristics: s = 0.30

Question

Suppose that the economy under study has the following characteristics:
s = 0.30 n = 0.02 g = 0.10 d = 0.03
K = 1600 Y = 800 N = 100 A = 2
Y = F(K, N, A) = AF(K, N) = A(K^(1/2))(N^(1/2))

What distinguishes the golden rule rate of capital accumulation from other steady-state
rates of capital accumulation? Is the rate at which capital is being accumulated in this economy consistent with the golden rule? Explain carefully using numerical results to support your conclusion.

Explanation / Answer

the Golden Rule savings rate is the rate of savings which maximizes steady state level or growth of consumption. a steady state savings rate of 100% implies that all income is going to investment capital for future production, implying a steady state consumption level of zero. A savings rate of 0% implies that no new investment capital is being created, so that the capital stock depreciates without replacement. This makes a steady state unsustainable except at zero output, which again implies a consumption level of zero. Somewhere in between is the "Golden Rule" level of savings, where the savings propensity is such that per-capita consumption is at its maximum possible constant value. Y = A(K^(1/2))(N^(1/2)) => y = Ak^.5 = f(k) =>df(k)/dk = .5*A/k^0.5 = 1/4 = .25 according to golden rule , df(k)/dk = n+d =0.02+0.03 = 0.05 hence rate at which capital is accumulated is not consistent with the golden rule.

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