Question

An economy with a population growth rate at 2 percent and a rate of technological growrh at 3 percent is in steady state. If the capital-output ratio is 2, depreciation amounts to 10 percent of GDP, and capital income is 20 percent of GDP, then this economy would need to ......... the Golden Rule steady state.

(Please, is it to decrease or increase saving rate, s, or do nothing. OR do I decrease the steady state stock of capital per effective worker to reach GR steady state. Kindly include workings - many thanks)

Answer 1

GIVEN:

1. Population growth rate, n = 2%,
2. Rate of technological growth, g = 3%,
3. Capital-Output ratio (k/y) = 2 or, k = 2y,
4. Depreciation of Capital (∂k) = 10% of GDP, or ∂k = 0.1y,
5. Capital Income, (MPK * k) = 0.2y

NOW,

• We solve for depreciation by dividing 4 by 3,

(∂k/k) = (0.1y/2y) = 0.05

Or, ∂ = 0.05

• We solve for MPK by dividing 5 by 3,

(MPK * k)/k = (0.2y/2y)

Or, MPK = 0.1

Thus, about 5% of Capital stock depreciates every year and the MPK is about 10% every year.

Return to Capital or, Net MPK is: (MPK - ∂) = 0.05 or 5% every year

Economy’s average growth rate: (n + g) = 5%

Thus, the economy has optimum savings rate and it does not have to do anything about the savings rate.