Exercise 1 (The Golden Rule) Consider an economy in which in any year t, output per capita,

denoted yt, is produced by the technology

yt = kt^0.3

where kt denotes capital per person. Assume that the capital stock depreciates at the rate of 10

percent per year. Assume further that population is constant.

1. Calculate the savings rate associated with the Golden Rule. In addition, calculate the

steady-state levels of capital per person, output per person, and consumption per person under

the Golden Rule, denoted kGR, yGR, and cGR, respectively.

2. Suppose that people discount future consumption. Specifically, assume that the subjective

discount factor, denoted , is 0.96. Calculate the optimal steady-state savings rate.

Calculate also the steady-state levels of capital per person, output per person, and

consumption per person under the optimal steady-state savings rate, denoted kOPT , yOPT ,

and cOPT , respectively

Can you please explain the second question? How do I derive the modified golden rule?