Final answer:
In a Cobb Douglas production function, the expressions for k∗, y∗, and c∗ can be derived using the parameters of the model. The saving rate needed to achieve the golden-rule capital stock can also be determined.
Step-by-step explanation:
In a Cobb Douglas production function, the output (Y) is a function of capital (K) and labor (L) raised to certain exponents, represented by α and (1-α) respectively. The expression for k∗, the golden-rule value of capital, is given by:
k∗ = (s/(n+g+δ))1/(1-α)
where s is the saving rate, n is the population growth rate, g is the technological growth rate, and δ is the depreciation rate. The expressions for y∗ (output per worker) and c∗ (consumption per worker) are:
y∗ = (k∗)α
c∗ = (1-s) * y∗
The saving rate needed to achieve the golden-rule capital stock is:
s∗ = (n+g+δ-αg)/(1-α)