Excel Problem. Suppose that you have a standard Solow model with a Cobb-Douglas production function.

The central equation of the model can be written: kt+1 = sA(kt)^ + (1 )kt .

Output per worker is given by: yt = A(kt)^.

Consumption per worker is given by: ct = (1 s)yt .

(a) Suppose that A is constant at 1. Solve for an expression for the steady state capital per worker, steady state output per worker, and steady state consumption per worker.

(b) Suppose that = 1/3 and = 0.1. Design an Excel sheet with a grid of values of s ranging from 0.01 to 0.5, with a gap of 0.01 between entries (i.e. you should have a column of values 0.01, 0.02, 0.03, and so on). For each value of s, numerically solve for the steady state values of capital, output, and consumption per worker. Produce a graph plotting these values against the different values of s. Comment on how the steady state values of capital, output, and consumption per worker vary with s.

(c) Approximately, what is the value of s which results in the highest steady state consumption per worker? Does this answer coincide with your analytical result on the previous question?