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Consider the basic solow model. Assume total labor is fixed at L = 1. Time is discrete, and indexed by t = 0; 1; 2; ::: The production function is Cobb Douglas:
yt = f (kt) = Akta
where yt is per capita income at time t and kt is capital per capita at time t. The law of motion for the capital stock is
kt+1 = (1?) kt + it
where it is per capita investment. The economy consumes a constant fraction of output:
ct = (1 s) yt
where s 2 (0; 1). Assume that the economy starts with initial capital k0 > 0:
1. Show that equation (1) implies that per capita investment is also a constant fraction of per capita income. Which equation, which was not stated in the set up of this question, do you need to show this?
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