Suppose an economy is described by the Solow model and output is produced using aCobb-Douglas production function:= K (A₁ Lt)¹-aIn per worker terms the production function can be written as:Y₁ Kt¥ - (K)* 4-²=Lt LtAssume that g = 0 and therefore A can be normalized to 1. Suppose the savingsbehavior is different from what we assumed in class. In particular, below a minimumlevel of output per worker, people cannot save at all because all of the income isused for survival. Above this income level, people are saving a constant fraction ofadditional income earned beyond.Ý₁Lt(a) Show what this means for the evolution of the capital stock per effective workerif output is below Lt'Y₁(b) Show graphically that in this economy it is (technically) possible to have one, twoor three different steady states. For each of the steady states that you identify(in each of the three cases) briefly discuss if the steady states are (locally) stable.

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Chapter1: Making Economics Decisions

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Question

Suppose an economy is described by the Solow model and output is produced using a
Cobb-Douglas production function:
= K (A₁ Lt)¹-a
In per worker terms the production function can be written as:
Y₁ Kt
¥ - (K)* 4-²
=
Lt Lt
Assume that g = 0 and therefore A can be normalized to 1. Suppose the savings
behavior is different from what we assumed in class. In particular, below a minimum
level of output per worker, people cannot save at all because all of the income is
used for survival. Above this income level, people are saving a constant fraction of
additional income earned beyond.
Ý₁
Lt
(a) Show what this means for the evolution of the capital stock per effective worker
if output is below Lt'
Y₁
(b) Show graphically that in this economy it is (technically) possible to have one, two
or three different steady states. For each of the steady states that you identify
(in each of the three cases) briefly discuss if the steady states are (locally) stable.

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