ECON 301 George Washington University Innovation and Growth Worksheet
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ECON 301: Homework 3
General guidelines
Answers must be clear, concise and legible (if hand-written). They
must demonstrate how you arrived at the solution, and make it clear
that you understand the underlying concepts.
Your submitted work must be original and submitted individually,
although you may work in groups to arrive at solutions. Academic
integrity is taken very seriously
1
Innovation and Growth
In the Robert Gordon reading (see Canvas), Robert Gordon talks about the three
industrial revolutions. Describe each revolution briefly and explain why he
believes that the third industrial revolutions was less potent for human economic
growth. Do you agree with him that the innovations of the last few decades are
less impressive than the earlier ones?
2
The Solow Growth Model
1. Generally speaking, how does the Solow Growth Model improve upon the
model of relying on TFP differences to explain growth across countries?
2. Describe, in your own words, the following terms in the Solow Growth Model.
(a) Steady state
(b) The Principle of Transition Dynamics
(c) The capital accumulation equation
3. Consider two countries, Macroland and Microland, that have the same
production function:
1
Y = F(K,L) = AK1/5L4/5
where A denotes the Total Factor Productivity (TFP), K denotes physical
capital and L denotes labor.
Assume that Macroland saves 10% of output a year, while Microland saves
15% of output a year. However, Macroland has better technology (i.e.,
TFP) – its TFP Amacro is 1.6, while the TFP of Microland Amicro is 1.0. Finally,
capital depreciates faster at 8% in Macroland than in Microland, where it
depreciates at 5%.
(a) What is the per worker production function y = f(k)?
(b) Find the steady-state level of capital k per worker for both countries.
Where is it higher?
(c) Find the steady state level of income y per worker for both countries.
Where is it higher?
(d) Draw the Solow diagram for both countries.
(e) Now assume Microland adopts the same technology as Macroland.
Does this help it achieve a higher income per worker?
(f) Suppose Microland cannot adopt the same technology as Macroland.
How would it need to affect its savings rate to achieve the same income
per worker as Macroland?
3
The Solow Model: Dynamics
Consider the Solow diagram below. How would this diagram change with each of
the following changes? For each of the scenarios below, answer the following:
1. Which line moves and how?
2. Does the steady state K increase or decrease?
3. Does total savings increase or decrease?
4. Does total consumption increase or decrease?
5. Does total steady state output increase or decrease?
You must include a diagram with each answer.
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Figure 1: Solow Model Diagram
Scenarios:
1. An increase in the depreciation rate d¯
2. A decrease in saving rate ¯s
3. An improvement in technology, captured in the parameter A
3
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Explanation & Answer:
12 pages
Tags:
macroeconomics
Innovation
growth
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