ECO362H1 Lecture Notes - Lecture 10: Root Mean Square, Productive Forces, Human Capital
Technology Adoption
1 Introduction
Up until now, we have treated economies in isolation. That is, we have assumed that the
decisions of households to accumulate physical and human capital occur in isolation of what
is occuring in other economies. Similarly, we have assume that agents make decisions in
isolation of the consideration of other economies.
In reality, economies are part of an increasingly globalized economy. We can broadly
consider two types of interactions in the global economy: (1) the trade of tangible goods
(e.g. oil); and (2) the trade of intangible goods (e.g. ideas). We will focus on the second
explanation in this note. Specifically, we want to consider the consequences of a country
developing below the frontier.
Until now we have treated all countries identically. There has been no difference in the
models studied between developed and developing countries. This leads to an apparent
inconsistency in the evidence presented at the beginning of the course and the predictions
of the model. We know that some countries experience prolonged periods of rapid growth.
However, throughout most of recent history, the United States and other developed countries
have grown at a consistent pace in terms of TFP. How then do we reconcile these two
differences?
We will consider a model in which innovations at the technology frontier spillover to
developing countries. That is, as innovations occur at the frontier, they reduce the costs of
existing technology, which can then be adopted in countries further from the frontier. This
drives growth in these countries as they are able to piggyback on the innovations of the
frontier economy.
As a final step, we reconcile the apparent contradiction above. Specifically, we show that
a reform in institutions can lead to a period of sustained TFP growth.
Objectives:
1
1. How do we reconcile the rapid growth of some countries with the predictions of our
model?
2. Model of non-frontier growth
References:
•Parente and Prescott (1994, JPE)
•Ayerst (2016, working paper)
2 Example
Before moving to the full model, let’s consider the mechanism in a simplified environment.
Consider a firm of fixed size nwith production technology:
y=zin
where ziis the technology of the firm. The firm chooses between two technologies: a modern
technology with productivity zMand a traditional technology with productivity zT. The
traditional technology can be used without cost while the modern technology has cost x > 0.
The term xcan be thought of as the cost of learning and implementing the technology.
The firm’s profits with technology i∈ {T, M}is then
π(i) = max
izin−xi
where xM=xand xT= 0.
The firm compares the relative profits under the two technologies and adopt the modern
technology if
zMn−x≥zTn
or equivalently if
zM−zT≥x
n
The above inequality highlights the important tradeoff in the adoption of technology: adopt-
ing a more modern technology increases productivity at the cost of a higher fixed cost.
2
There are three important relationships in the above inequality:
1. The higher the technology gap zM−zT, the more likely a firm will adopt the more
productive technology.
2. The lower the cost xof the technology, the more likely a firm will adopt the technology.
3. Larger firms (high n) are able to spread the benefits of the technology over a larger
base. Since the fixed cost is independent of size (xdoes not vary with n), larger firms
are more likely to adopt newer technologies.
The simple model in this section highlights the key features and considerations of technology
adoption. However, we would like to embed this mechanism in a General Equilibrium model
that can incorporate other factors that we have found to be important. The next section
introduces a full model that embeds this type of technology choice in a heterogeneous firm
model. We will see that while the model generalizes the environment, the above three features
of technology adoption still hold.
3 Model
The basic structure of the model follows the firm heterogeneity note. As in the misallocation
note, we assume that there is no entry or exit and that the mass of firms is normalized to
unity.
Households: The economy is populated by households with unit mass.
As there are no dynamics in the households problem, we can solve the household’s problem
period-by-period. The household’s problem is given by
max
ctlog(ct)
subject to
ct≤wt+ Πt
where variables are defined as in the neoclassical growth model. The term Πtis net profits
of firms - that is, households own a portfolio of the equity on any new and existing firms in
the economy. In the representative firm framework we ignored this term as it was equal to
3
Document Summary
Up until now, we have treated economies in isolation. That is, we have assumed that the decisions of households to accumulate physical and human capital occur in isolation of what is occuring in other economies. Similarly, we have assume that agents make decisions in isolation of the consideration of other economies. In reality, economies are part of an increasingly globalized economy. We can broadly consider two types of interactions in the global economy: (1) the trade of tangible goods (e. g. oil); and (2) the trade of intangible goods (e. g. (e. g. oil); and (2) the trade of intangible goods (e. g. ideas). We will focus on the second explanation in this note. Speci cally, we want to consider the consequences of a country developing below the frontier. Until now we have treated all countries identically. There has been no di erence in the models studied between developed and developing countries.
