The Economics of Ideas

ECOS2002 Intermediate Macroeconomics
Week 3:
Christopher Gibbs
University of Sydney
Semester 1, 2021
The Economics of Ideas
• As we have seen K and L have a hard time explaining
growth.
• We are mostly left with A (TFP) to do the heavy lifting.
• Today we are going to try to give the A some substance.
– Paul Romer’s “idea about ideas.”
The Economics of Ideas
The Ideas Diagram
Ideas ) nonrivalry ) increasing returns ) problems with pure
competition.
Ideas
• the raw materials of universe”
– How the physical world works.
– How to manipulate the physical world.
– The amount of resources on the planet is finite, but the
ways in which we can manipulate them for our benefit is
seemingly endless.
Nonrivalry
Definition (Rivalrous)
One person’s use of a good reduces its inherent usefulness to
someone else.
• Example
1. Pizza
2. Cars
3. Clean drinking water
Nonrivalry
Definition (Nonrivalrous)
One person’s use of a good does not reduce its usefulness to
someone else.
• Example
1. Ideas
2. Software
Nonrivalry
Definition (Excludability)
The extent to which someone has property rights over a good
and can exclude others from using it.
• This of course is a huge issue because the creation of new
ideas is costly, but once created it is hard to profit from an
idea because it is hard to exclude others from using it.
Increasing Returns
• Ideas can generate increasing returns to scale production.
– A good example of this is in the case of software.
– Suppose it costs $1,000,000 to produce a new piece of
software.
– The first copy of that software literally costs $1,000,000.
– However, the marginal cost of production of the software is
essentially zero. Therefore, we can scale production up
without needing to add more labor or capital.
Problems with Pure Competition
• Recall the conclusions of perfect competition:
– Price is competed down to the point where
Marginal Cost = Marginal Revenue = P
• Now in our software example, if price is equal to marginal
cost, then firms will receive zero income for their ideas.
• They cannot recover their development costs and therefore
have no incentive to create new ideas.
Problems with Pure Competition
• Therefore, in order to incorporate innovation into a model
we need to step away from perfect competition.
• Recall that this was a key assumption behind the models
we have seen so far.
– Prices P are taken to be exogenous.
– This assumption is only valid in the perfectly competitive
world.
Problems with Pure Competition
• Implications of this insight:
– Clear role for government
– Role for patents and copyrights
– Explanation for trade secrets
– Example: Only a few people in the world have ever seen
the exact recipe for Coca-Cola.
– Government subsidized research and development
Summary
• Solow model does not predict sustained growth.
– Capital does not grow indefinitely in the model.
• Ideas, however, can make the same capital produce more
over time and encourage long run growth.
• Ideas, therefore, may explain sustained growth.
– However, there must exist proper mechanisms to sustain
production of ideas because under perfect competition the
production of new ideas may not be profitable.
The Romer Model
• Now let formalize the idea of “ideas” into a model.
• What are the components we need?
1 A theory of how ideas are produced i.e. an ideas
production function.
2 A way to integrate the ideas into our old production
function.
3 A way to allocate resources into the ideas production
function and goods production function.
The Romer Model
Goods Production:
Yt = AtLy;t (1)
where At is the stock of ideas and Ly;t is the labour working in
goods production.
Ideas Production:
∆At+1 = ¯ zAtLa;t (2)
where ∆At+1 = At+1 – At, ¯ z is our new TFP variable, and La;t
is labour devoted to the production of new ideas.
The Romer Model
Labour:
L = La;t + Ly;t (3)
where L is total labour available in the economy.
For simplicity we assume
La;t = γL
where 0 < γ < 1.
The Romer Model
The Romer Model
Unknowns/Endogenous Variables Yt, At, Ly;t, La;t
Goods Production Function Yt = AtLy;t

Parameters: ¯ z, L¯, γ, A¯0
The Romer Model
Solution to the Romer Model:
yt = A¯0(1 – γ)(1 + g)t (4)
where g = ¯ zγL¯.
The Romer Model
yt = A¯0(1 – γ)(1 + g)t
Note that this model predicts sustained growth.
• Intuition:
– There is no diminishing returns to the stock of ideas.
– As long as researcher keep producing new ideas, the effect
of the new ideas continually increases productivity.
The Romer Model
∆At+1 = ¯ zAtLa;t
• Note:
1 Production is linear.
2 No diminishing returns to production of new ideas.
3 Old ideas continue to help us produce new ideas.
4 This is due to nonrivalry.
The Romer Model
• The Balanced Growth Path
– There are no transition dynamics in the Romer Model.
– GDP per capita just grows at a constant rate equal to the
growth rate ¯ g.
– There is no steady state in the model.
– The equivalent notion we use is called the balanced
growth path, which means the growth rates of all
endogenous variables are constant.
The Romer Model
• What does the Romer model tell us?
1 Sustained economic growth requires increasing returns.
2 Increasing returns requires nonrivalrous goods.
3 Ideas are nonrivalrous because one person’s or firm’s use
does not diminish its value.
Extensions of the Romer Model
• Diminishing returns to ideas:
∆At+1 = A¯β t La;t (5)
where β controls the degree of returns to ideas.
• Note about Cobb-Douglas production: there is
increasing returns to scale in production as long as
the exponents on the factors add to more than 1.
Extensions of the Romer Model
• Connecting the Romer Model to the Solow Model.
Yt = AtKt1=3L2 y;t =3
∆Kt+1 = ¯ sYt – δKt
∆At+1 = ¯ zAtLa;t
Ly;t + La;t = L¯
La;t = γL¯
The Romer Model
• Growth rate of output on the balanced growth path:
gY∗ = 3
2
g¯ =
3 2
zγ ¯ L¯ (6)
• Output per person on the balanced growth path:
yt∗ = YL¯t∗ = 3 s¯
2zγ ¯ L¯ + δ!1=2 A3 t =2(1 – γ) (7)
Growth Accounting
Growth Accounting
Production Function:
Yt = AtKt1=3L2 y;t =3
In growth rates this is
gY;t = gA;t +
1 3
gK;t +
2 3
gLy;t
Assume that total hours worked may also change over time, i.e
gY;t – gL;t = gA;t +
1 3
(gK;t – gL;t) + 2
3
(gLy;t – gL;t)
Note if gL;t = 0, we return to the above.
Growth Accounting
gY;t – gL;t = gA;t +
1 3
(gK;t – gL;t) + 2
3
(gLy;t – gL;t) (8)
• Equation (8) tells us that growth can be broken up into
three terms.
• Now everything in equation (8) is measurable with the
exception of TFP. So let’s take it to the data.
Growth Accounting
Growth Accounting for the US
1948-11 1948-73 1973-95 1995-07 2007-11
Output per hour 2.5 3.3 1.5 2.7 1.9
Contribution of K=L 0.9 0.9 0.7 1.1 1.1
Contribution of Ly 0.2 0.2 0.3 0.2 0.4
Contribution of TFP 1.4 2.2 0.5 1.5 0.4
Table: y Labour composition. Source: Jones (2013)
Growth Accounting
Parting thoughts on Long-run Growth
• What we know:
– Capital accumulation alone cannot account for economic
growth.
– However, capital accumulation does explain some of the
cross-sectional differences.
– Ideas and technology may be an explanation for sustained
growth.
• What we don’t know:
– Why such a large part of growth (TFP) cannot be
explained.

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