Download Dupuit triangle and dynamic costs

 Charles van Marrewijk
Growth and the costs of protection, Romer model; 1
Suppose a producer is about to introduce a new good on the market;
the demand schedule for the good is given in the figure below.
The producer has to determine the price to
charge the consumers. Whatever the method
she uses to do this, let’s say this price is P.
price
demand
The consumers then demand Q
units of the new good.
P
Q
quantity
 Charles van Marrewijk
Growth and the costs of protection, Romer model; 2
The value to consumers of Q units of the new good is represented by
the area under the demand curve.
The revenue for the producer, what she can
price
use to recover her cost, is only P*Q
demand
The difference between the value to the
consumers and the revenue for a producer
is a surplus generated by the market.
So what are the costs of NOT
introducing a new good on the market?
P
They can be represented by the
DUPUIT triangle measuring
market surplus.
Q
quantity
 Charles van Marrewijk
Growth and the costs of protection, Romer model; 3
Imagine a small developing economy that depends on R&D in the
rest of the world for developing new types of capital goods. The
capital goods are indexed by i = 1,..,N; the volume of capital good i
imported is xi; the country has L labor available; output is Y and the
N
production function is given by:
0.5 
0.5 
Y  L  xi 
 i 1

The producers in the small developing economy are price takers,
while the producers of capital goods are engaged in monopolistic
price competition; they thus charge twice the marginal cost of
production and earn operating profits [p(1-1/) = MC;  = 1/0.5 = 2].
The marginal costs are the same for all producers (so they all charge
the same price), but the fixed cost of introducing the capital good on
the market of the small developing economy varies from one
producer of capital goods to another: we arrange them such that
the fixed introduction costs increase with i, say linearly.
 Charles van Marrewijk
Growth and the costs of protection, Romer model; 4
We can draw a diagram of operating profits and introduction costs.
We depict the operating profits as a horizontal line because
they are the same for all producers of capital goods.
The costs of
Introduction costs
introducing
new varieties
rises with i (by
construction)
profits
The point of intersection determines
which capital goods will be
profitable to introduce and which
will not, that is it determines N
N
i
 Charles van Marrewijk
Growth and the costs of protection, Romer model; 5
What happens if the small developing country imposes import
restrictions, say a tax tau on the purchases of foreign goods?
It lowers the revenue for producers of capital goods to (1-tau)*p*x
Thus operating profits fall.
Introduction We now distinguish
between 2 different
costs
scenarios:
profits
The ‘surprise’ scenario,
which we will associate
with short term
and the ‘expected’ scenario,
which we will associate with
long term cost of protection.
N
i
 Charles van Marrewijk
Growth and the costs of protection, Romer model; 6
In the ‘surprise’ scenario the tax is imposed after the producers of
capital goods have made their entry decision.
The number of capital goods introduced on the market remains N
The ‘surprise’ tax
implies some of the
Introduction producers of capital
costs
goods will make a
profits
loss; it is still the best
they can do in the new
situation because the
introduction costs are
sunk cost.
It turns out that the production loss
for the developing economy of the
tax is then given by:
tau2.
i
N
 Charles van Marrewijk
Growth and the costs of protection, Romer model; 7
In the ‘expected’ scenario the producers know that the tax is
introduced before they make their entry decision.
The number of capital goods introduced on the market
falls as a consequence of the tax (from N to N)
It turns out that the
Introduction production loss for the
costs
developing economy
of the tax is then given
by:
2*tau2*tau3+tau4.
NB 1: the introduction of new
capital goods raises productivity;
NB 2: this is an example only.
profits
N
N
i
 Charles van Marrewijk
Growth and the costs of protection; 8
1
welfare loss
Dynamic; include
variety effect
E1
Static; ignore
variety effect
E0
0
0
1
tariffs