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Chapter 11. Market and Price Discrimination
Price discrimination is also known as two-price and multiple price or
market prorates plans. The main idea behind price discrimination is
total revenue can be increased by charging higher (lower) prices and
selling less (more) to consumers with inelastic (elastic) demand. For
this to happen, it is necessary there is no arbitrage between two
groups of consumers and also there should be some centralized
monopoly authority that controls the distribution of total supplies into
each separate market.
Because the international market is generally larger in total than the
domestic market, demand responsiveness to price can be expected to
be larger in the international market than in the domestic market.
This chapter covers the following aspects of price discrimination:
1. Consequences of discriminatory allocation of fixed supply.
2. We will discuss how enhanced returns from discrimination can
be distributed among producers and how it affects output supply
and resource allocation.
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Total supply is q = ac
Dh is domestic demand drawn with a as origin
Dx is export demand drawn with c as origin
Free market without price discrimination: q =Dx + Dh (total
supply=total demand) and price is at po and quantity is at d.
But revenue can be maximized by setting prices such that MR in both
markets are equal. MRh is the MR curve of the domestic demand
curve. MRx is the MR curve of the export demand curve.
Under price discrimination domestic price is Ph and export price is Px.
Caution should be taken to impose binding import controls to prevent
the domestic market from being inundated from abroad.
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Math to show the price discrimination:
Revenue from domestic (home) market: ph(qh) * qh
Revenue from foreign market: px(qx) * qx
Total revenue from both the markets: ph(qh) * qh + px(qx) * qx
Total sales in both markets should equal to total supply: q = q h + q x
The objective is to maximize total revenue with respect to qh and qx
and subject to a given supply.
£ = p h (q h ) * q h + p x (q x )* q x + λ (q − q h − q x )
 q dp 
d£
dp
= p h + q h h − λ = p h 1 + h h  − λ = 0
dq h
dq h
 p h dq h 
 q dp 
d£
dp
= p x + q x x − λ = p x 1 + x x  − λ = 0
dq x
dq x
 p x dq x 
Note, the elasticity of domestic demand is - e h =
−
p h dq h
, and thus,
q h dp h
1 q h dp h
. Note, the elasticity of foreign demand is
=
e h p h dq h
-ex =
p x dq x
1 q dp
, and thus, − = x x .
q x dp x
e x p x dq x

1
p h 1 −
 eh


1
and
,
=
λ
p
1−

x 
 ex


=λ

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
1
ph 1 −
 eh


1  MR = MR
h
x
=
p
1
−

,
x 
e


x 

1
1
−


ph  ex 
, p h > p x if e x > e h
=
px 
1
1 − 
 eh 
Price will be lower in the market with more elastic demand.
Market discrimination of this kind with a fixed supply uses unequal
market prices to redistribute economic value away from domestic
consumers toward domestic producers.
Now we will examine how the distribution of revenue occurs. There
are two approaches. First, to pool the aggregate proceeds of all sales
from domestic and foreign markets, subtract operating expenses, then
pay producers a weighted average or blend price for each unit
marketed. Second, to distribute the higher domestic returns among
eligible producers according to pre-arranged formula (entitlement or
quota approach)
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It is also possible for the board to keep all or part of the
discrimination proceeds as government revenue, returning only the
world price (or less) to its producers.
ph is domestic price
pw is world price
pb is weighted average of ph and pw
The blend price situation (first approach) generates a different result.
Since pb is higher than pw, an individual grain producer receiving the
blend price will equate marginal revenue and marginal cost at point g.
This generates the larger grain output oe. But each output beyond d is
sold at pw, and each costs an incrementally higher amount. The
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shaded area is the individual producer’s loss because of producing de
units of grain and selling them at pw.
oc is prorated entitlement (second approach) sold in the domestic
market. Under the entitlement approach, producers receive the
amount haco from the domestically sold portion of output, and bfdc
based on the per-unit value of pw from the world market. Hence, pw is
the producer’s marginal revenue. In principle the producers will
equate that value with marginal cost, producing a total output of od.
The marginal value on the last unit of output price is equal to
marginal cost at point f.
Both approaches lead to more exports than with free trade, but the
blend-price approach is the more expansionary of the two.
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In the blend-price case, the blend price will lie above pw but below ph.
This blend price will generate more output than oe and result in more
exports than oa.
In the entitlement case, domestic consumption is fixed at ph. For this
ph, the corresponding excess supply is ES*. When the market
discriminating board employs a producer payment scheme based on
pw for output beyond oc, exports are ob. The higher domestic price
shrinks internal use below free market consumption. This amount
must then be exported by the board