# Degree Of Price Discrimination

__Illustration 85__

Presume the single monopoly price is $30 and price elasticity of demand in markets X and Y are 4 and 10 correspondingly. Determine the Marginal revenues of X and Y.

__Solution__

MR
in Market X = ARx __ex– 1 __

ex

= 30 __4 – 1__

4

= 30 * ¾

= 22.5

MR
in Market Y = ARy __ey– 1 __

ey

= 30 __10 – 1__

10

= 30 * 9/10

= 27

It is therefore unambiguous that marginal revenue in the two markets is varied when price elasticities of demand at the single monopoly price are diverse. Moreover from the above, illustration it is obvious that the marginal revenue in the market in which price elasticity is lesser.

Now, it is profitable for the monopolist to transfer some volume of the commodity from the market X where elasticity is low and thus marginal revenue is less to the market Y where elasticity is low and thus marginal revenue is huge.

In this method the loss of revenue by decreasing sales in market X by some marginal units will be smaller than the gain in revenue from enhancing sales in market Y by those units.

Therefore, in the above illustration, if one unit of commodity is reserved from market X the loss in income will be $22.5 whilst with the supplementary to sales by one by additional unit of the commodity in market Y the gain in income will be about $27.

It is unambiguous that the devolution of some units of the commodity will be profitable when there is diversity in price elasticities of demand and hence in marginal revenues.

__Illustration 86__

Presume complete value of price elasticity in market X parities to 4 and in market Y
parities to 6, then

__6 – 1__ __5__

__Px__ = __ 6 __ = __ 6 __

Py __4 – 1__ __3__

4 4

= __5 __* __ 4__

6 3

= 10 / 9

Therefore, when elasticities in markets X and Y are 4 and 6 correspondingly, the prices in the two markets will be in the ration 10:9.

From the foregoing study it follows that the subsequent two clauses are needed to be fulfilled for the symmetry of a discriminating monopolist:

(1) Aggregate Marginal Revenue AMR = Marginal Cost MC of the aggregate productivity.

(2) MRx = MRy = MC

__Illustration 87__

Presume a discriminating monopolist is selling a commodity in two diverse markets in which demand functions are:

R1 = 24 – V1

R2 = 40 – V2

The monopolist’s aggregate cost function is

TC = 6 + 4V

As an economic adviser you are asked to ascertain the prices to be charged in the two markets and volume of productivity to be sold in each market so that profits are optimised. You are also required to compute the aggregate profits to be made from the strategy of price discrimination. What advice will you provide?

__Solution__

As profits in case of price discrimination are optimised when MR1 = MR2 = MC. Thus, we have to compute the marginal revenue in the two markets from the provided demand functions of the two markets.

Aggregate revenue in market 1 = R1V1 = 24V1 – V1^2 …..(1)

MR1 in market 1 = __Δ(R1V1)__ = 24 – 2V1

ΔV1

Aggregate revenue in market 2 = R2V2 = 40V2 – V2^2 …..(2)

MR2 in market 2 = __Δ(R2V2)__ = 40 – 2V2

ΔV2

We can obtain the marginal cost from the aggregate cost function

TC = 6 + 4V

MC = __ΔTC__ = 4

ΔV

Profit optimising volume of productivity to be sold in the two markets is ascertained by applying the symmetry condition MR1 = MR2 = MC and solving the following equations:

MR1 = MC

24 – 2V1 = 4

2V1 = 24 – 4

V1 = 20 / 2

V1 = 10

MR2 = MC

40 – 2V2 = 4

2V2 = 40 – 4

V2 = 36 / 2

V2 = 18

Substituting these symmetry productivities V1 and V2 in the demand functions we procure the profit optimising prices:

R1 = 24 – V1 = 24 – 10 = 14

R2 = 40 – V2 = 40 – 18 = 22

Aggregate profits can be procured in the usual method.

Aggregate Profits π = (TR1 + TR2) – TC

= P1V1 + P2V2 – (6 + 4V)

= (14*10) + (22*18) – [6 + 4(10 +18)]

= 140 + 396 – 280 = 256

__Illustration 88__

A developing nation’s monopoly industry sells its commodity in its and to a developed nation’s markets. The developing nation’s demand function for the commodity is Ri = 200 – Vi and the US demand function for the commodity is Ru = 160 – 4Vu where both prices are measured in dollars.

The industry’s marginal cost of commodity is $40 in both the nations. If the developing nation’s monopoly industry can prevent any resale what price will it charge in both markets?

__Solution__

It is to be noted that the markets inverse demand functions are provided such as Ri = 200 – V1 and Ru = 160 – 4Vu. In order to ascertain the symmetry productivity prices in the two markets we have to first ascertain the marginal revenue functions corresponding to the provided linear demand functions.

Moreover, the marginal revenue is twice as sheer as the incline of the linear demand function. Thus,

Marginal revenue
in the developing nation's market MRi = 200 – 2Vi

Marginal
revenue in the developed nation is MRu
= 160 – 8Vu

As resale of the commodity among one market to another is not feasible the monopolist industry will equate the marginal revenue in each market with the provided marginal cost which parities to 40.

Therefore, in developing
nation,

MRi = 200 – 2Vi = 40

200 - 40 = 2Vi

160 = 2Vi

160 / 2 = Vi = 80 units

Likewise in developed nation,

MRu = 160 – 8Vu = 40

160 – 40 = 8Vu

120 = 8Vu

120 / 8 = Vu = 15 units.

Now, in order to ascertain the prices varied in the two markets we substitute the symmetry volumes sold in the two markets in their demand functions. Therefore,

Substituting, Vi = 40 in the demand function of developing nation, we get

Ri = 200 – Vi

= 200 – 40 = 160

Substituting, Vu = 15 in the demand function of developed nation, we get

Ru = 160 – 4*15

= 160 – 60 = 100

Therefore, price discriminating monopolist charges price of $160 in developing nation whilst he sells at $100 in the developed nations.

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