# Surplus Capacity Under Monopoly Rivalry And Price Productivity Equilibrium

__Illustration 80__

Presume price elasticity of demand for the product of a monopolist is 4.0. Demonstrate that price set by him will be twice the marginal cost of manufacturing.

__Solution__

In Price-Productivity Symmetry of the monopolist MR = MC

Therefore,

MR = R (1 - 1/e)

MC = R (1 - 1/e)

e = 4.0

MC = R (1 – ¼)

= ¾ R

**Or, R = 4/3
MC**

__Illustration 81__

Provided the following linear demand and cost functions, demonstrate that monopolist will manufacture one half the productivity under perfect rivalry.

V = 200 – 4R (it’s a linear demand function)

TC = 100 + 20R

__Solution__

TC = 100 + 20R

MC = __ΔTC__ = 20 …..Equation
(1)

ΔV

Now, the provided linear demand function is

V = 200 – 4R

4R = 200 – V

R = __200__ - __V__

4 4

= 50 – ¼ V ….Equation (2)

TR = R*V = 50V – 0.25V^2

MR = __dRC__ = 50 – 0.5V …..Equation
(3)

dV

Productivity under perfect rivalry is ascertained where MC = R

Therefore, under perfect competition

20 = 50 – 0.25V

0.5V = 50 – 20

V = 30 / 0.25

Hence, Vrc = 120 …..Equation (4)

At Symmetry, under monopoly,

MR = MC

From Equation (3) we know MR = 50 – 0.5V and from Equation (1) we know MC = 20.

Therefore, at symmetry under monopoly

50 – 0.5V = 20

0.5V = 50 – 20

V = 30 / 0.5

Vm = 60 …..Equation (5)

**Comparing (4) and (5) we find that productivity under monopoly is half of that
manufactured under perfect rivalry.**

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**Other topics under Prices And Productivity Decisions In Various Market Structures:**

- Dead Weight Loss in Welfare under Monopoly
- Establishment of Price and Productivity under Oligopoly Rivalry
- Government Strategies towards Monopoly and Rivalry
- Non-Price Rivalry Advertising Outlay
- Perfect Rivalry under Short Run
- Price and Productivity Determination under Perfect Rivalry
- Pricing and Productivity under Monopoly Rivalry
- Perfect Rivalry at Symmetry Level
- Selling Outlay Distinguished from Production Outlay
- Stackelberg's Model
- Surplus Capacity under Monopolistic Competition