    # 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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