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Surplus Capacity under Monopoly Rivalry and Price Productivity Equilibrium Homework Help, Tutoring
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Surplus Capacity under Monopoly Rivalry and Price Productivity Equilibrium
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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