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Dead Weight Loss In Welfare Under Monopoly

  Dead Weight Loss in Welfare under Monopoly

Illustration 77

A monopolist countenances a demand curve R = 500 – 5V. If marginal invariable and is equal to $40. What is the volume of profits made by the monopolist? What is dead weight welfare loss with regards to monopoly?

Solution

For monopoly symmetry, MR = MC

The provided demand curve is:          R         =          500 – 5V

                                    TR       =          R.V     =          500V – 5V^2

                                    MR      =          dTR     =          dRV    =          500 – 10V
                                                             dV                   dV

Equating MR with MC = 40, we have,

                                    500 – 10V       =          40

                                                10V     =          460

                                                V         =          460 / 10           =          46

To procure symmetry price, we substitute V = 46 in the provided demand equation. Therefore,

                                    R         =          500 – 5 (46)

                                                =          500 – 230

                                    R         =          270

Welfare is optimised when at the productivity manufactured price equals marginal cost as under conditions of perfect rivalry. Therefore, equating price with marginal cost we have,

                                    R         =          MC

                        500 – 5V         =          40

                                    5V       =          460

                                    V         =          460 / 5 =          92

Dead weight loss of welfare from monopoly is shown in the below graphic presentation. Consumer’s excess with productivity equal to 92 parities to the region DPE.

Monopoly limits productivity to 92 and enhances rate R to $270 or OP’. Therefore, under monopoly, consumer excess is diminished to the region DP’H. Therefore, consumers undergo a loss of welfare that is consumer’s surplus) parities to the region PP’HE.

The monopolist’s profits as a consequent of limitation of productivity from 92 units to 46 units and enhancing of rate R of the commodity from $40 to $270 which is equal to the region PNPH’ that is 92 * 46 = $4,232.

However consumers undergo a greater loss of consumer excess, which parities the region PP’HE, i.e. NHE more than the profits of the monopolist. The welfare loss of consumers’ parities to the region NHE denotes the dead weight loss of welfare and is:

            =          ½ (92*46)        =          4232 / 2           =          2,116.

This dead weight loss denotes social cost of monopoly.

Illustration 78

The following demand function and total cost function of a monopolist are provided. Compute his marginal revenue and marginal cost. At what level of productivity, the monopolist will be in symmetry.

What price will be set at the symmetry productivity and compute total profits made by him?


Rate – R in $

Volume Sold – V in units

Total Cost in $

20

1

18

18

2

22

16

3

30

15

4

42

14

5

52

13

6

65

12

7

74

Solution

On account to determine the marginal revenue MR we have to first compute total revenue MR = TRn – TRn-1 and marginal cost which is TCn – TCn-1. The monopolist will be at symmetry at the level of productivity at which MR = MC we have the below tablet.

Rate – R in $

Volume Sold – V in units

Total Revenue (R * V)

Marginal Revenue (TRn – TRn - 1)

Total Cost in $

Marginal Cost (TCn – TCn - 1)

20

1

20

20

18

18

18

2

36

16

22

4

16

3

48

12

30

8

15

4

60

12

42

12

14

5

70

10

52

10

13

6

78

8

65

13

12

7

84

6

74

9

It is to be noted from the above that the tablet shows MR = MC when the volume of units sold is 5. Hence to be at symmetry the monopolist will manufacture 5 units to optimise his profits.

Price    =          AR      =          TR
                                                 V

                                    =          70        =          14
                                                 5

Total profits   =          TR – TC         =          70 – 52            =          18

Illustration 79

Presume a monopolist faces the following demand agenda.

Demand Agenda

Rate – R

Volume - V

80

0

70

5

60

10

50

15

40

20

30

25

20

30

  1. Compute the Marginal Revenue. If marginal cost is $30, what would be the profit optimising level of productivity and price?
  1. If price is fixed to marginal cost, what would be the productivity that the monopolist would manufacture?

Solution

  1. It is to be noted in this problem that volume demanded or sold enhances by difference of 5 units. And rate varies by 10 units. This is an important factor to be remembered while calculating marginal revenue.

To procure, marginal revenue we have to first compute total revenue TR which parities to V * R. Then marginal revenue MR = ΔTR / ΔV. We can compute the MR as below…

Rate – R
In $

Volume Demanded or Sold – V

Total Revenue – TR – V*R

Marginal Revenue ΔTR / ΔV

80

0

0

0

70

5

350

350/5 = 70

60

10

600

250/5 = 50

50

15

750

150/5 = 30

40

20

800

50/5 = 10

30

25

750

-50/5 = -10

20

30

600

-150/5 = -30

Provided marginal cost parities to $30, the profit optimising clause of MC = MR is satisfied when 15 units of commodities are demanded. It will be seen from the above table that with 15 units of productivity sale price of the commodity is $50 per unit.

  1. If price is set parity to marginal cost i.e. at $30, then as in the table above, 25 units of commodities will be manufactured and sold by the monopolist.

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