Monopolist optimizing price: Dead weight loss (video) | Khan Academy

Determining Deadweight Loss

In economics, deadweight loss is a loss of economic efficiency that occurs when equilibrium for a good or service is not Pareto optimal. When a good or service is not Pareto optimal, the economic efficiency is not at equilibrium.

As a result, when resources are allocated, it is impossible to make any one individual better off without making at least one person worse off. When deadweight loss occurs, there is a loss in economic surplus within the market. Deadweight loss implies that the market is unable to naturally clear.

Deadweight loss is the result of a market that is unable to naturally clear, and is an indication, therefore, of market inefficiency. The supply and demand of a good or service are not at equilibrium.

  • imperfect markets
  • externalities
  • taxes or subsides
  • price ceilings
  • price floors

In order to determine the deadweight loss in a market, the equation P=MC is used. The deadweight loss equals the change in price multiplied by the change in quantity demanded. This equation is used to determine the cause of inefficiency within a market.

For example, in a market for nails where the cost of each nail is $0.10, the demand will decrease from a high demand for less expensive nails to zero demand for nails at $1.10. In a perfectly competitive market, producers would charge $0.

10 per nail and every consumer whose marginal benefit exceeds the $0.10 would have a nail. However, if one producer has a monopoly on nails they will charge whatever price will bring the largest profit.

If they charge $0.60 per nail, every party who has less than $0.60 of marginal benefit will be excluded. When equilibrium is not achieved, parties who would have willingly entered the market are excluded due to the non-market price.

An example of deadweight loss due to taxation involves the price set on wine and beer. If a glass of wine is $3 and a glass of beer is $3, some consumers might prefer to drink wine. If the government decides to place a tax on wine at $3 per glass, consumers might choose to drink the beer instead of the wine.

image

Deadweight loss: This graph shows the deadweight loss that is the result of a binding price ceiling. Policy makers will place a binding price ceiling when they believe that the benefit from the transfer of surplus outweighs the adverse impact of the deadweight loss.

Monopolist optimizing price: Dead weight loss

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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In economics, deadweight loss is a loss of economic efficiency that occurs when equilibrium for a good or service is not Pareto optimal.

Learning Objectives

Define deadweight loss, Explain how to determine the deadweight loss in a given market.

Key Takeaways

Key Points

  • When deadweight loss occurs, there is a loss in economic surplus within the market.
  • Causes of deadweight loss include imperfect markets, externalities, taxes or subsides, price ceilings, and price floors.
  • In order to determine the deadweight loss in a market, the equation P=MC is used. The deadweight loss equals the change in price multiplied by the change in quantity demanded.

Key Terms

  • equilibrium: The condition of a system in which competing influences are balanced, resulting in no net change.
  • deadweight loss: A loss of economic efficiency that can occur when equilibrium for a good or service is not Pareto optimal.

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Analyse the equilibrium price and output equilibrium under monopoly and perfect competition. Show and explain the deadweight welfare loss under monopoly and consider when a monopoly might be more productively efficient than a competitive market.

A profit-maximising firm in a perfectly competitive industry will produce at the productively and allocatively efficient level of output

The conventional argument against market power is that monopolists can earn abnormal (supernormal) profits at the expense of efficiency and the welfare of consumers and society.

The monopoly price is assumed to be higher than both marginal and average costs leading to a loss of allocative efficiency and a failure of the market. The monopolist is extracting a price from consumers that is above the cost of resources used in making the product and, consumers’ needs and wants are not being satisfied, as the product is being under-consumed.

The higher average cost if there are inefficiencies in production means that the firm is not making optimum use of scarce resources. Under these conditions, there may be a case for government intervention for example through competition policy or market deregulation.

X Inefficiencies under Monopoly

The lack of competition may give a monopolist less incentive to invest in new ideas. Even if the monopolist benefits from economies of scale, they have little incentive to control their costs and ‘X’ inefficiencies will mean that there will be no real cost savings compared to a competitive market.

A competitive industry will produce in the long run where market demand = market supply. Consider the diagrams below. Equilibrium output and price is at Q1 and Pcomp on the left hand diagram and Pcomp and Q1 on the right hand diagram. At this point, Price = MC and the industry meets the conditions for allocative efficiency.

Monopolist optimizing price: Dead weight loss (video) |
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If the industry is taken over by a monopolist the profit-maximising point (MC=MR) is at price Pmon and output Q2. The monopolist is able to charge a higher price restrict total output and thereby reduce welfare because the rise in price to Pmon reduces consumer surplus. 

Some of this reduction in welfare is a pure transfer to the producer through higher profits, but some of the loss is not reassigned to any other agent. This is known as the deadweight welfare loss or the social cost of monopoly and is equal to the area ABC.

Monopolist optimizing price: Dead weight loss (video) |
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A monopolist might be better placed to exploit increasing returns to scale leasing to an equilibrium that gives a higher output and a lower price than under competitive conditions. This is illustrated in the next diagram, where we assume that the monopolist is able to drive marginal costs lower in the long run, finding an equilibrium output of Q2 and pricing below the competitive price.

Monopolist optimizing price: Dead weight loss (video) |
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 Market Power and Market Pricing

Learning Objectives

Evaluate the economic inefficiency created by monopolies

In a monopoly, the firm will set a specific price for a good that is available to all consumers. The quantity of the good will be less and the price will be higher (this is what makes the good a commodity).

The monopoly pricing creates a deadweight loss because the firm forgoes transactions with the consumers. The deadweight loss is the potential gains that did not go to the producer or the consumer. As a result of the deadweight loss, the combined surplus (wealth) of the monopoly and the consumers is less than that obtained by consumers in a competitive market. A monopoly is less efficient in total gains from trade than a competitive market.

Monopolies can become inefficient and less innovative over time because they do not have to compete with other producers in a marketplace. For private monopolies, complacency can create room for potential competitors to overcome entry barriers and enter the market.

When a market fails to allocate its resources efficiently, market failure occurs. In the case of monopolies, abuse of power can lead to market failure. Market failure occurs when the price mechanism fails to take into account all of the costs and/or benefits of providing and consuming a good.

As a result, the market fails to supply the socially optimal amount of the good. A monopoly is an imperfect market that restricts output in an attempt to maximize profit. Market failure in a monopoly can occur because not enough of the good is made available and/or the price of the good is too high.

image

Imperfect competition: This graph shows the short run equilibrium for a monopoly. The gray box illustrates the abnormal profit, although the firm could easily be losing money. A monopoly is an imperfect market that restricts the output in an attempt to maximize its profits.

Define deadweight loss, Explain how to determine the deadweight loss in a given market.

Key Points

  • The monopoly pricing creates a deadweight loss because the firm forgoes transactions with the consumers.
  • Monopolies can become inefficient and less innovative over time because they do not have to compete with other producers in a marketplace.
  • In the case of monopolies, abuse of power can lead to market failure. Market failure occurs when the price mechanism fails to take into account all of the costs and/or benefits of providing and consuming a good.
  • A monopoly is an imperfect market that restricts output in an attempt to maximize profit. Without the presence of market competitors it can be challenging for a monopoly to self-regulate and remain competitive over time.
  • When deadweight loss occurs, there is a loss in economic surplus within the market.
  • Causes of deadweight loss include imperfect markets, externalities, taxes or subsides, price ceilings, and price floors.
  • In order to determine the deadweight loss in a market, the equation P=MC is used. The deadweight loss equals the change in price multiplied by the change in quantity demanded.
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