Market Power
Lecture 7

 

Social Welfare

1. Consumers' surplus – consumers willingness to pay for a product or service

  • Willingness to pay (WTP) is measured in dollars

  • Some consumers are willing to pay more

  • An aggregate benefit to all consumers in the market

Consumers' surplus

  • Example: One consumer is willing to pay $2.50, but he does not have to. He pays $1.50

  • If the market price increases, then consumers' surplus falls

Consumers' surplus decreases when the market price increases

  • If the market price decreases, then consumers' surplus increase

Consumers' surplus increases when the market price decreases

2. Producers' surplus – an aggregate benefit to all producers in a market

Producers' surplus

  • Note – Qm is minimum supply

  • Producers' surplus – profits plus total fixed costs

    • Also called quasi-rent

  • Example – One producer could produce item for $8; however, he gets $10 per unit

  • If market price increases, then producers' surplus increases

Producers' surplus increases, when the market price increases

  • If market price decreases, then producers' surplus decreases

Producers' surplus decreases, when the market price decreases

3. Social Welfare / Total Surplus = producers' surplus + consumers' surplus

  • Amount society benefits

Social welfare equals consumers' plus producers' surpluses

  • Competitive markets give the highest social welfare

  • All other market structures have lower social welfare

  • Note – skip Pareto Optimality

  • Two types of demand functions

    • Marshallian demand function – standard demand function

      • Law of Demand – a lower market price causes higher market quantity

      • Income effect – a lower price increases consumers' real income (i.e. higher utility)

      • Substitution effect – changes consumers' buying behavior

    • Hicksian demand function – theoretical

      • Remove the income effect, so consumers' utility remains constant

      • Used for welfare analysis

    • If the income effect is small, then social welfare from a Marshallian demand function is similar to a Hicksian

How Market Power can influence the Market Price

1. Characteristics

  1. Supply side substitution – if firm raises prices, consumers switch to another firm

    • Not possible for a monopoly

  2. Demand side substitution – if firm raises prices, consumers switch to another product

    • Market: Breakfast cereals appear to be a concentrated industry

    • However, if firms raise prices, then consumers switch to other breakfast cereals

  3. Monopoly – price maker

    • Demand for monopolist's product is all consumers in the market

A monopolst's demand function

  • Monopoly's profits

Equation 7

  • Law of Demand – if Q decreases, then P increases

  • Therefore, P > MC

  • Not in book

Equation 8

  • Competitive firms do not earn rent, so this term is zero

Using, Equation 9

Approximation, Equation 10

  • (Q1, P1) is original point, thus

Change in revenue when the market price increases

  • Monopoly raises the market price by lowering production

Equation 11

  • So, P > MR = MC

  1. Assume demand is linear, P(Q) = A – bQ

    • Total revenue (TR) = P Q

    • Thus, TR = P(Q) Q = (A – bQ) Q = A Q – b Q2

Equation 12

  • X-intercepts

    • If Q = 0, then MR = 0

    • If MR = 0, then Q = A / 2b

  • Assume MC = c, where c is a constant

    • Means TC = FC + cQ

    • FC is fixed cost

    • cQ is variable cost

  • Graph is below:

A monopolist's profit when the demand function is linear

  • Solve for market quantity,

    • Set MR = MC

    • A – 2bQ = c

    • Qm = (A –c)/2b

  • Solve for market price

    • P(Q) = A – bQ

    • Pm = A – b(A – c)/2b

    • Pm = A – A/2 + c/2 = (A + c)/2

  • Profits

Equation 13

  1. Competitive solution

    • Quantity

      • P = MC

      • P(Q) = A – bQ and MC(Q) = c

      • A –bQ = c, where Qc = (A – c)/b

      • Competitive market has twice the production

    • Price

      • P(Q) = A – b(A – c)/b = c

      • Thus, P(Q) = c

      • Competitive market has a lower price

    • Profits

      • P = TR – TC = P(Q)Q – cQ – FC = cQ – cQ – FC = -FC

      • Fixed costs have to be zero for a competitive industry

      • Fixed cost create a market barrier

Deadweight Loss

1. Deadweight Loss (DWL) of a monopoly

  • Monopoly causes a higher price and lower quantity

  • Demand function is linear; thus, DWL is an area of a triangle

Deadweight loss of a monopoly

  • DWL = ½ (base) (height)

  • DWL = ½ (Pm – c) (Qc - Qm)

2. An example

  • The milk industry has an inverse demand function, P(Q) = 100 – Q and a total cost function, T(q) = 30q

  • The industry has a monopoly

    • TR(Q) = P(Q)Q = 100Q – Q2

    • MR(Q) = 100 – 2Q

  • Graph is below:

A numerical example of a monopoly

  • The average cost (AC) and marginal cost (MC) functions are:

    • AC = TC / q = 30 q / q =30

    • MC = (d/dq) 30q = 30

  • Find Pm and Qm

    • Set MC(Q) = MR(Q)

    • 100 – 2Qm = 30

    • Thus, Qm = 35

    • Pm = P(Qm) = 100 – Qm = 100 – 35 = 35

  • Efficient level of milk production

    • Pc = MC and MC(Q) = 30

    • Thus, Pc = 30

    • Pc = 100 – Qc

    • Qc = 100 – 30 = 70

  • Consumers' surplus (CS) under a competitive market

    • CS = ½ (base)(height)

    • CS = ½ (70 – 0)(100 – 30) = 2,450

  • Consumers' surplus under a monopoly market

    • CS = ½ (100 – 65)(35 – 0) = 612.50

  • Profits under a competitive market

    • p = P Q – TC = 30(70) – 30(70) = 0

  • Profits under a monopoly

    • p = P Q – TC = 65(35) – 30(35) = 35(35) = 1,225

    • Profits in the long run depend on

      • Market barriers

      • Demand substitution

  • Deadweight Loss (DWL)

    • DWL = ½ (65 – 30)(70 – 35) = 612.50

  • Refer to the table

  Competitive Market Monopoly
Consumer Surplus 2,450.00 612.50
Profits 0.00 1,225.00
Total Social Welfare 2,450.00 1,837.50
Deadweight Loss 0.00 612.50

 

The Lerner Index

Lerner Index – measure of market power

  • Price elasticity of demand – responsiveness of demand to changes in price

Equation 14

  • Example: If the price (P) increases by 1% and e = -3, then quantity demanded (Q) decreases by 3%

    • Elastic – consumers are sensitive

  • Example: e = -0.5

    • If the price (P) increases by 1%, then quantity demanded (Q) decreases by ½%

    • Inelastic because consumers are not sensitive

    • Note: e is unitless

Equation 15

  • Using small increments, then:

Equation 16

  • Solve for 1/e

Equation 17

  • Purely competitive market

Equation 18

  • Pure monopoly

Equation 19

  • No units; ratio of rent to the market price

  • Example, e =-0.5

Equation 20

  • Example, e =-2.0

Equation 21

  • Consumers are more sensitive to price changes, so monopolies have less market power

 

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