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

• 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

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

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

• Note – Q ^m 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

• If market price decreases, then producers' surplus decreases

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

• Amount society benefits

• 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

• Monopoly's profits

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

• Therefore, P > MC

• Not in book

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

Using,

Approximation,

• (Q ₁, P ₁) is original point, thus

• Monopoly raises the market price by lowering production

• So, P > MR = MC

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

   • Total revenue (TR) = P Q

   • Thus, TR = P(Q) Q = (A – bQ) Q = A Q – b Q ²

• 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:

• Solve for market quantity,

  • Set MR = MC

  • A – 2bQ = c

  • Q ^m = (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

6. 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

• DWL = ½ (base) (height)

• DWL = ½ (P ^m – c) (Q ^c - Q ^m)

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 – Q ²

  • MR(Q) = 100 – 2Q

• Graph is below:

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

  • AC = TC / q = 30 q / q =30

  • MC = (d/dq) 30q = 30

• Find P ^m and Q ^m

  • Set MC(Q) = MR(Q)

  • 100 – 2Q ^m = 30

  • Thus, Q ^m = 35

  • P ^m = P(Q ^m) = 100 – Q ^m = 100 – 35 = 35

• Efficient level of milk production

  • P ^c = MC and MC(Q) = 30

  • Thus, P ^c = 30

  • P ^c = 100 – Q ^c

  • Q ^c = 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

The Lerner Index

Lerner Index – measure of market power

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

• 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

• Using small increments, then:

• Solve for 1/ e

• Purely competitive market

• Pure monopoly

• No units; ratio of rent to the market price

• Example, e =-0.5

• Example, e =-2.0

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