Chapter 4 Appendix: In-Depth

Appendix to Chapter 4: CS, PS, and Market Efficiency

Welfare Analysis

• Overview of welfare analysis in markets focusing on Consumer Surplus (CS), Producer Surplus (PS), and Total Surplus (TS).

Definitions

• Consumer Surplus (CS):
  • Defined as the area that is above the price level and below the demand curve.
• Producer Surplus (PS):
  • Defined as the area that is below the price level and above the supply curve.
• Total Surplus (TS):
  • Total surplus in a market:
    $TS = CS + PS$
  • Represents the total welfare or economic efficiency of the market at equilibrium.

Consumer Surplus (CS)

• The demand curve also represents how much consumers are willing to pay at different quantities.
• Equilibrium Price (P*):
  • The price at which quantity demanded equals quantity supplied.
  • In this context, P* is identified as the equilibrium price.
• Some consumers are willing to pay a price higher than P, but they do not have to due to the existence of P.
• This results in the area above the price level and below the demand curve representing the welfare of consumers in the market.

Producer Surplus (PS)

• The supply curve also represents how much producers are willing to produce at prices lower than P*.
• Equilibrium Price (P*):
  • Again, the price at which quantity supplied equals quantity demanded.
• Some producers are willing to produce goods for sale at prices lower than P*, but they are not required to.
• Thus, the area below the price level and above the supply curve indicates the welfare of producers in the market.

Total Welfare

• Relationship between CS and PS:
  • If P* increases:
  • CS decreases
  • PS increases
• If P* decreases:
  • CS increases
  • PS decreases
• The overall total welfare of society is given by:
  $TS = CS + PS$

Deadweight Loss (DWL)

• Definition:
  • Deadweight loss refers to the net loss of consumer and producer surplus that occurs due to inefficient levels of production or consumption in the market as a result of underproduction or overproduction.
• Both under-production and over-production can lead to a deadweight loss, representing inefficiency in market outcomes.

Price Controls and Efficiency Loss

• Price controls can disrupt market equilibrium and lead to efficiency losses.

(1) A Binding Price Ceiling

• Defined as a maximum allowable price, which is set below the equilibrium price (P*), denoted by:
  • Condition: Pc < P*
  • Consequences:
  • Quantity supplied (Qs) is less than quantity demanded (Qd): Qs < Qd
  • This situation results in underproduction and leads to deadweight loss (DWL).
  • Example:
    • Rent Control: When government limits the price landlords can charge, leading to shortages in housing.

(2) A Binding Price Floor

• Defined as a minimum allowable price, which is set above the equilibrium price (P*), denoted by:
  • Condition: Pf > P*
  • Consequences:
  • Quantity supplied (Qs) exceeds quantity demanded (Qd): Qs > Qd
  • This scenario results in overproduction and leads to deadweight loss (DWL).
  • Example:
    • Agricultural Price Support: When governments set minimum prices for food production, leading to surpluses.

Numerical Example of Price Ceiling

• Market Example: Milk

• Given data for price and quantity demanded (Qd) and supplied (Qs) is as follows:

  • Price per Gallon:
  • $10.00: Qd = 100, Qs = 500 (millions of gallons)
  • $8.00: Qd = 200, Qs = 400 (millions of gallons)
  • $6.00: Qd = 300, Qs = 300 (millions of gallons)
  • $4.00: Qd = 400, Qs = 200 (millions of gallons)
  • $2.00: Qd = 500, Qs = 100 (millions of gallons)

• Demand curve equation:
  $P = 12 - 0.02Q$

• Supply curve equation:
  $P = 0.02Q$

• Equilibrium:

  • Equilibrium price and quantity calculated as:
  • $P* = 6$
  • $Q* = 300$

• Calculating Surplus at Equilibrium:

  • Consumer Surplus (CS):
    $CS = \frac{(12 - 6)(300)}{2} = 900 \, \text{(million dollars)}$
  • Producer Surplus (PS):
    $PS = \frac{(6 - 0)(300)}{2} = 900 \, \text{(million dollars)}$
  • Total Surplus (TS):
    $TS = CS + PS = 1800 \, \text{(million dollars)}$

• Price Ceiling:

  • If the government sets a price ceiling of $4:
  • Shortage is calculated as:
    $Qs - Qd = 400 - 200 = 200 \, \text{(million gallons)}$
  • Calculating New Surpluses under Price Ceiling:
  • New Consumer Surplus (CS):
    $CS = \frac{(4 + 8)(200)}{2} = 1200 \, \text{(million dollars)}$
  • New Producer Surplus (PS):
    $PS = \frac{(4)(200)}{2} = 400 \, \text{(million dollars)}$
  • New Total Surplus (TS):
    $TS = CS + PS = 1600 \, \text{(million dollars)}$
  • Deadweight Loss (DWL):
    $DWL = \frac{(4)(100)}{2} = 200 \, \text{(million dollars)}$