EC 1450 - Exam 2 Review Notes

Exam 2 Notes: Chapters 5-9, 11

Game Theory (Chapter 9)

In-Class Assignment: Price-Cutting Game

  • Scenario: Two players, Joe and Sam, must decide whether to cut the price of their product to 2.90 or keep it at 3.

  • Payoff Matrix:

    Sam: Cut price to 2.90Sam: Keep price at 3
    Joe: Cut price to 2.90900, 9001,350, 500
    Joe: Keep price at 3500, 13501000, 1000
    • The numbers represent the payoffs for Joe and Sam, respectively (Joe's payoff, Sam's payoff).

  • Dominant Strategy

    • Sam's Dominant Strategy: Regardless of what Joe does, Sam is better off cutting the price.
    • Joe's Dominant Strategy: Joe is also better off cutting the price, regardless of Sam's actions.

  • Solution/Optimum: Both Joe and Sam cut their prices to 2.90, resulting in payoffs of 900, 900. This is the Nash Equilibrium.

Game Theory Example: Player Choices

  • Scenario: Two players (Player 1 and Player 2) make choices that affect their payoffs.
  • Decision Tree:
    • Player 1 chooses between Option A and Option C.
    • If Player 1 chooses A, Player 2 then chooses between Up (B) and Down.
    • If Player 1 chooses C, Player 2 then chooses between Up and Down.
  • Payoffs:
    • A-Up (B): Player 1 gets 100, Player 2 gets 30.
    • A-Down: Player 1 gets 30, Player 2 gets 50.
    • C-Up: Player 1 gets 10, Player 2 gets 31.
    • C-Down: Player 1 gets 20, Player 2 gets 21.
  • Optimal Play: Player 2's choice at B (between Up and Down) is determined by which yields the higher payoff for Player 2. Player 2 will choose Down because 50 is greater than 30.
  • Optimal Play: Player 2's choice at C (between Up and Down) is determined by which yields the higher payoff for Player 2. Player 2 will choose Up because 31 is greater than 21.
  • Best Play for Player 1: Considering Player 2's rational choices, Player 1 needs to anticipate what Player 2 will do. Since Player 2 chooses Down at A (With player 1's choice), and Up at C, Player 1 should choose A to get 30 instead of choosing C, to get 10.

Externalities and Property Rights (Chapter 11)

Externalities

  • Definition: An externality is an external cost or external benefit of an activity that affects people other than those who pursue the activity.
  • External Cost (Negative Externality): An unintended cost associated with an activity that affects others.
  • External Benefit (Positive Externality): An unintended benefit of an activity that affects others.

Negative Externality

  • Example: Sara playing the violin in her backyard, disturbing her neighbor Harry who dislikes classical music.
    • Sara produces a negative externality, Harry is the recipient (he bears the external cost).
  • Problem: The amount of the activity (Sara playing violin) is not socially optimal.
    • Sara plays where Private Marginal Cost (PMC) = Private Marginal Benefit (PMB).
    • She doesn’t include the full Social Marginal Cost (SMC) of her activity.
  • Graphical Representation:
    • Private Marginal Cost (MC), Social Marginal Cost (SMC), Demand (D).
    • Socially Optimal Quantity: Q, Price: P.
    • Market produces Q1 at P1 (too much of the activity).
    • Deadweight loss present due to overproduction.
  • Takeaway: With a negative externality, there is too much of the activity that produces the externality.
    • For optimality: Social Marginal Cost (SMC) = Private Marginal Benefit (PMB).

Positive Externality

  • Example: Sara playing the violin, enjoyed by her neighbor Tom.
    • Sara produces a positive externality, Tom is the recipient (he receives the external benefit).
  • Problem: The quantity produced (Sara playing) is not optimal.
    • Sara behaves rationally: Private Marginal Cost (PMC) = Private Marginal Benefit (PMB).
    • She doesn’t consider all Social Benefit (MSB) = Private Marginal Benefit (MBPVT) + External Benefit (XB, or the benefits to Tom).
  • Graphical Representation:
    • Marginal Cost (MC), Private Demand (MBPVT), Social Demand (MBSOC).
    • Socially Optimal Quantity: QSOC . Private Equilibrium Quantity: QPVT
    • Deadweight loss present due to underproduction.
  • Takeaway: Sara produces less classical music than is socially optimal.
    • For optimality: Private Marginal Cost (PMC) = Social Marginal Benefit (MSB).

Effects of Externalities

  • With externalities, society does not achieve the largest possible economic surplus.

Solutions for Externalities

  • Arthur Pigou's Solution:

    • Government intervention by imposing a tax on the producer of the external cost (Pigouvian Tax).

  • Example: Pollution Tax

    • Without tax, Private Equilibrium is at 12,000 tons/year, Price is 1,300.
    • Social optimum is at 8,000 tons/year, Price is 2,000.
    • Pollution tax of 1,000/ton is imposed.
    • Tax shifts the Private MC curve to Private MC + Tax curve.
    • After-tax equilibrium is at 8,000 tons/year, Price is $$2,300.