BackECN104 Lecture 3
Study Guide - Smart Notes
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Optimization, Games, and Equilibrium
Introduction to Optimization
In microeconomics, optimization refers to the process by which economic agents (such as individuals, firms, or governments) select the best feasible option from a set of alternatives. This selection is based on maximizing their benefit or utility, given constraints such as budget, time, or resources.
Optimizing Agent: An agent who chooses the best feasible option available.
Feasible Option: An alternative that is possible given the agent's constraints.
Optimization Using Total Value
One method of optimization is to calculate the total value of each feasible option and select the one with the highest total value.
Total Value: The sum of all benefits minus the sum of all costs for each option.
Net Benefit Formula:
Application: Used to compare alternatives directly by their overall impact.
Optimization Using Marginal Analysis
Another method is marginal analysis, which focuses on the change in total value when moving from one option to another. The agent compares the marginal benefit and marginal cost of each incremental change.
Marginal Benefit (MB): The additional benefit from choosing one more unit of an activity.
Marginal Cost (MC): The additional cost from choosing one more unit of an activity.
Optimization Rule: The optimal choice is where .
Equivalence: Both total value and marginal analysis methods yield identical answers for the optimal choice.
Challenges in Optimization
Making optimal choices can be difficult due to several factors:
Limited Information: Agents may not have all relevant data.
Complexity: Sorting through information can be complicated.
Inexperience: Agents may lack experience in similar situations.
Uncertainty: Even the best choice can sometimes lead to a bad outcome due to unpredictable factors.
Optimization Techniques
Total Value vs. Marginal Analysis
Microeconomics uses two main techniques for optimization:
Total Value: Calculate net benefit for each alternative and choose the highest.
Marginal Analysis: Compare the change in net benefit between alternatives; choose the option where MB = MC.
Steps in Optimization Using Total Value
Translate all costs and benefits into common units (e.g., dollars per month).
Calculate the total net benefit of each alternative.
Pick the alternative with the highest net benefit.
Steps in Optimization Using Marginal Analysis
Translate all costs and benefits into common units.
Calculate the marginal consequences of moving between alternatives.
Choose the best alternative such that moving to it makes you better off, and moving away makes you worse off.
Optimization Application: Scrolling Tablet or Phone
Example: Choosing Hours Spent on Tablet/Phone
Suppose you must decide how many hours per day to spend watching videos or reading news on your tablet or smartphone. The following table summarizes the benefits and costs:
Hours (watching/reading) | Total Benefits (amusement or knowledge) | Total Costs (mental & physical fatigue; missing out on lecture, homework, and social activities) |
|---|---|---|
1 | $35 | $20 |
2 | $70 | $40 |
3 | $90 | $65 |
4 | $100 | $100 |
Net Benefit Calculation
Hours | Benefit | Cost | Net Benefit |
|---|---|---|---|
0 | 0 | 0 | 0 |
1 | 35 | 20 | 15 |
2 | 70 | 40 | 30 |
3 | 90 | 65 | 25 |
4 | 100 | 100 | 0 |
Optimal Choice: The highest net benefit is at 2 hours ($30).
Marginal Analysis Table
Hours | Benefit | Marginal Benefit | Cost | Marginal Cost | MB-MC | Net Benefit |
|---|---|---|---|---|---|---|
0 | 0 | - | 0 | - | - | 0 |
1 | 35 | 35 | 20 | 20 | 15 | 15 |
2 | 70 | 35 | 40 | 20 | 15 | 30 |
3 | 90 | 20 | 65 | 25 | -5 | 25 |
4 | 100 | 10 | 100 | 35 | -25 | 0 |
Optimal Choice: The best choice is where MB-MC is maximized and positive, which occurs at 2 hours.
Example: New Tablet with Lower Costs
If costs are reduced (e.g., less eye fatigue), the net benefit changes:
Hours | Benefit | Cost | Net Benefit |
|---|---|---|---|
0 | 0 | 0 | 0 |
1 | 35 | 20 | 15 |
2 | 70 | 35 | 35 |
3 | 90 | 50 | 40 |
4 | 100 | 75 | 25 |
Optimal Choice: The highest net benefit is at 3 hours ($40).
Game Theory and Strategic Play
Introduction to Game Theory
Game theory is a branch of microeconomics that studies strategic interactions among multiple agents, where the outcome for each participant depends on the actions of others.
Game: A multi-person decision problem.
Players: The agents involved in the game (individuals, firms, countries).
Strategy: A plan of action chosen by each player.
Payoff: The benefit or utility received by each player for each possible outcome.
Nash Equilibrium
A Nash equilibrium is a set of strategies, one for each player, such that no player can benefit by changing their strategy while the other players keep theirs unchanged.
Definition: Each player chooses a strategy that maximizes their payoff, given the strategies of others.
Best Response: For each player, their strategy is the best response to the equilibrium strategies of the other players.
Applications of Game Theory
Economics: International trade agreements, firm strategy, tax compliance, teamwork, lobbying.
International Diplomacy: War, peace, treaties.
Politics: Voting methods, candidate platforms, lobbying.
Biology and Medicine: Competition, genetic traits, pandemics.
Formalizing a Game
Players: Who are the participants?
Strategy Set: What actions can each player take?
Timing: Who moves when?
Information Structure: What do players know when they move?
Payoffs: What does each player receive at each outcome?
Example: Rock, Paper, Scissors
Players: Alex and Betty
Strategy Set: Rock (R), Paper (P), Scissors (S)
Timing: Simultaneous moves
Information: Both know the rules
Payoffs: Win (1), Lose (-1), Draw (0)
Zero-Sum Games
In zero-sum games, one player's gain is exactly another player's loss. Examples include rock-paper-scissors, chess, poker, and elections.
Zero-Sum Thinking: Ignores the possibility of mutual gains from trade.
Non-Zero-Sum Games: Allow for mutual benefit through cooperation or exchange.
Prisoners' Dilemma
The prisoners' dilemma is a classic example of a game where individual rationality leads to a suboptimal outcome for all players. It is equivalent in structure to many real-world strategic interactions, such as tariff games, business competition, and nuclear proliferation.
Key Feature: Each player has an incentive to defect, even though cooperation would yield a better outcome for both.
Summary Table: Optimization Techniques
Technique | Definition | Key Formula | Optimality Condition |
|---|---|---|---|
Total Value | Calculate net benefit for each alternative | Choose option with highest net benefit | |
Marginal Analysis | Compare change in net benefit between alternatives |
| Choose option where |
Example Application
Suppose you are deciding how many hours to spend on an activity. Calculate the net benefit for each option and use marginal analysis to find the optimal point. The optimal choice is where the net benefit is maximized and where marginal benefit equals marginal cost.
Additional info: The notes also introduce game theory concepts relevant for later chapters, including Nash equilibrium, zero-sum games, and the prisoners' dilemma, which are foundational for understanding strategic interactions in microeconomics.
