BECC-108 Solved Assignment

Title of Course: Intermediate Microeconomics-II

1. (a) Explain the features of a monopoly market structure. What are the characteristics of a natural monopoly?
   (b) How does a monopolist decide its profit maximising output? Explain with the help of appropriate diagram.
2. (a) Consider a duopoly of firm 1 and 2 producing a homogenous product, the demand of which is described by the following demand function:

3. Consider a monopolist facing an inverse demand function $P(Q)=10-Q$$P(Q)=10-Q$P(Q)=10-QP(Q)=10-Q$P(Q)=10-Q$, and total cost function $2Q$$2Q$2Q2 Q$2Q$ $+Q^2$$+Q^2$+Q^(2)+Q^2$+Q^2$. Calculate the deadweight loss associated with this market condition.
4. What do you understand by the term ‘adverse selection’? Discuss with the reference to market for lemons.
5. Explain the concept of contract curve by showing efficiency in production. How is pareto optimality related to the contract curve? Discuss.

6. Bring out the difference between the general equilibrium analysis and partial equilibrium analysis.
7. What are the inefficiencies related to a positive externality? Explain with the help of a diagram.
8. Explain the concept of price discrimination with reference to first degree price discrimination.
9. Distinguish between the classical utilitarian social welfare function and the minimax social welfare function.
10. Differentiate between a sequential game and a simultaneous game with the help of examples.

EXPERT ANSWER

Explain the features of a monopoly market structure. What are the characteristics of a natural monopoly?

Answer:

Features of a Monopoly Market Structure

1. Single Seller: In a monopoly, there is only one producer or seller in the market. This single entity has complete control over the supply of the product or service, making it the sole provider.
2. No Close Substitutes: The product offered by the monopolist has no close substitutes, meaning consumers cannot easily switch to a different product. This lack of alternatives gives the monopolist significant market power.
3. Price Maker: Unlike in competitive markets, where prices are determined by the forces of supply and demand, a monopolist can set prices. As a price maker, the monopolist can influence the price by adjusting the level of output.
4. High Barriers to Entry: Monopolies are characterized by significant barriers to entry, which prevent other firms from entering the market. These barriers can include high startup costs, control over essential resources, legal restrictions, or technological superiority.
5. Profit Maximization: The monopolist seeks to maximize profits by setting a price where marginal cost equals marginal revenue (MC = MR). By restricting output, the monopolist can charge higher prices, leading to supernormal profits.
6. Limited Consumer Choice: With only one supplier in the market, consumers have limited options and must purchase the product at the price set by the monopolist.
7. Potential for Inefficiency: Monopolies may lead to allocative and productive inefficiency. Since there is no competition, the monopolist may not have an incentive to minimize costs or innovate, leading to higher prices and lower-quality products for consumers.

Characteristics of a Natural Monopoly

1. Economies of Scale: A natural monopoly arises when a single firm can produce at a lower average cost than any combination of two or more firms. As the firm expands production, the average cost per unit decreases, making it inefficient for multiple firms to compete.
2. High Fixed Costs: Natural monopolies typically involve industries with very high fixed costs, such as utilities (electricity, water, gas). These high fixed costs make it impractical for new entrants to compete, as they would need to invest heavily in infrastructure.
3. Essential Services: Natural monopolies often provide essential services that require significant infrastructure, such as railways, water supply, and electricity distribution. These services are critical for public welfare, and having multiple providers would lead to unnecessary duplication of resources.
4. Regulation: Because natural monopolies provide essential services, they are often subject to government regulation to prevent the monopolist from exploiting its market power. Regulators may control prices, set quality standards, and ensure that the service is accessible to all consumers.
5. Inelastic Demand: The demand for the products or services provided by a natural monopoly is often inelastic, meaning that consumers are less sensitive to changes in price. This inelasticity further reinforces the monopolist’s control over the market.
6. Single Provider Efficiency: In a natural monopoly, having a single provider is more efficient than having multiple providers because it minimizes costs associated with infrastructure and production. This efficiency justifies the existence of a monopoly in such markets.

How does a monopolist decide its profit maximising output? Explain with the help of appropriate diagram.

Answer:

Consider a duopoly of firm 1 and 2 producing a homogenous product, the demand of which is described by the following demand function:

Answer:

1. Determine the market demand function in terms of price (P).
2. Find the residual demand function for each firm.
3. Determine the reaction functions for each firm.
4. Solve for the Cournot-Nash equilibrium quantities.

1. Market Demand Function

2. Residual Demand Function for Each Firm

3. Reaction Functions

4. Cournot-Nash Equilibrium

Conclusion

Discuss the dominant strategy and dominated strategy in a game through an example. Is Nash equilibrium always indicated dominant strategy? Why or why not? Explain.

Answer:

Dominant and Dominated Strategies in Game Theory

• If Player A cooperates: If Player B cooperates, Player A gets 2 (light sentence). If Player B defects, Player A gets 0 (heavy sentence).
• If Player A defects: If Player B cooperates, Player A gets 3 (goes free). If Player B defects, Player A gets 1 (moderate sentence).

Nash Equilibrium and Dominant Strategies

• In some games, a Nash Equilibrium exists even when no player has a dominant strategy. This can happen in games where the best response of a player depends on the strategy chosen by the other player, and no single strategy is optimal regardless of what the opponent does.

• If the man chooses ballet, the best response for the woman is to choose ballet, and vice versa for football.
• If the man chooses football, the woman’s best response is to choose football, and vice versa.

Conclusion

Consider a monopolist facing an inverse demand function $P(Q)=10-Q$$P(Q)=10-Q$P(Q)=10-QP(Q)=10-Q$P(Q)=10-Q$, and total cost function $2Q$$2Q$2Q2 Q$2Q$ $+Q^2$$+Q^2$+Q^(2)+Q^2$+Q^2$. Calculate the deadweight loss associated with this market condition.

Answer:

Step 1: Find the Monopolist’s Quantity and Price

1. Inverse demand function: $P(Q)=10-Q$$P(Q)=10-Q$P(Q)=10-QP(Q) = 10 – Q$P(Q)=10-Q$
2. Total cost function: $C(Q)=2Q+Q^2$$C(Q)=2Q+Q^2$C(Q)=2Q+Q^(2)C(Q) = 2Q + Q^2$C(Q)=2Q+Q^2$
3. Marginal revenue (MR):
   The revenue function is $R(Q)=P(Q)\times Q=(10-Q)Q=10Q-Q^2$$R(Q)=P(Q)\times Q=(10-Q)Q=10Q-Q^2$R(Q)=P(Q)xx Q=(10-Q)Q=10 Q-Q^(2)R(Q) = P(Q) \times Q = (10 – Q)Q = 10Q – Q^2$R(Q)=P(Q)\times Q=(10-Q)Q=10Q-Q^2$.
   The marginal revenue is the derivative of the revenue function with respect to $Q$$Q$QQ$Q$:
   $$MR=\frac{dR(Q)}{dQ}=10-2Q$$$$MR=\frac{dR(Q)}{dQ}=10-2Q$$MR=(dR(Q))/(dQ)=10-2QMR = \frac{dR(Q)}{dQ} = 10 – 2Q$$MR=\frac{dR(Q)}{dQ}=10-2Q$$
4. Marginal cost (MC):
   The marginal cost is the derivative of the total cost function with respect to $Q$$Q$QQ$Q$:
   $$MC=\frac{dC(Q)}{dQ}=2+2Q$$$$MC=\frac{dC(Q)}{dQ}=2+2Q$$MC=(dC(Q))/(dQ)=2+2QMC = \frac{dC(Q)}{dQ} = 2 + 2Q$$MC=\frac{dC(Q)}{dQ}=2+2Q$$
5. Monopolist’s optimal output:
   The monopolist maximizes profit by setting $MR=MC$$MR=MC$MR=MCMR = MC$MR=MC$:
   $$10-2Q=2+2Q$$$$10-2Q=2+2Q$$10-2Q=2+2Q10 – 2Q = 2 + 2Q$$10-2Q=2+2Q$$
   $$8=4Q\Rightarrow Q_m=2$$$$8=4Q\Rightarrow Q_m=2$$8=4Q quad=>quadQ_(m)=28 = 4Q \quad \Rightarrow \quad Q_m = 2$$8=4Q\Rightarrow Q_m=2$$
6. Monopolist’s price:
   Substitute $Q_m=2$$Q_m=2$Q_(m)=2Q_m = 2$Q_m=2$ into the inverse demand function to find the monopolist’s price:
   $$P_m=10-Q_m=10-2=8$$$$P_m=10-Q_m=10-2=8$$P_(m)=10-Q_(m)=10-2=8P_m = 10 – Q_m = 10 – 2 = 8$$P_m=10-Q_m=10-2=8$$

Step 2: Find the Competitive Market Quantity and Price

1. Set $P(Q)=MC$$P(Q)=MC$P(Q)=MCP(Q) = MC$P(Q)=MC$:
   $$10-Q_c=2+2Q_c$$$$10-Q_c=2+2Q_c$$10-Q_(c)=2+2Q_(c)10 – Q_c = 2 + 2Q_c$$10-Q_c=2+2Q_c$$
   $$8=3Q_c\Rightarrow Q_c=\frac{8}{3}\approx 2.67$$$$8=3Q_c\Rightarrow Q_c=\frac{8}{3}\approx 2.67$$8=3Q_(c)quad=>quadQ_(c)=(8)/(3)~~2.678 = 3Q_c \quad \Rightarrow \quad Q_c = \frac{8}{3} \approx 2.67$$8=3Q_c\Rightarrow Q_c=\frac{8}{3}\approx 2.67$$
2. Competitive price:
   Substitute $Q_c=\frac{8}{3}$$Q_c=\frac{8}{3}$Q_(c)=(8)/(3)Q_c = \frac{8}{3}$Q_c=\frac{8}{3}$ into the inverse demand function:
   $$P_c=10-\frac{8}{3}=\frac{30}{3}-\frac{8}{3}=\frac{22}{3}\approx 7.33$$$$P_c=10-\frac{8}{3}=\frac{30}{3}-\frac{8}{3}=\frac{22}{3}\approx 7.33$$P_(c)=10-(8)/(3)=(30)/(3)-(8)/(3)=(22)/(3)~~7.33P_c = 10 – \frac{8}{3} = \frac{30}{3} – \frac{8}{3} = \frac{22}{3} \approx 7.33$$P_c=10-\frac{8}{3}=\frac{30}{3}-\frac{8}{3}=\frac{22}{3}\approx 7.33$$

Step 3: Calculate the Deadweight Loss

1. Find the DWL area:
   The DWL is the area of a triangle with the base $Q_c-Q_m$$Q_c-Q_m$Q_(c)-Q_(m)Q_c – Q_m$Q_c-Q_m$ and height $P_m-MC$$P_m-MC$P_(m)-MCP_m – MC$P_m-MC$ at the monopolist’s output level.
   $$\text{DWL}=\frac{1}{2}\times (Q_c-Q_m)\times (P_m-M{C}_m)$$$$\text{DWL}=\frac{1}{2}\times (Q_c-Q_m)\times (P_m-M{C}_m)$$“DWL”=(1)/(2)xx(Q_(c)-Q_(m))xx(P_(m)-MC_(m))\text{DWL} = \frac{1}{2} \times (Q_c – Q_m) \times (P_m – MC_m)$$\text{DWL}=\frac{1}{2}\times (Q_c-Q_m)\times (P_m-M{C}_m)$$
   Where $M{C}_m$$M{C}_m$MC_(m)MC_m$M{C}_m$ is the marginal cost at the monopolist’s output level $Q_m=2$$Q_m=2$Q_(m)=2Q_m = 2$Q_m=2$:
   $$M{C}_m=2+2(2)=6$$$$M{C}_m=2+2(2)=6$$MC_(m)=2+2(2)=6MC_m = 2 + 2(2) = 6$$M{C}_m=2+2(2)=6$$
   So,
   $$\text{DWL}=\frac{1}{2}\times (\frac{8}{3}-2)\times (8-6)$$$$\text{DWL}=\frac{1}{2}\times \left(\frac{8}{3}-2\right)\times (8-6)$$“DWL”=(1)/(2)xx((8)/(3)-2)xx(8-6)\text{DWL} = \frac{1}{2} \times \left(\frac{8}{3} – 2\right) \times (8 – 6)$$\text{DWL}=\frac{1}{2}\times (\frac{8}{3}-2)\times (8-6)$$
   $$\text{DWL}=\frac{1}{2}\times (\frac{8}{3}-\frac{6}{3})\times 2$$$$\text{DWL}=\frac{1}{2}\times \left(\frac{8}{3}-\frac{6}{3}\right)\times 2$$“DWL”=(1)/(2)xx((8)/(3)-(6)/(3))xx2\text{DWL} = \frac{1}{2} \times \left(\frac{8}{3} – \frac{6}{3}\right) \times 2$$\text{DWL}=\frac{1}{2}\times (\frac{8}{3}-\frac{6}{3})\times 2$$
   $$\text{DWL}=\frac{1}{2}\times \frac{2}{3}\times 2=\frac{2}{3}$$$$\text{DWL}=\frac{1}{2}\times \frac{2}{3}\times 2=\frac{2}{3}$$“DWL”=(1)/(2)xx(2)/(3)xx2=(2)/(3)\text{DWL} = \frac{1}{2} \times \frac{2}{3} \times 2 = \frac{2}{3}$$\text{DWL}=\frac{1}{2}\times \frac{2}{3}\times 2=\frac{2}{3}$$

Final Answer:

What do you understand by the term ‘adverse selection’? Discuss with the reference to market for lemons.

Answer:

Adverse Selection in the Market for Lemons

The Market for Lemons Explained:

1. Information Asymmetry:
   • In the used car market, sellers often have more information about the quality of the car than buyers do. Sellers know whether a car is a "lemon" (a low-quality, defective car) or a "peach" (a high-quality car), but buyers typically cannot tell the difference before purchasing.
2. Impact on the Market:
   • Due to this information asymmetry, buyers are unable to accurately assess the quality of a car before buying. They might suspect that there is a higher chance of getting a lemon, leading them to offer lower prices for used cars in general.
   • High-quality car sellers, knowing that their cars are worth more, might withdraw from the market because they cannot get a fair price. As a result, the market becomes increasingly populated with lemons, as the presence of lemons drives down the average price buyers are willing to pay.
3. Adverse Selection:
   • This situation exemplifies adverse selection: the market tends to attract more lemons than peaches because the buyers’ inability to differentiate between good and bad cars drives good cars out of the market.
   • The market for lemons becomes dominated by low-quality products, leading to market inefficiency. Ultimately, the market may even collapse if buyers lose trust entirely and decide not to participate.

Broader Implications:

• Insurance: Individuals with high health risks are more likely to purchase health insurance, driving up costs and potentially leading to a situation where only those with poor health are insured, while healthy individuals opt out.
• Credit Markets: Borrowers with poor credit histories may be more likely to apply for loans, making it harder for lenders to distinguish between high-risk and low-risk borrowers, leading to higher interest rates or reduced lending.

Conclusion

Explain the concept of contract curve by showing efficiency in production. How is pareto optimality related to the contract curve? Discuss.

Answer:

Concept of the Contract Curve in Production

Production Efficiency and the Contract Curve

1. Edgeworth Box for Production:
   • The Edgeworth Box is a useful tool to illustrate the contract curve in production. It graphically represents the allocation of two inputs (such as labor and capital) between two firms.
   • The dimensions of the box are determined by the total amount of each input available in the economy. Each point within the box represents a possible allocation of the two inputs between the two firms.
2. Isoquants and Production Efficiency:
   • Each firm’s production function can be represented by isoquants within the Edgeworth Box. An isoquant shows all the combinations of inputs that produce a given level of output.
   • Production efficiency is achieved when the marginal rate of technical substitution (MRTS) between the two inputs is equal for both firms. This means that the rate at which one firm is willing to substitute one input for another, while maintaining the same level of output, is equal to that of the other firm.
3. Deriving the Contract Curve:
   • The contract curve is derived by finding all the points within the Edgeworth Box where the isoquants of the two firms are tangent to each other. At these tangency points, the MRTS is the same for both firms, indicating that the inputs are being allocated efficiently between the two firms.
   • Any point on the contract curve represents a Pareto efficient allocation of resources between the two firms.

Pareto Optimality and the Contract Curve

1. Relation to the Contract Curve:
   • The contract curve consists entirely of Pareto optimal points. Every point on the contract curve represents an allocation of inputs between the two firms where no further reallocation can improve the production of one firm without reducing the production of the other.
   • Thus, the contract curve is the locus of all Pareto optimal allocations of resources.
2. Points Off the Contract Curve:
   • Any point inside the Edgeworth Box that is not on the contract curve represents an inefficient allocation of resources. At these points, it is possible to reallocate resources to make at least one firm better off without making the other worse off.
   • Moving towards the contract curve from any inefficient point represents a move towards greater efficiency and Pareto optimality.

Conclusion

Bring out the difference between the general equilibrium analysis and partial equilibrium analysis.

Answer:

Partial Equilibrium Analysis

Key Characteristics:

1. Scope:
   • Focuses on a single market or sector.
   • Analyzes how changes in supply, demand, or external factors affect the equilibrium price and quantity in that particular market.
2. Ceteris Paribus Assumption:
   • Assumes that all other factors outside the market being analyzed remain unchanged (ceteris paribus). This includes prices in other markets, consumer incomes, and the availability of goods in other sectors.
3. Application:
   • Useful for analyzing the effects of specific policies, taxes, or subsidies on a particular market, such as the impact of a tax on cigarettes or a subsidy for renewable energy.
4. Complexity:
   • Simpler and more straightforward to apply, as it deals with fewer variables and interactions.

Example:

• If analyzing the market for bread, partial equilibrium would focus solely on the supply and demand for bread, assuming that prices of other goods (like butter or jam) do not change, even though they might in reality.

General Equilibrium Analysis

Key Characteristics:

1. Scope:
   • Focuses on the entire economy, analyzing how different markets interact with each other.
   • Considers how changes in one market affect other markets, leading to a new overall equilibrium in the economy.
2. Interdependence:
   • Assumes that all markets are interrelated. A change in one market can affect supply, demand, and prices in other markets.
   • For example, a change in the labor market could affect the production costs and prices in the goods market.
3. Application:
   • Used to analyze the overall impact of policies, shocks, or changes in technology on the entire economy. It helps understand how various sectors and markets are interconnected.
   • Useful in assessing the welfare implications of policy changes or understanding the ripple effects of a shock (e.g., a sudden increase in oil prices) across the economy.
4. Complexity:
   • More complex, as it involves analyzing multiple markets and their interactions simultaneously. Requires a more sophisticated mathematical framework.

Example:

• In analyzing the impact of an increase in the price of oil, general equilibrium would consider how this affects not only the oil market but also transportation costs, consumer goods prices, labor markets, and ultimately, the overall economy.

Key Differences

Conclusion

What are the inefficiencies related to a positive externality? Explain with the help of a diagram.

Answer:

Inefficiencies Related to a Positive Externality

The Nature of the Inefficiency

• Underproduction: The market equilibrium quantity (where private marginal benefit equals private marginal cost) is lower than the socially optimal quantity (where social marginal benefit equals marginal cost). This is because producers and consumers do not take into account the external benefits to others.
• Deadweight Loss: The inefficiency caused by the positive externality leads to a deadweight loss, which is a loss of economic efficiency that could have been avoided if the market produced at the socially optimal level.

Diagram Explanation

1. Axes:
   • The horizontal axis represents the quantity of the good or service.
   • The vertical axis represents the price or marginal benefit/cost.
2. Curves:
   • Private Marginal Cost (PMC): This represents the cost to producers for each additional unit produced. It also reflects the supply curve in a competitive market.
   • Private Marginal Benefit (PMB): This represents the benefit to consumers from each additional unit consumed. It reflects the demand curve.
   • Social Marginal Benefit (SMB): This represents the total benefit to society from each additional unit, including both the private benefit to consumers and the external benefit to third parties. In the case of a positive externality, $SMB>PMB$$SMB>PMB$SMB > PMBSMB > PMB$SMB>PMB$.
3. Market Equilibrium:
   • The market equilibrium occurs where the PMC (supply curve) intersects the PMB (demand curve). At this point, the quantity produced and consumed is $Q_m$$Q_m$Q_(m)Q_m$Q_m$, and the price is $P_m$$P_m$P_(m)P_m$P_m$.
4. Socially Optimal Equilibrium:
   • The socially optimal quantity occurs where the PMC intersects the SMB curve. This is at a higher quantity $Q_{opt}$$Q_{opt}$Q_(opt)Q_{opt}$Q_{opt}$ and reflects the point where the total benefit to society equals the cost. The corresponding price would be $P_{opt}$$P_{opt}$P_(opt)P_{opt}$P_{opt}$.
5. Deadweight Loss:
   • The deadweight loss is the area between the SMB and PMC curves over the range of quantities between $Q_m$$Q_m$Q_(m)Q_m$Q_m$ and $Q_{opt}$$Q_{opt}$Q_(opt)Q_{opt}$Q_{opt}$. This area represents the loss in total welfare due to the underproduction of the good or service.

Diagram

• $Q_m$$Q_m$Q_(m)Q_m$Q_m$: Market equilibrium quantity (underproduction due to positive externality).
• $Q_{opt}$$Q_{opt}$Q_(opt)Q_{opt}$Q_{opt}$: Socially optimal quantity.
• $P_m$$P_m$P_(m)P_m$P_m$: Market equilibrium price.
• $P_{opt}$$P_{opt}$P_(opt)P_{opt}$P_{opt}$: Socially optimal price.

Explanation

• Underproduction: The quantity $Q_m$$Q_m$Q_(m)Q_m$Q_m$ is lower than $Q_{opt}$$Q_{opt}$Q_(opt)Q_{opt}$Q_{opt}$, indicating that the market fails to produce enough of the good from a societal perspective.
• Deadweight Loss: The shaded area between the SMB and PMC curves from $Q_m$$Q_m$Q_(m)Q_m$Q_m$ to $Q_{opt}$$Q_{opt}$Q_(opt)Q_{opt}$Q_{opt}$ represents the welfare loss. This area reflects the benefits that could have been achieved if the good were produced at the socially optimal level.

Conclusion

Explain the concept of price discrimination with reference to first degree price discrimination.

Answer:

Types of Price Discrimination

1. First-Degree (or Perfect) Price Discrimination: Charging each consumer the maximum price they are willing to pay.
2. Second-Degree Price Discrimination: Charging different prices based on the quantity consumed or the version of the product.
3. Third-Degree Price Discrimination: Charging different prices to different groups of consumers based on their price elasticity of demand.

First-Degree Price Discrimination (Perfect Price Discrimination)

Key Characteristics:

1. Individual Pricing:
   • The seller must know the exact maximum price each consumer is willing to pay for the product or service. This requires detailed knowledge of each consumer’s demand curve, which is often difficult to obtain in practice.
2. Elimination of Consumer Surplus:
   • In first-degree price discrimination, the consumer surplus is completely transferred to the producer. Consumers pay a price exactly equal to their maximum willingness to pay for each unit they purchase.
3. Efficiency:
   • First-degree price discrimination can lead to allocative efficiency, as the product is provided to everyone who values it at least as much as the cost of production. However, the entire surplus is captured by the producer, which might raise concerns about fairness.

Example:

Implications of First-Degree Price Discrimination:

1. Producer Benefit:
   • The producer captures all the surplus, maximizing their profits.
2. Consumer Impact:
   • Consumers end up paying the maximum they are willing to pay, leaving them with no surplus. This can be seen as a disadvantage for consumers in terms of their welfare.
3. Market Efficiency:
   • The market can be more efficient in terms of allocation because the good or service is distributed to those who value it the most. However, the distribution of surplus is entirely skewed towards the producer.

Conclusion:

Distinguish between the classical utilitarian social welfare function and the minimax social welfare function.

Answer:

Classical Utilitarian Social Welfare Function

• $W$$W$WW$W$ is the total social welfare.
• $U_i$$U_i$U_(i)U_i$U_i$ is the utility of individual $i$$i$ii$i$.
• $n$$n$nn$n$ is the number of individuals in society.

Key Characteristics:

1. Maximization of Total Utility:
   • The objective is to maximize the sum of utilities across all individuals, leading to the greatest total happiness or well-being.
2. Equality vs. Efficiency:
   • Utilitarianism tends to focus more on efficiency (maximizing total welfare) rather than on equality. As a result, it may justify unequal distributions of resources if that leads to a higher total utility.
3. Interpersonal Comparisons of Utility:
   • It assumes that utilities can be compared and summed across individuals, which implies a form of interpersonal utility comparison.
4. Implication for Resource Allocation:
   • Utilitarianism might support policies that increase total welfare, even if they lead to significant inequality. For example, if giving more resources to wealthier individuals (who might have higher marginal utility for those resources) increases total utility, it could be justified under utilitarianism.

Example:

• Imagine a policy that provides significant benefits to a wealthy person and smaller benefits to a poor person, such that the total benefit (in utility terms) is maximized. A classical utilitarian approach would endorse this policy if it results in the highest aggregate utility, even if it increases inequality.

Minimax Social Welfare Function (Rawlsian Approach)

• $W$$W$WW$W$ is the social welfare.
• $U_i$$U_i$U_(i)U_i$U_i$ is the utility of individual $i$$i$ii$i$.
• The function $min$$min$min\min$min$ takes the minimum utility among all individuals.

Key Characteristics:

1. Maximization of the Minimum Utility:
   • The goal is to maximize the welfare of the individual with the least utility, ensuring that the worst-off person is as well-off as possible.
2. Focus on Equality and Fairness:
   • The minimax approach prioritizes equality and fairness over efficiency. It advocates for reducing inequalities and improving the welfare of the least advantaged members of society.
3. No Interpersonal Comparisons Needed:
   • Unlike utilitarianism, the minimax criterion does not require summing up or comparing utilities across individuals. It only requires identifying the person with the lowest utility and improving their welfare.
4. Implication for Resource Allocation:
   • Policies under the minimax criterion would be designed to improve the situation of the worst-off individuals, even if it means sacrificing some overall efficiency or total welfare. This could lead to more equitable distributions of resources.

Example:

• Suppose a policy could either increase the utility of the poorest individual slightly or significantly increase the utility of a wealthier individual. A minimax approach would favor the policy that improves the utility of the poorest individual, regardless of the impact on total utility.

Key Differences

Conclusion

Differentiate between a sequential game and a simultaneous game with the help of examples.

Answer:

Sequential Game:

Example:

• Players: Two (Player 1 and Player 2).
• Turns: Player 1 moves first, and Player 2 responds, knowing Player 1’s move.
• Strategy: Since Player 2 knows what Player 1 has done, Player 2 can choose a move that best responds to Player 1’s strategy.
• Representation: The game can be represented as a tree, where each branch represents a possible move by a player.

Simultaneous Game:

Example:

• Scenario: Two suspects are arrested and interrogated separately. They can either cooperate with each other by staying silent or betray the other by confessing.
• Players: Two (Prisoner 1 and Prisoner 2).
• Choices: Both prisoners must decide simultaneously whether to confess or remain silent.
• Strategy: Each prisoner has to make a decision without knowing what the other will do.
• Representation: The game is represented by a payoff matrix showing the outcomes for each combination of choices (e.g., both confess, both stay silent, one confesses while the other stays silent).

Key Differences:

• Order of Play: In sequential games, players take turns making decisions, while in simultaneous games, all players make decisions at the same time.
• Information: In sequential games, players can observe previous moves, whereas in simultaneous games, decisions are made without knowledge of the others’ choices.
• Representation: Sequential games are often represented by game trees, while simultaneous games are represented by payoff matrices.

Summary Example:

• Sequential Game: A chess match where each player takes turns and can see the previous move.
• Simultaneous Game: The Prisoner’s Dilemma where both players choose their actions (confess or stay silent) without knowing what the other will do.