ECN1202 Intermediate Microeconomics UM Assignment

ECN1202 Intermediate Microeconomics, a course offered at the University of Miami! In this comprehensive course, we delve into the fascinating world of microeconomics, exploring the behavior of individual consumers and firms and their interactions in various market settings. Building upon the foundational concepts introduced in introductory economics, this course equips you with a deeper understanding of the principles that govern decision-making at the microeconomic level.

Throughout this course, we will examine the intricacies of consumer choice, exploring topics such as utility theory, demand analysis, and the role of preferences in decision-making. By examining the behavior of individual consumers, we aim to uncover the underlying factors that influence their choices and the subsequent impact on market equilibrium. Moreover, we will delve into the world of firms and production, studying topics such as cost analysis, market structures, and strategic decision-making. Understanding the behavior of firms and their interactions within different market environments is crucial in comprehending the dynamics of supply and how it relates to market outcomes.

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In this section, we will describe some assignment briefs. These are:

Assignment Brief 1: Theory of Consumer Choice: budget line; preferences of the consumer; indifference curve and map; utility functions; consumer’s optimisation problem; individual and market demand; weak axiom of revealed preference; strong axiom of revealed preference; Slutsky equation; Slutsky substitution effect; income effect.

The theory of consumer choice is a fundamental concept in economics that analyzes how individuals make decisions about allocating their limited resources to different goods and services. It provides insights into consumer behavior and helps understand how consumers maximize their satisfaction or utility.

Here are the key components of the theory of consumer choice:

Budget Line: The budget line represents the different combinations of goods and services that a consumer can afford given their income and the prices of the goods. It shows the trade-off between two goods and determines the consumer’s budget constraint.
Preferences of the Consumer: The preferences of the consumer reflect their subjective judgments about the desirability or utility of different goods and services. These preferences are typically represented through indifference curves.
Indifference Curve and Map: An indifference curve shows the various combinations of two goods that yield the same level of satisfaction or utility to the consumer. Indifference curves are typically downward sloping and convex to represent the principle of diminishing marginal utility. An indifference map is a graphical representation of a set of indifference curves, illustrating the consumer’s preferences.
Utility Functions: Utility functions assign a numerical value or utility level to different combinations of goods and services based on the consumer’s preferences. These functions are used to measure and compare the levels of utility derived from different consumption bundles.
Consumer’s Optimization Problem: The consumer’s optimization problem is to choose the consumption bundle that maximizes their utility while staying within their budget constraint. This involves finding the point of tangency between the highest attainable indifference curve and the budget line.
Individual and Market Demand: Individual demand refers to the quantity of a good or service that an individual consumer is willing and able to purchase at different price levels. Market demand represents the sum of the individual demand of all consumers in a particular market.
Weak Axiom of Revealed Preference: The weak axiom of revealed preference states that if a consumer chooses one bundle over another when both are affordable and available, the consumer will not choose the previously rejected bundle when it becomes unaffordable or unavailable.
Strong Axiom of Revealed Preference: The strong axiom of revealed preference extends the weak axiom by assuming that consumer choices are consistent and do not depend on changes in prices or income.
Slutsky Equation: The Slutsky equation decomposes the total effect of a price change into the substitution effect and the income effect. It shows how changes in the price of a good affect the quantity demanded through these two distinct effects.
Slutsky Substitution Effect and Income Effect: The Slutsky substitution effect refers to the change in the quantity demanded of a good resulting from a change in its price while holding utility constant. The income effect refers to the change in the quantity demanded of a good resulting from a change in purchasing power or income, assuming that the prices remain constant.

These concepts and theories provide a framework for understanding consumer behavior, demand analysis, and the effects of price and income changes on consumption patterns.

Assignment Brief 2: General Equilibrium: trade between 2 agents in a general equilibrium context, within an Edgeworth box and with initial endowments; efficiency of allocation (Pareto optimality); first theorem of welfare economics; second theorem of welfare economics.

In a general equilibrium context, the interaction between two agents and trade can be analyzed using an Edgeworth box. The Edgeworth box is a graphical representation that allows us to examine the allocation of goods and resources between two individuals or agents.

The Edgeworth box consists of a rectangular diagram where the horizontal axis represents one agent’s consumption or bundle of goods, and the vertical axis represents the other agent’s consumption or bundle of goods. The diagonal line in the box represents the total resources or endowments available to the two agents. Each point within the box represents a possible allocation of goods between the two agents.

Efficiency of allocation, or Pareto optimality, refers to a situation where it is impossible to reallocate goods in a way that makes at least one person better off without making someone else worse off. In other words, an allocation is Pareto optimal if it maximizes overall welfare and there is no room for mutually beneficial trade or redistribution.

The first theorem of welfare economics, also known as the welfare theorem or the fundamental theorem of welfare economics, states that under certain idealized conditions, a competitive equilibrium will be Pareto optimal. This theorem establishes a link between the concept of efficiency in resource allocation and the functioning of competitive markets. It suggests that if markets are perfectly competitive and there are no externalities or market failures, the resulting equilibrium will be both efficient and Pareto optimal.

The second theorem of welfare economics, often called the second fundamental theorem of welfare economics, states that any Pareto optimal allocation can be achieved as a competitive equilibrium with the appropriate redistribution of initial endowments. In other words, if the initial distribution of resources does not result in a Pareto optimal outcome, it is possible to redistribute resources through taxes, subsidies, or other mechanisms in a way that achieves Pareto optimality. This theorem highlights the role of government intervention and redistribution in achieving efficient outcomes.

Both the first and second theorems of welfare economics provide important insights into the relationship between market mechanisms, efficiency, and Pareto optimality. While the first theorem suggests that competitive markets can lead to efficient outcomes, the second theorem acknowledges the potential need for government intervention to correct initial resource distributions and achieve Pareto optimality.

Assignment Brief 3: Theory of Production: Cobb Douglas production function; short run and long run production responses; cost of production in the short run and the long run; using Lagrangian to optimise output subject to a budget constraint.

The theory of production is a fundamental concept in economics that analyzes how inputs are transformed into outputs in the production process. Several key components of production theory include the Cobb-Douglas production function, short-run and long-run production responses, the cost of production in the short run and long run, and the use of the Lagrangian optimization technique to maximize output subject to a budget constraint.

Cobb-Douglas Production Function:

The Cobb-Douglas production function is a widely used mathematical representation of production that shows how inputs, such as labor (L) and capital (K), are combined to produce output (Y). The general form of the Cobb-Douglas production function is:

Y = A * L^α * K^β,

where Y represents output, A is the total factor productivity (TFP) or technological progress, L is the quantity of labor, K is the quantity of capital, and α and β are the output elasticities of labor and capital, respectively. The exponents α and β determine the share of each input in the production process.

Short Run and Long Run Production Responses:

2. In the short run, at least one input is fixed, typically capital, while one or more inputs, like labor, are variable. This means that the production function cannot be fully adjusted in the short run. As a result, changes in output are primarily driven by varying the variable inputs within the constraints of the fixed input.

In the long run, all inputs are variable, allowing firms to adjust their production processes more extensively. This flexibility enables firms to choose the optimal combination of inputs to produce the desired level of output. Long-run production responses consider adjustments in both the scale and mix of inputs.

Cost of Production in the Short Run and Long Run:

The cost of production depends on the prices of inputs and the quantities used. In the short run, firms have fixed costs (e.g., capital costs) that do not change with the level of output. Variable costs (e.g., labor, raw materials) vary with the quantity of output. Total cost is the sum of fixed costs and variable costs, given the fixed input.

In the long run, firms have the flexibility to adjust their scale of production, including all inputs. Thus, both fixed and variable costs can be adjusted. Long-run costs can be influenced by factors such as economies of scale, changes in input prices, and technological advancements.

Lagrangian Optimization for Output Maximization under a Budget Constraint:

2. The Lagrangian optimization technique is often employed to maximize output subject to a budget constraint, such as limited resources or a fixed budget. This approach involves constructing a Lagrangian function that combines the production function and the budget constraint.

For example, if a firm wants to maximize output (Y) subject to a budget constraint represented by the cost of inputs (C), the Lagrangian function would be:

L = Y – λC,

where λ is the Lagrange multiplier representing the shadow price of the budget constraint. The optimization process involves differentiating the Lagrangian function with respect to the inputs and the Lagrange multiplier, setting the derivatives equal to zero, and solving the resulting equations to find the optimal values of the inputs.

By using the Lagrangian method, firms can determine the combination of inputs that maximizes output while still satisfying the budget constraint imposed by the costs of inputs.

Assignment Brief 4: Strategic behaviour through Game theory: including: normal form representation and decision trees; static & dynamic games; dominant strategies; Nash Equilibrium and best response.

Game theory is a mathematical framework used to analyze strategic interactions among multiple decision-makers, called players, who seek to maximize their own outcomes. It provides a way to understand and predict how rational players will behave in competitive situations. Let’s explore some key concepts in game theory.

Normal Form Representation: The normal form of a game is a matrix that captures the possible strategies and payoffs for each player. In a two-player normal form game, each player chooses a strategy, and their resulting payoffs are specified in the matrix. This representation is also known as the payoff matrix.
Decision Trees: Decision trees are graphical representations of sequential decision-making in games. They are used to analyze games with multiple stages or moves. Each node in the tree represents a decision point, and the branches represent the possible choices and their associated payoffs.
Static and Dynamic Games: In game theory, games can be classified as static or dynamic. Static games involve simultaneous decision-making, where players choose their strategies without knowledge of the other players’ choices. Dynamic games, on the other hand, involve sequential decision-making, where players take turns making choices, and their decisions can be influenced by the previous choices made.
Dominant Strategies: A dominant strategy is a strategy that yields the highest payoff for a player, regardless of the strategies chosen by other players. If a player has a dominant strategy, it is in their best interest to choose that strategy regardless of what the other players do.
Nash Equilibrium: Nash Equilibrium is a central concept in game theory. It occurs when each player’s strategy is a best response to the strategies chosen by the other players. In other words, no player can unilaterally improve their payoff by changing their strategy, given the strategies of the other players. Nash Equilibrium represents a stable state where no player has an incentive to deviate from their chosen strategy.
Best Response: A best response is a strategy that maximizes a player’s payoff, given the strategies chosen by the other players. It is the strategy that a rational player would choose, assuming the other players’ strategies are fixed. In a game with multiple Nash Equilibria, a player’s best response will depend on the strategies chosen by the other players.

By analyzing the normal form representation, decision trees, dominant strategies, and Nash Equilibrium, game theory provides insights into how strategic behavior can emerge in various contexts, such as economics, politics, and social interactions. It helps to predict and understand the outcomes of strategic interactions among rational decision-makers.

Assignment Brief 5: Monopoly: sources of monopoly power; solving for the optimal profit of a monopolist, and comparing with the competitive case; natural monopoly; deadweight loss of monopoly; cartel.

Monopoly refers to a market structure in which there is a single seller or producer of a product or service, with no close substitutes available. As a result, the monopolist has substantial control over the market and can influence prices and output levels. Let’s discuss the various aspects of monopoly you mentioned:

Sources of Monopoly Power:

Exclusive control over a crucial resource or input: If a firm has exclusive control over a key resource required to produce a particular good or service, it can establish a monopoly by preventing others from accessing that resource.
Legal barriers: Governments may grant exclusive rights or patents to a particular firm, thereby restricting competition in a specific industry.
Economies of scale: Some industries have significant economies of scale, meaning that larger firms can produce goods or services at lower average costs. If a firm can achieve a significant cost advantage over its competitors, it may become a monopolist.
Network effects: In certain industries, the value of a product or service increases as more people use it. This creates a barrier to entry for potential competitors, allowing the dominant firm to maintain a monopoly.

Optimal Profit for a Monopolist:

A monopolist aims to maximize its profit by setting the level of output and price that maximizes the difference between total revenue and total cost. The optimal profit occurs when the marginal revenue (MR) equals marginal cost (MC). However, unlike in a competitive market, a monopolist does not have to set the price equal to the marginal cost.

Comparison with the Competitive Case:

Compared to a perfectly competitive market, a monopolist typically produces a lower quantity of output and charges a higher price. This leads to several differences:

Higher prices: Monopolists have the power to set prices above the marginal cost, which leads to higher prices for consumers.
Lower output: Due to the higher prices, monopolists often produce less output compared to a competitive market.
Lower consumer surplus: Consumer surplus, which represents the value consumers receive above what they pay, is typically reduced under monopoly.
Higher profit: Monopolists can earn substantial profits in the long run due to their market power.

Natural Monopoly:

A natural monopoly occurs when a single firm can efficiently provide the entire output of a particular good or service at a lower cost than multiple competing firms. It arises primarily due to significant economies of scale. In natural monopolies, competition is not feasible because it would result in duplication of infrastructure and higher costs. Examples include utilities such as water, electricity, and natural gas.

Deadweight Loss of Monopoly:

Deadweight loss refers to the loss of economic efficiency that occurs when the output level of a market deviates from the perfectly competitive equilibrium. In the case of a monopoly, deadweight loss arises because the monopolist restricts output below the level that would occur in a competitive market. As a result, consumer surplus is reduced, and overall social welfare decreases.

Cartel:

A cartel is an agreement or collaboration between multiple firms in an industry to restrict competition and maximize joint profits. Cartels typically involve price-fixing, market sharing, output quotas, or bid-rigging, all of which eliminate or reduce competition among the cartel members. By colluding, cartel members can behave collectively as a monopolist, effectively controlling prices and quantities in the market. Cartels are generally illegal in most countries due to their negative impact on competition and consumer welfare.

Assignment Brief 6: Monopolistic Competition and Oligopolies: monopolistic competition in the short run and long run; deriving a Cournot equilibrium; deriving a Bertrand equilibrium; mapping of reaction functions both mathematically and graphically.

Monopolistic Competition in the Short Run:

In monopolistic competition, there are many firms in the market, each producing slightly differentiated products. In the short run, firms can make independent decisions about their production levels and prices.

Profit Maximization: Firms maximize their profits by producing where marginal cost (MC) equals marginal revenue (MR) and then setting their price based on the demand curve they face.
Price-Output Decision: In the short run, if a firm’s price is greater than average variable cost (AVC), it continues to operate. If price is less than average variable cost, the firm shuts down.
Entry and Exit: In monopolistic competition, there is free entry and exit in the long run. If firms are making positive economic profits, new firms will enter the market, increasing competition and reducing profits. Conversely, if firms are making losses, some firms will exit the market, reducing competition and potentially allowing the remaining firms to earn positive profits.

Monopolistic Competition in the Long Run:

In the long run, firms in monopolistic competition will adjust their production levels and prices to achieve an equilibrium situation. Here are the key aspects:

Zero Economic Profits: In the long run, firms in monopolistic competition will earn zero economic profits. New firms can enter the market and offer similar products, increasing competition and reducing profits.
Excess Capacity: In the long run, firms in monopolistic competition operate with excess capacity because they produce at a quantity lower than the one associated with minimum average total cost (ATC). This is due to product differentiation and the desire to maintain a unique market position.
Product Differentiation: Firms engage in product differentiation through branding, marketing, quality, or other factors to create a perceived difference between their products and those of their competitors.

Deriving a Cournot Equilibrium:

Cournot competition is a model of oligopoly where firms compete in terms of quantities produced. Here’s how to derive a Cournot equilibrium:

Assumptions: Assume there are two firms, Firm 1 and Firm 2, producing homogeneous goods. Both firms choose their quantities simultaneously.
Reaction Functions: Each firm determines its quantity based on its belief about the quantity the other firm will produce. The reaction function for Firm 1 represents the quantity Firm 1 will produce as a function of the quantity chosen by Firm 2, and vice versa.
Best Response: Each firm selects the quantity that maximizes its profit, taking into account the quantity produced by the other firm.
Equilibrium: The Cournot equilibrium occurs when both firms’ quantities are such that they are simultaneously maximizing their profits, given the quantity chosen by the other firm.

Deriving a Bertrand Equilibrium:

Bertrand competition is another model of oligopoly where firms compete in terms of prices. Here’s how to derive a Bertrand equilibrium:

Assumptions: Assume there are two firms, Firm 1 and Firm 2, producing homogeneous goods. Both firms choose their prices simultaneously.
Reaction Functions: Each firm determines its price based on its belief about the price set by the other firm. The reaction function for Firm 1 represents the price Firm 1 will charge as a function of the price chosen by Firm 2, and vice versa.
Best Response: Each firm selects the price that maximizes its profit, taking into account the price set by the other firm.
Equilibrium: The Bertrand equilibrium occurs when both firms’ prices are such that they are simultaneously maximizing their profits, given the price set by the other firm.

Mapping of Reaction Functions:

The reaction functions of firms in oligopoly can be expressed mathematically and graphically. Let’s consider a simple example with two firms, Firm 1 and Firm 2:

Mathematically: The reaction function for Firm 1 can be denoted as Q1 = R1(Q2), where Q1 represents the quantity produced by Firm 1, and Q2 represents the quantity produced by Firm 2. Similarly, the reaction function for Firm 2 can be denoted as Q2 = R2(Q1).
Graphically: On a graph where the x-axis represents the quantity produced by Firm 1 (Q1) and the y-axis represents the quantity produced by Firm 2 (Q2), the reaction functions can be plotted as curves or lines. The intersection of the two reaction functions represents the equilibrium quantities chosen by the firms.

Assignment Brief 7: Externalities and Public Goods consumption and production externalities; solutions to externalities; properties of public goods; free-rider problem.

Externalities:

Externalities are the spillover effects of economic activities on third parties who are not directly involved in the production or consumption of goods or services. There are two types of externalities: consumption externalities and production externalities.

Consumption Externalities: These occur when the consumption of a good or service by one individual affects the well-being of others. Positive consumption externalities arise when the consumption of a good generates benefits for others, such as education or vaccinations. Negative consumption externalities occur when the consumption of a good imposes costs on others, like secondhand smoke from tobacco consumption.
Production Externalities: These arise when the production of a good or service affects the well-being of others who are not involved in the production process. Positive production externalities occur when the production process generates benefits for others, such as research and development leading to technological advancements. Negative production externalities occur when the production process imposes costs on others, such as pollution emitted by a factory.

Solutions to Externalities:

There are several ways to address externalities:

Government Regulation: Governments can impose regulations and standards to reduce negative externalities, such as setting emission limits for factories or implementing restrictions on smoking in public places. Similarly, governments can provide subsidies or tax incentives to promote positive externalities, like grants for research and development.
Pigouvian Taxes/Subsidies: These are taxes or subsidies imposed by the government to align private costs or benefits with social costs or benefits. For example, a tax on carbon emissions would internalize the negative externality of pollution by making producers pay for the environmental damage they cause.
Tradable Permits: Tradable permits, also known as cap-and-trade systems, can be used to control pollution. The government sets a limit on the total allowable emissions and issues permits to firms. Companies that can reduce their emissions more efficiently can sell their excess permits to those that find it more difficult or costly to do so.
Coase Theorem: The Coase Theorem suggests that if property rights are clearly defined and transaction costs are low, parties can negotiate and reach mutually beneficial agreements to internalize externalities without government intervention. However, in practice, transaction costs and complex negotiations can limit the applicability of this approach.

Properties of Public Goods:

Public goods are goods or services that are non-excludable and non-rivalrous. Non-excludability means that individuals cannot be effectively excluded from using the good, and non-rivalry means that one person’s consumption of the good does not reduce its availability for others. Some key properties of public goods include:

Non-Excludability: It is difficult or impractical to exclude individuals from using public goods once they are provided. For example, street lighting benefits everyone in the area, and it is challenging to prevent non-payers from benefiting.
Non-Rivalry: Consumption of a public good by one individual does not reduce its availability for others. For instance, the enjoyment of a beautiful view by one person does not diminish the ability of others to appreciate the same view.

Free-Rider Problem:

The free-rider problem is a phenomenon that occurs with public goods. Since public goods are non-excludable, individuals can benefit from their provision without contributing to their production or maintenance. This creates an incentive for individuals to “free ride” and avoid paying for the public good, relying on others to bear the costs. The free-rider problem can lead to underproduction or underinvestment in public goods since there is no direct financial incentive for individuals to contribute.

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