Let c be the marginal cost of the firm, and p is the price of the product. What is the definition of M argin? 2. Suppose two identical firms with the constant marginal cost produce the same product and compete in the market. under which model the equilibrium profit for each firm must be zero? Bertrand or Cournot model, or neither 3. In the finite-period sequential game, we can use the backward-induction method to find all Nash equilibria. Is this statement true?

QUESTION

1. Let c be the marginal cost of the firm, and p is the price of the product.

What is the definition of M argin?

2. Suppose two identical firms with the constant marginal cost produce the same product and compete in the market.

under which model the equilibrium profit for each firm must be zero? Bertrand or Cournot model, or neither

3. In the finite-period sequential game, we can use the backward-induction method to find all Nash equilibria.

Is this statement true?

4. Suppose price is the long-run choice for firms in the market.

which model is better to capture the competition among firms? Bertrand or Cournot model, or neither 3

5. Suppose in the market there are n ≥ 2 firms. For each firm i = 1, · · · , n, marginal cost is ci , market share is si , the market price is p.

What is the definition of Lerner index?

ANSWER

The term “margin” refers to the incremental or additional change in a certain variable. In economics, the concept of margin is often used to analyze the impact of small changes on various economic indicators. Specifically, the marginal cost of a firm represents the cost of producing one additional unit of output. It is calculated by dividing the change in total cost by the change in quantity produced. On the other hand, the price of a product, denoted as p, represents the amount of money that consumers are willing to pay to acquire each unit of the product.

In the context of two identical firms with constant marginal cost competing in the market, the model that results in an equilibrium profit of zero for each firm is the Bertrand model. The Bertrand model assumes that firms set prices rather than quantities. In this model, firms engage in price competition, where each firm independently selects a price for its product. If the two firms set prices equal to their marginal cost, they will effectively compete away any profit, leading to a zero-profit equilibrium.

In contrast, the Cournot model assumes that firms compete by choosing quantities rather than prices. Each firm determines the quantity it will produce, taking into account the quantity produced by the other firm. In this model, the equilibrium typically results in positive profits for each firm, as the quantity competition allows for some market power to be exerted by each firm.

The statement that we can use the backward-induction method to find all Nash equilibria in a finite-period sequential game is not true. The backward-induction method is a technique used in game theory to solve extensive-form games, where players move sequentially and have perfect information about the previous players’ actions. While backward induction can help identify subgame-perfect Nash equilibria in certain finite games, it does not guarantee the discovery of all Nash equilibria in general. Some games may have multiple Nash equilibria that cannot be fully captured through the backward-induction method alone.

When considering the long-run choice for firms in the market, neither the Bertrand nor the Cournot model can be definitively categorized as better at capturing competition among firms. Both models provide different perspectives on how firms interact and compete, with their own assumptions and implications.

The Bertrand model assumes that firms compete on prices and that consumers always choose the product with the lowest price. In this model, firms engage in aggressive price competition, potentially driving prices down to the marginal cost level, resulting in zero-profit equilibrium. This model is more suitable for markets where firms have low production costs and can easily adjust their prices.

On the other hand, the Cournot model assumes that firms compete on quantities. Each firm determines its output level, taking into account the expected response of other firms. This model allows firms to have some market power and capture positive profits, as they set quantities that balance the trade-off between market demand and the actions of other competitors. The Cournot model is often used to analyze industries where firms have production capacity constraints and cannot adjust output levels as easily.

The choice of which model is more appropriate depends on the specific characteristics of the market under consideration, such as the nature of the product, market demand, cost structure, and strategic behavior of firms. It is essential to carefully assess these factors to determine the model that best captures the dynamics of competition in a given market.

The Lerner index is an economic measure used to quantify the degree of market power or market concentration held by a firm in a specific industry. It is named after economist Abba Lerner, who introduced the index in 1934. The Lerner index is calculated as the difference between the firm’s price and its marginal cost, divided by the price:

Lerner Index = (p – c) / p

where “p” represents the market price of the product, and “c” represents the firm’s marginal cost.

The Lerner index ranges from 0 to 1, with higher values indicating a greater degree of market power. When the Lerner index is close to 0, it suggests that the firm operates in a highly competitive market where prices align closely with marginal costs. Conversely, a Lerner index closer to 1 indicates a higher level of market power, where the firm can set prices significantly above its marginal cost.

The Lerner index provides valuable insights into the competitiveness of a market and the ability of firms to influence prices. Policymakers and regulators often use this index to assess market concentration, antitrust concerns, and the potential for market abuse by dominant firms. Additionally, the Lerner index is widely employed in empirical studies and economic research to analyze market structures and conduct policy evaluations related to market competition.