## MEC 101 Microeconomic Analysis Assignment Solution pdf

# SECTION B

#### Answer the following questions in about 400 words each. Each question carries 12 marks.

#### (5) A. Differentiate between the Cournot and the Bertrand model of Oligopoly.

An oligopoly is a market structure in which there are a few large firms that dominate the market and compete with each other. The Cournot model and the Bertrand model are two different ways of analyzing oligopoly markets and predicting the behaviour of firms in these markets.

The Cournot model, developed by French economist Antoine Cournot in 1838, is based on the assumption that firms in an oligopoly market compete by setting their output levels. In the Cournot model, each firm takes into account the output level of its rivals when deciding how much to produce, and the market price is determined by the total output of all firms.

The Bertrand model, developed by French economist Joseph Bertrand in 1883, is based on the assumption that firms in an oligopoly market compete by setting their prices. In the Bertrand model, each firm takes into account the prices of its rivals when deciding how much to charge for its products, and the market quantity is determined by the total output of all firms.

There are several key differences between the Cournot model and the Bertrand model:

Output versus price: In the Cournot model, firms compete by setting their output levels, while in the Bertrand model, they compete by setting their prices.

Equilibrium: In the Cournot model, the equilibrium is a Nash equilibrium in output, while in the Bertrand model, it is a Nash equilibrium in prices.

Profit: In the Cournot model, firms may earn positive profits even in equilibrium, while in the Bertrand model, firms earn zero profits in equilibrium.

Price elasticity of demand: In the Cournot model, the demand curve is relatively inelastic, while in the Bertrand model, the demand curve is relatively elastic.

Overall, the Cournot model and the Bertrand model are two different approaches to analyzing oligopoly markets and predicting the behaviour of firms in these markets. They are useful tools for understanding how firms may compete and make decisions in oligopoly markets.

#### (5) B.Â Consider an industry with two firms 1 and 2, each producing output Q1 and Q2respectively and facing the industry demand given by P=140-Q, where P is the market price and Q represents the total industry output, that is Q= Q1 + Q2. Assume that each faces a marginal cost of â‚¹ 20 per unit with no fixed costs. Solve for the Cournot equilibrium in such an industry.

To solve for the Cournot equilibrium in an industry with two firms facing the given demand function, you can use the following steps:

- Set up the profit maximization problem for each firm: Each firm aims to maximize its profits by choosing the output level that maximizes its total revenue minus its total cost. In this case, the total revenue of firm 1 is P * Q1, and its total cost is 20 * Q1. The total revenue of firm 2 is P * Q2, and its total cost is 20 * Q2.
- Determine the optimal output level for each firm: To find the optimal output level for each firm, you can set the first-order condition for profit maximization, which states that the marginal revenue of each firm (the derivative of its total revenue with respect to its output) must equal its marginal cost (20).

For firm 1, the marginal revenue is given by the derivative of P * Q1 with respect to Q1, which is P. For firm 2, the marginal revenue is given by the derivative of P * Q2 with respect to Q2, which is also P.

Thus, the first-order condition for profit maximization for both firms is:

P = 20

- Substitute in the demand function: Substituting the demand function P = 140 – Q into the first-order condition gives us:

140 – Q = 20

Solving this equation gives us Q = 120.

- Calculate the output levels of each firm: The total industry output is equal to the sum of the output levels of each firm, which is Q = Q1 + Q2 = 120. Therefore, each firm produces an output of Q1 = Q2 = 60.
- Calculate the equilibrium price: The equilibrium price is given by the demand function, which is P = 140 – Q = 140 – 120 = 20.

Therefore, the Cournot equilibrium in this industry is Q1 = Q2 = 60 and P = 20. This represents the output levels and price at which each firm maximizes its profits and the industry reaches equilibrium.

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