Question

1.Using a linear demand function and constant marginal cost function as illustration, explain the Cournot model with product differentiation. Derive the sufficient condition that all firms have no incentive to cheat.

2.In the context of a static duopoly model explain why the joint profit maximizing solution is unstable. Discuss some factors that may engender collusion.

3.Using a quadratic net birth function, and linear total cost and catch functions as illustration, derive the supply function of fishery. Why this supply function is backward bending?

Answer 1

1.Using a linear demand function and constant marginal cost function as illustration, explain the Cournot model with product differentiation. Derive the sufficient condition that all firms have no incentive to cheat.

Cournot model is a model where the firms decides the quantity simultaneously given other firms quantity decision.

Suppose there are 2 firms which are producing differentiated product. The demand curve for the commodity is given below:

P=a-bQ1-bQ2

The marginal cost for both firms are 0.

The cournot model equilibrium and sufficient condition is calculated below:

Profit1= (a-bQ1-bQ2)*Q1-0*Q1

Profit2= (a-bQ1-bQ2)*Q2-0*Q2

dProfit1/dQ1=(a-2bQ1-bQ2)

(a-2bQ1-bQ2)=0

Q1=(a-bQ2)/2b

dProfit2/dQ2=(a-2bQ2-bQ1)

(a-2bQ2-bQ1)=0

Q2=(a-bQ1)/2b

Solving the 2 equations, the value of quantites are :

Q1=(a)/3b

Q2=(a)/3b

P=a-bQ1-bQ2

P=a/3

Profit1=a2/9b

Profit2=a2/9b

The sufficient conditions for firms not deviating fron the equilibrium are :

d2Profit1/dQ12=-2b

d2Profit2/dQ22=-2b

Given b is positive, the second order is negative which implies the profit is maximised at the equilibrium quantity.

If any firm increases its quantity, the price will fall and the firm profit will fall. Therefore, no firm has incentive to deviate from the equilibrium

2.In the context of a static duopoly model explain why the joint profit maximizing solution is unstable. Discuss some factors that may engender collusion.

There are two companies in the Duopoly model, each with its own profits Assume that the Other Company in the future will continue to produce the same amount.
This assumption constrains the pricing strategy, because it is not necessary to devise what The other company is going to do something to repress.

The companies involved are called a cartel when collusion is concluded. The Elements The collusion which could not succeed is as follows:

As the number of firms increases, collusion becomes more difficult, There is a tendency of collusion when the few companies have similar market shares
It may not be successful if the products are more differentiated. If there is a similar situation It could succeed goods. Goods.
If there is a different cost structure collaboration can occur
The collusion can occur less if the threat of retaliation. When is the danger It may not happen very high collusion.
Collusion may occur if there is a high external competition.

3.Using a quadratic net birth function, and linear total cost and catch functions as illustration, derive the supply function of fishery. Why this supply function is backward bending?

In the bioeconomic thesis, the long term fish catch supply is described by a backward-bending supply curve. The shape of the curve always show in a bell- shape.

Diagram

In most of the sectors supply increases if the price increases, but in fishery sector supply curve may goes to bend as pointed by copes.

Reasons behind the supply is backward bending:-

1. Reduction of labour

2. Scarcity of particular spices

3. Change in technology

4. Climate conditions

5. Natural disasters

6. Lack of cold storages