Question

Define and Illustrate the Following:

1. A production function showing Increasing returns to Scale

2. A Long-Run Cost Function showing decreasing returns to Scale

3. Nash Equilibrium (Construct your Own example)

4. Cartel –like Oligopoly

Answer 1

1. Increasing returns to scale or diminishing cost refers to a situation when all factors of production are increased, output increases at a higher rate. It means if all inputs are doubled, output will also increase at the faster rate than double. Hence, it is said to be increasing returns to scale. This increase is due to many reasons like division external economies of scale.

Suppose, initially production function is as follows:

P = f (L, K)

Now, if both the factors of production i.e., labour and capital are increased in same proportion i.e., x, product function will be rewritten as:

P₁ = f(xL,xK)

If P₁ increases more than proportionate increase in the factors of production, i.e, P₁/P>x, it will be increasing return to scale.

2. When the increase in output is less than proportional to the increase in inputs, we say that there is decreasing returns to scale. Decreasing returns implies increasing average costs.
In the long run all inputs are variable. The production function is homogeneous if all inputs factors are increased in the same proportions in order to change the outputs.

A Production function Q = f (L, K )

An increase in Q> Q^ =f (L+L.10%, K+K.10% )- Inputs increased same proportion
Therefore,

Decreasing returns to scale : Inputs increased 10% => output increased 8%

3. The Nash Equilibrium is a concept of game theory where the optimal outcome of a game is one where no player has an incentive to deviate from his chosen strategy after considering an opponent's choice. Overall, an individual can receive no incremental benefit from changing actions, assuming other players remain constant in their strategies. A game may have one or multiple Nash Equilibria or none at all.

Let us take an example:

Two firms are merging into two divisions of a large firm, and have to choose the computer system to use. In the past the firms have used different systems, I and A; each prefers the system it has used in the past. They will both be better off if they use the same system then if they continue to use different systems.

We can model this situation by the following two-player strategic game.

		Player 2
		I	A
Player 1	I	2,1	0,0
	A	0,0	1,2

To find the Nash equilibria, we examine each action profile in turn.

(I,I) : Neither player can increase her payoff by choosing an action different from her current one. Thus this action profile is a Nash equilibrium.

(I,A) : By choosing A rather than I, player 1 obtains a payoff of 1 rather than 0, given player 2's action. Thus this action profile is not a Nash equilibrium. [Also, player 2 can increase her payoff by choosing I rather than A.]

(A,I) : By choosing I rather than A, player 1 obtains a payoff of 2 rather than 0, given player 2's action. Thus this action profile is not a Nash equilibrium. [Also, player 2 can increase her payoff by choosing A rather than I.]

(A,A) : Neither player can increase her payoff by choosing an action different from her current one. Thus this action profile is a Nash equilibrium.

We conclude that the game has two Nash equilibria, (I,I) and (A,A).

4. A cartel is defined as a group of firms that gets together to make output and price decisions. The conditions that give rise to an oligopolistic market are also conducive to the formation of a cartel; in particular, cartels tend to arise in markets where there are few firms and each firm has a significant share of the market. Now, Cartels are more prevalent in such oligopoly markets where there are few numbers of firms or where the number of sellers or producers is few in number. The firms which are members of cartel agree of several matters. Such matters include setting target prices or it can also be regarded as price fixing in order to cover major portion of the market. They also unanimously agree on reducing the total output level. It is the one of the tactics to control demand and supply of the product. They may also agree on minimum production cost. In the U.S., cartels are illegal; however, internationally, there are no restrictions on cartel formation. The organization of petroleum?exporting countries (OPEC) is perhaps the best?known example of an international cartel; OPEC members meet regularly to decide how much oil each member of the cartel will be allowed to produce.