Question

During the $\mathbf{1980}$s, most of the world’s supply of lysine was produced by a Japanese company named Ajinomoto. Lysine is an essential amino acid that is an important livestock feed component. At this time, the United States imported most of the world’s supply of lysine—more than$\mathbf{30},\mathbf{000}$tons—to use in livestock feed at a price of$\mathbf{\text{(1.65}}$per pound. The worldwide market for lysine, however, fundamentally changed in$\mathbf{1991}$when U.S.-based Archer Daniels Midland (ADM) began producing lysine—a move that doubled worldwide production capacity. Experts conjectured that Ajinomoto and ADM had similar cost structures and that the marginal cost of producing and distributing lysine was approximately \)$\mathbf{0}.\mathbf{70}$per pound. Despite ADM’s entry into the lysine market, suppose demand remained constant at$\mathbf{\text{Q=208-80P}}$(in millions of pounds). Shortly after ADM began producing lysine, the worldwide price dropped to \($\mathbf{0}.\mathbf{70}$. By,$\mathbf{1993}$ however, the price of lysine shot back up to$\mathbf{\text{)1.65}}$. Use the theories discussed in this chapter to provide a potential explanation for what happened in the lysine market. Support your answer with appropriate calculations.

Short answer

The Japanese company finds itself in a situation in which it faces a new rival firm, it will agree to collusion with its rival to obtain a profit of$\mathrm{\$}36.1$ per pound to earn$0$ under the Bertrand model.

Step-by-step solution

Given 

In this first scenario, the Japanese company Ajinomoto has a monopoly on theproduction of lysine and has the following information on demand, cost and price.

Demand function:$\text{Q}=208-80\text{P}$

Monopoly Price$\text{(P):1.65}$

Marginal Cost:$\$0.70$

To substitute the monopoly price

We can substitute the monopoly price in the demand function to obtain the monopoly equilibrium output.

$\begin{array}{c}\mathrm{Q}=208-80\mathrm{P}\\ =208-80(1.65)\\ =76\end{array}$

The company Ajinomoto, having total control of the supply, will have an equilibrium output level of $76$.

To obtain the monopoly profit

We can now obtain the monopoly profit through the following equation:

$\begin{array}{c}\mathrm{\Pi }=\text{TotalRevenue}-\text{TotalCost}\\ =(\text{Price}\times \text{Quantity})-(\text{MarginalCost}\times \text{Quantity})\\ =(1.65\times 76)-(0.70\times 76)\\ =125.4-53.2\\ =72.2\end{array}$

Step 4:To determinate the level of output

In this other scenario, when a new competitor entered the lysine market (ADM), it caused production to double, causing an excess supply and therefore the price equalled the marginal costs by$0.70\mathrm{\$}.$ Therefore, we can determine the level of production and profit.

Fulfilling the condition that:

${\text{P}}_{\text{1}}{\text{=P}}_{\text{2}}\text{=MC=0.70}$

We can determinate the level of output:

$\begin{array}{c}Q=208-80\left(0.70\right)\\ =152\end{array}$

Therefore, the total output of lysine will be$152$ and since the two companies have the same demand function, each one will produce the same, that is,$76(152/2)$ for each firm.

To obtain under this oligopoly scheme

The profit that each firm will obtain under this oligopoly scheme can be calculated as follows:

$\mathrm{\Pi }=(0.70\times 76)-(0.70\times 76)=0$

It can be seen that when a new competitor enters they will face a price war to the point where their prices are equal to their marginal costs and their profit is zero, so it is a Bertrand oligopoly model.

To find the expected benefits

However, two years later the price of lysine rises again to$\mathrm{\$}1.65$(the initial level of the monopoly), therefore both firms will colluding and agree to maintain the same level of output from the monopoly level.

$\begin{array}{c}\mathrm{Q}=208-80\mathrm{P}\\ =208-80\left(1.65\right)\\ =76\end{array}$

The difference is that now there are two firms, so each one will produce exactly the same as having the same demand function, that is,$38$units$(76/2).$

Under the Collusion oligopoly model the expected benefits of each firm will be as follows:

$\begin{array}{c}\mathrm{\Pi }=(1.65\times 38)-(0.70\times 38)\\ =62.7-26.6\\ =36.1\end{array}$

Therefore, when the Japanese company finds itself in a situation in which it faces a new rival firm, it will agree to collusion with its rival to obtain a profit of$\$36.1$ per pound to earn$0$ under the Bertrand model.