Question

You are a pricing manager at Argyle Inc.—a medium-sized firm that recently introduced a new product into the market. Argyle’s only competitor is Baker Company, which is significantly smaller than Argyle. The management of Argyle has decided to pursue a short-term strategy of maximizing this quarter’s revenues, and you are in charge of formulating a strategy that will permit the firm to do so. After talking with an employee who was recently hired from the Baker Company, you are confident that

(a) Baker is constrained to charge for its product,

(b) Baker’s goal is to maximize this quarter’s profits, and

(c) Baker’s relevant unit costs are identical to yours. You have been authorized to price the product at two possible levels) and know that your relevant costs areper unit. The marketing department has provided the following information about the expected number of units sold (in millions) this quarter at various prices to help you formulate your decision:

Argyle and Baker currently set prices at the same time. However, Argyle can become the first-mover by spending \(2 million on computer equipment that would permit it to set its price before Baker. Determine Argyle’s optimal price and whether you should invest the \)2 million.

Short answer

The optimal price of Argyle will be $5. It will not be necessary to incur the expense of $2 million on computer equipment that would allow it to set its price before Baker. The Baker will choose regardless of the price that we will maximize our revenues charging a price of $5.

Step-by-step solution

Given by

As there are two companies in the market, Argyle (A) and Baker Company (B), each one has short-term objectives:

1. Argyle wants to maximize this quarter's revenues.

2. Baker wants to maximize this quarter's profits.

Likewise, it is important to keep in mind that the prices that Argyle can charge for its products is while the prices that Baker can charge is according to its cost structure.

Expanding the information table

With the information given on the prices charged by each firm and the quantities sold (measured in millions of quantities), we can obtain the income, and profits. Argyle and Baker's costs will be the same, $2 for every million unit produced.

Therefore, we can expand the information table of each company as follows:

Taking the results of the possible revenue for Argyle and the possible profit for Baker, together with the price options for each firm, we can build this payoff matrix:

Argyle's dominant strategy

Argyle's dominant strategy will be to charge a price of $5. Even though Baker charges $10 or $20, revenue of $15 will be obtained. If we choose a price of $10 we would obtain a less revenue of $10.

On Baker's side, the dominant strategy will be to charge a price of $20.Regardless of whether Argyle is priced a $5 or $10, Baker's profits will be $18.

Therefore, the optimal price of Argyle will be $5. It will not be necessary to incur the expense of $2 million on computer equipment that would allow it to set its price before Baker. The Baker will choose regardless of the price that we will maximize our revenues charging a price of $5.