Re: Help with a question...



On 05/25/2006 10:51:10 "Raquel" <raquel_rodriguezus@xxxxxxxxx> wrote:

My first mail to the group and if this is not the right place for this,
please let me know a better one. A colleague of mine posed this question
to me and I have no clue.

Any firm that wants to produce soma needs to build an integer number of
plants: 0,1,2. Each plant costs the firm 3 dollars, with each plant
producing a single unit of SOMA. Market price p for one unit of soma is
5-(Q1+Q2) where Q1 is the #plants by firm 1 and Q2 is #plants by firm 2.
Suppose firm 1 builds before firm 2. How many plants should firm 1 build
and what will firm 2's reaction be.

I am not really sure how to handle this question.

The problem is not well posed. Do the managers of firm 1 take Q2 as given?
That is, do they assume that firm 2 keeps on producing the same quantity,
no matter how much firm 1 produces? Some such Cournot assumption is
typical of introductory economics.

Given the above assumption, can you write down the economic profit
firm 1 makes as a function of the number of plants firm 1 builds?

The constraint that the answer is an integer makes the problem hard. I
would solve it with calculus, ignoring this constraint. Then I would
check the results of rounding up and rounding down my answer.

But perhaps if I were to go through these steps, I would have some
other idea.

--
r c
v s a
i m p
e a e
n e .
@ r c m
d o
.

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