<p>Given the problem details, it is not a two plant problem. It is a problem with only one plant, with an option of upgrade. Clearly, the firm will exercise the upgrade option only if it is beneficial for it. So the cost function is simply:
<span class="math-container">$$c(q) = \min\left(wq^2, \frac{wq^2}{4} + F\right)$$</span>
where <span class="math-container">$w$</span> is the per unit price of the input <span class="math-container">$z$</span>.</p>

CC BY-SA 4.0
2023-04-20T17:13:13.753Z
2023-04-20T17:13:13.753Z
Amit
<p>Imagine hypothetically, there is a firm that has two option for production technology:</p>
<p>f(z) = √z but also the option to increase efficiency to g(z) = 2√z but this choice includes fixed cost F &gt; 0.</p>
<p>What would be the firms cost function if the cost minimizing choice is choosen.</p>
<p>Here's what I've done:</p>
<p>C = wz + F
C = Q^2 /4 + F</p>
<p>But I'm struggling to figure out which choice would be the cost minimizing choice as I could solve the cost function but don't understand which is cost minimizing in this regard.</p>

<microeconomics><producer-theory>
Firms choosing upgrade & minimizing choice
Lily B
# Firms choosing upgrade & minimizing choice

(Asked by: username_0 on 2023-04-19)

Imagine hypothetically, there is a firm that has two option for production technology:

f(z) = √z but also the option to increase efficiency to g(z) = 2√z but this choice includes fixed cost F > 0.

What would be the firms cost function if the cost minimizing choice is choosen.

Here's what I've done:

C = wz + F
C = Q^2 /4 + F

But I'm struggling to figure out which choice would be the cost minimizing choice as I could solve the cost function but don't understand which is cost minimizing in this regard.

**Tags:** microeconomics, producer-theory

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## 1 answers

### Answer by username_1 on 2023-04-20. Score: 2 | Accepted answer

Given the problem details, it is not a two plant problem. It is a problem with only one plant, with an option of upgrade. Clearly, the firm will exercise the upgrade option only if it is beneficial for it. So the cost function is simply:
$$c(q) = \min\left(wq^2, \frac{wq^2}{4} + F\right)$$
where $w$ is the per unit price of the input $z$.


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