<p>To be formal, the production function is (under strict positiivity constraints)</p>

<p><span class="math-container">$$y = F(x) = 2x \implies x(y) = \frac{y}{2}$$</span></p>

<p>and the Total cost function is </p>

<p><span class="math-container">$$TC = p_x\cdot x(y) = p_x \cdot \frac{y}{2}$$</span></p>

<p>Then the Average Cost function is</p>

<p><span class="math-container">$$AC = \frac {TC}{y} = \frac{p_x}{2}$$</span></p>

<p>So the exercise gives the correct answer. Where did the OP's logic went wrong?</p>

<p>The OP wrote</p>

<blockquote>
  <p>...because to create another unit of <span class="math-container">$y$</span> I need <span class="math-container">$2$</span> units of <span class="math-container">$x$</span></p>
</blockquote>

<p>Is the OP sure about the correctness of that statement? It seems to me that if I have one unit of <span class="math-container">$x$</span> I can produce <em>two</em> units of <span class="math-container">$y$</span> since <span class="math-container">$y=2x\implies y = 2\cdot 1 = 2$</span>,  therefore to <em>one</em> unit of <span class="math-container">$y$</span> corresponds <em>half</em> a unit of <span class="math-container">$x$</span>.</p>

CC BY-SA 4.0
2019-07-29T13:28:52.940Z
2019-07-29T13:28:52.940Z
Alecos Papadopoulos
<p>I have a given product <span class="math-container">$y$</span> that is produced by the input <span class="math-container">$x$</span> in the following relation: <span class="math-container">$2x=y$</span>. In our example, we are given the unit price of <span class="math-container">$x$</span> is <span class="math-container">$16$</span>. Find the unit cost of <span class="math-container">$y$</span>. The answer is <span class="math-container">$8$</span>. But I strongly disagree: surely it should be <span class="math-container">$32$</span> because to create another unit of <span class="math-container">$y$</span> I need <span class="math-container">$2$</span> units of <span class="math-container">$x$</span> each at cost <span class="math-container">$16$</span>, and therefore <span class="math-container">$32$</span> is the cost. Why is my answer wrong? I can’t see a fault in my logic?</p>

<microeconomics><production-function>
Production technology of $y=2x$
user9078057
# Production technology of $y=2x$

(Asked by: username_0 on 2019-07-29)

I have a given product $y$ that is produced by the input $x$ in the following relation: $2x=y$. In our example, we are given the unit price of $x$ is $16$. Find the unit cost of $y$. The answer is $8$. But I strongly disagree: surely it should be $32$ because to create another unit of $y$ I need $2$ units of $x$ each at cost $16$, and therefore $32$ is the cost. Why is my answer wrong? I can’t see a fault in my logic?

**Tags:** microeconomics, production-function

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## 1 answers

### Answer by username_1 on 2019-07-29. Score: 2 | Accepted answer

To be formal, the production function is (under strict positiivity constraints)

$$y = F(x) = 2x \implies x(y) = \frac{y}{2}$$

and the Total cost function is

$$TC = p\_x\cdot x(y) = p\_x \cdot \frac{y}{2}$$

Then the Average Cost function is

$$AC = \frac {TC}{y} = \frac{p\_x}{2}$$

So the exercise gives the correct answer. Where did the OP's logic went wrong?

The OP wrote

> ...because to create another unit of $y$ I need $2$ units of $x$

Is the OP sure about the correctness of that statement? It seems to me that if I have one unit of $x$ I can produce *two* units of $y$ since $y=2x\implies y = 2\cdot 1 = 2$, therefore to *one* unit of $y$ corresponds *half* a unit of $x$.


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