<p>If our consumer buys more than 2 units of <span class="math-container">$x$</span> we can rewrite his budget constraint in the following way.</p>
<p><span class="math-container">$$
\begin{align*}
&amp;\underbrace{2 \times 2}_{\text{first 2 units of $x$ at price 2}} + \underbrace{(x-2)}_{\text{remaining units of $x$ at price 1}} + y = 12,\\
\leftrightarrow &amp; 2+ 2 + (x - 2) + y = 12,\\
\leftrightarrow &amp;
2 + (2 + x - 2) + y = 12,\\
\leftrightarrow &amp;x + y = 10.
\end{align*} 
$$</span></p>

CC BY-SA 4.0
2023-09-18T10:19:14.370Z
2023-09-18T10:19:14.370Z
tdm
<p>A consumer has the utility function:</p>
<p>u(x,y) = x*y</p>
<p>his initial budget constraint is: 12 = 2<em>x+ 1</em>y. He has a budget of $12 for the whole question, which has to be completely used.</p>
<p>so that he consumes 3 x and 6 y.</p>
<p>Now he gets a quantity discount: the first two units of x cost <span class="math-container">$ 2 and every additional unit costs $</span>1.</p>
<p>How much x and y does he consume now?</p>
<p>I’ve already posted the question on Chegg several times and always got a different answer. Please help me.</p>
<p>My thought: the consumption if y doenst depend on the price of x, so he keeps consuming 6y. That means he has <span class="math-container">$10 left for x. The first two untits cost $</span>2. So 6-2*2= 2, because half of his budget is used for x. So he can buy 2+2 units of x.</p>
<p>textbook solution: He consumes 5x and 5y, because if he consumes more than 2x his budget constraint is 10 = x + y. (why 10? not 8?)</p>

<microeconomics><consumer-theory>
Consumption with quantity discount
AJl
# Consumption with quantity discount

(Asked by: username_0 on 2023-09-18)

A consumer has the utility function:

u(x,y) = x\*y

his initial budget constraint is: 12 = 2*x+ 1*y. He has a budget of $12 for the whole question, which has to be completely used.

so that he consumes 3 x and 6 y.

Now he gets a quantity discount: the first two units of x cost $ 2 and every additional unit costs $1.

How much x and y does he consume now?

I’ve already posted the question on Chegg several times and always got a different answer. Please help me.

My thought: the consumption if y doenst depend on the price of x, so he keeps consuming 6y. That means he has $10 left for x. The first two untits cost $2. So 6-2\*2= 2, because half of his budget is used for x. So he can buy 2+2 units of x.

textbook solution: He consumes 5x and 5y, because if he consumes more than 2x his budget constraint is 10 = x + y. (why 10? not 8?)

**Tags:** microeconomics, consumer-theory

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## 1 answers

### Answer by username_1 on 2023-09-18. Score: 1 | Accepted answer

If our consumer buys more than 2 units of $x$ we can rewrite his budget constraint in the following way.

$$
\begin{align\*}
&\underbrace{2 \times 2}\_{\text{first 2 units of $x$ at price 2}} + \underbrace{(x-2)}\_{\text{remaining units of $x$ at price 1}} + y = 12,\\
\leftrightarrow & 2+ 2 + (x - 2) + y = 12,\\
\leftrightarrow &
2 + (2 + x - 2) + y = 12,\\
\leftrightarrow &x + y = 10.
\end{align\*}
$$


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