<p>Let <span class="math-container">$x = D(p)$</span> be the demand for a good if the price is equals to <span class="math-container">$p$</span>. The inverse demand curve (as you would draw it) is then given by <span class="math-container">$p = D^{-1}(x)$</span>. It gives the price as a function of the quantity.</p>
<p>If there is a rebate of <span class="math-container">$r$</span> and if <span class="math-container">$p$</span> is the price, then the consumer only pays <span class="math-container">$p^\ast = p - r$</span>. Then the demand is given by:
<span class="math-container">$$
x = D(p^\ast) = D(p - r).
$$</span>
Inverting this gives:
<span class="math-container">$$
p - r = D^{-1}(x),\\
 \to p = D^{-1}(x) + r
$$</span>
So the inverse demand curve (as you would draw it) shifts up by an amount <span class="math-container">$r$</span>.</p>

CC BY-SA 4.0
2021-07-15T05:40:45.193Z
2021-07-15T05:40:45.193Z
tdm
<p>I am currently working on an assignment and needed some help.</p>
<p>My assignment requires me to find an article relating to a form of government intervention such as taxes or subsidies and analyse the article using a supply and demand diagram.</p>
<p>For my essay, I have chosen an article that essentially talks about a rebate that should be removed. So far I have written that the consumer subsidy causes negative externalities and the removal of these rebates would help reallocate resources for incentivizing other methods. I know that rebates are essentially subsidies given to consumers to increase consumption, so they would affect the demand curve. However, I am stuck on the diagram as I am confused on which way the demand curve shifts and why. Would you please help me?</p>
<p>Thanks in Advance</p>

<microeconomics><supply-and-demand><subsidies>
How to show consumer subsidy (rebate) on supply and demand diagram?
NAthan
# How to show consumer subsidy (rebate) on supply and demand diagram?

(Asked by: username_0 on 2021-07-12)

I am currently working on an assignment and needed some help.

My assignment requires me to find an article relating to a form of government intervention such as taxes or subsidies and analyse the article using a supply and demand diagram.

For my essay, I have chosen an article that essentially talks about a rebate that should be removed. So far I have written that the consumer subsidy causes negative externalities and the removal of these rebates would help reallocate resources for incentivizing other methods. I know that rebates are essentially subsidies given to consumers to increase consumption, so they would affect the demand curve. However, I am stuck on the diagram as I am confused on which way the demand curve shifts and why. Would you please help me?

Thanks in Advance

**Tags:** microeconomics, supply-and-demand, subsidies


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## 1 answers

### Answer by username_1 on 2021-07-15. Score: 2

Let $x = D(p)$ be the demand for a good if the price is equals to $p$. The inverse demand curve (as you would draw it) is then given by $p = D^{-1}(x)$. It gives the price as a function of the quantity.

If there is a rebate of $r$ and if $p$ is the price, then the consumer only pays $p^\ast = p - r$. Then the demand is given by:
$$
x = D(p^\ast) = D(p - r).
$$
Inverting this gives:
$$
p - r = D^{-1}(x),\\
\to p = D^{-1}(x) + r
$$
So the inverse demand curve (as you would draw it) shifts up by an amount $r$.


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