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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

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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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