<p>There is an exercise in a Microeconomics book that says an income grant to a person provides more utility than does a subsidy on one good that costs the same amount to the government. Something like <a href="https://www.economicsdiscussion.net/wp-content/uploads/2014/06/image_thumb109.png" rel="nofollow noreferrer">this</a> gives a rough idea but not the complete picture. If I don't know the consumer's utility function, how can I reach a conclusion?</p>
<p>In other words, we have to show that <span class="math-container">$V(p_x, p_y, I+i_g) &gt; V(p_x - s_g, p_y, I)$</span> where <span class="math-container">$s_g$</span> is set appropriately to ensure the government subsidizes the first good only so much that the subsidy (in unit currency) is <span class="math-container">$i_g$</span>.</p>

CC BY-SA 4.0
2022-07-08T12:57:57.450Z
Hello! I don't know how this site works, can anyone tell me how to bring up my post so others can see it? ^_^
Isa
CC BY-SA 4.0
2022-07-14T17:29:40.063Z
Your claim is the symmetric case of Example 3.1.1 in MWG, where a detailed proof is available.
Herr K.
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2022-07-15T10:18:05.617Z
@HerrK. I think it is 3.I.1. I found it in the book you suggested. Thank you.
Isa
<microeconomics><consumer-theory><choice-theory>
Lump sum income grant is better than a subsidy grant
Isa
# Lump sum income grant is better than a subsidy grant

(Asked by: username_0 on 2022-07-07)

There is an exercise in a Microeconomics book that says an income grant to a person provides more utility than does a subsidy on one good that costs the same amount to the government. Something like [this](https://www.economicsdiscussion.net/wp-content/uploads/2014/06/image_thumb109.png) gives a rough idea but not the complete picture. If I don't know the consumer's utility function, how can I reach a conclusion?

In other words, we have to show that $V(p\_x, p\_y, I+i\_g) > V(p\_x - s\_g, p\_y, I)$ where $s\_g$ is set appropriately to ensure the government subsidizes the first good only so much that the subsidy (in unit currency) is $i\_g$.

**Tags:** microeconomics, consumer-theory, choice-theory

> **Comments:**
> **username_0**: Hello! I don't know how this site works, can anyone tell me how to bring up my post so others can see it? ^_^  
> **username_1**: Your claim is the symmetric case of Example 3.1.1 in MWG, where a detailed proof is available.  
> **username_0**: @HerrK. I think it is 3.I.1. I found it in the book you suggested. Thank you.  

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## 0 answers

