<p>You just need to use the condition <span class="math-container">$$ MRS_{q_{1j},q_{2j}} = \frac{p_{1}}{p_{2}} $$</span> to obtain <span class="math-container">$$ 3 \frac{q_{2j}}{q_{1j}} = \frac{p_{1}}{p_{2}} \;\;\;\; \text{(1)}$$</span> Then solving for <span class="math-container">$p_{1}$</span> and plugging this into the budget constraint you obtain: <span class="math-container">$$ y = 3p_{2} \frac{q_{2j}}{q_{1j}}q_{1j} - p_{2}q_{2j}$$</span> <span class="math-container">$$ \Rightarrow q_{2j} = \frac{y/4}{p_{2}} $$</span> Accordingly, solving for <span class="math-container">$p_{2}$</span> from condition (1) and plugging this into the budget constraint yields: <span class="math-container">$$ q_{1j} = \frac{3y/4}{p_{1}} $$</span>. </p>

<p>From this you can obtain your function for the aggregated demand for goods <span class="math-container">$q_{1j},q_{2j}$</span>, as a function of the prices.  </p>

CC BY-SA 4.0
2019-05-06T18:24:51.700Z
2019-05-06T18:24:51.700Z
Ali
<p>I have an utility function given, </p>

<p><span class="math-container">$\ u_j(q_{j1},q_{j2} )=q^{3/4}_{1j}*q^{1/4}_{2j}  $</span></p>

<p><span class="math-container">$\ s.t.:  y=p_1*q_{1i} +p_2*q_{2i}$</span></p>

<p>I do know that the for <span class="math-container">$\ q_{1j}$</span> the marginal prospensity to consume is 3/4 of y given prices <span class="math-container">$\ p_1$</span>. 
But I dont acutally get how my teacher calculated the aggregated demand: 
<span class="math-container">$\ q^*_j(p_1,p_2)=(\frac{1/4y}{p}, \frac{3/4y}{p}) $</span>.</p>

<p>I  set up the Lagrangean but then end up with <span class="math-container">$\ p_1=\frac{1}{3}\frac{q_2}{q_1}*p_2$</span>, which does not seem too helpful for me. </p>

<p>Can someone give me a hint how to derive aggregate demand from a given utility function, please. </p>

<p>Thanks </p>

CC BY-SA 4.0
2019-05-06T13:40:52.580Z
There is a constraint missing here?
Ali
CC BY-SA 4.0
2019-05-06T17:24:53.773Z
Oh, yes thats true.  I added that.
Pete
<utility><demand>
Aggregated demand of households given utility function
Pete
# Aggregated demand of households given utility function

(Asked by: username_0 on 2019-05-06)

I have an utility function given,

$\ u\_j(q\_{j1},q\_{j2} )=q^{3/4}\_{1j}\*q^{1/4}\_{2j} $

$\ s.t.: y=p\_1\*q\_{1i} +p\_2\*q\_{2i}$

I do know that the for $\ q\_{1j}$ the marginal prospensity to consume is 3/4 of y given prices $\ p\_1$.
But I dont acutally get how my teacher calculated the aggregated demand:
$\ q^\*\_j(p\_1,p\_2)=(\frac{1/4y}{p}, \frac{3/4y}{p}) $.

I set up the Lagrangean but then end up with $\ p\_1=\frac{1}{3}\frac{q\_2}{q\_1}\*p\_2$, which does not seem too helpful for me.

Can someone give me a hint how to derive aggregate demand from a given utility function, please.

Thanks

**Tags:** utility, demand

> **Comments:**
> **username_1**: There is a constraint missing here?  
> **username_0**: Oh, yes thats true.  I added that.  

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## 1 answers

### Answer by username_1 on 2019-05-06. Score: 2 | Accepted answer

You just need to use the condition $$ MRS\_{q\_{1j},q\_{2j}} = \frac{p\_{1}}{p\_{2}} $$ to obtain $$ 3 \frac{q\_{2j}}{q\_{1j}} = \frac{p\_{1}}{p\_{2}} \;\;\;\; \text{(1)}$$ Then solving for $p\_{1}$ and plugging this into the budget constraint you obtain: $$ y = 3p\_{2} \frac{q\_{2j}}{q\_{1j}}q\_{1j} - p\_{2}q\_{2j}$$ $$ \Rightarrow q\_{2j} = \frac{y/4}{p\_{2}} $$ Accordingly, solving for $p\_{2}$ from condition (1) and plugging this into the budget constraint yields: $$ q\_{1j} = \frac{3y/4}{p\_{1}} $$.

From this you can obtain your function for the aggregated demand for goods $q\_{1j},q\_{2j}$, as a function of the prices.


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