How do I derive the aggregate demand function given two utilities functions?

Economics Asked by user25621 on August 21, 2020

Assume that we have two people with the same utility function of $U_i = x^{1/2} + y^{1/2}$ where $i=1,2$ and $I_i$ is the income. Let $P_x$ denote price of good $x$ and $P_y$ denote price of good $y$.

I’m being asked to derive the aggregate demand function. The only thing I got so far was finding the market demand for each good per person, which is

$x^*_1 = {I_1}/2P_x$ , $y^*_1 = {I_1}/2P_y$, for person 1

$x^*_2 = {I_2}/2P_x$, $y^*_2 = {I_2}/2P_y$ for person 2

Am I missing something? Please help.


One Answer

If you have $J$ consumers therefore $J$ demands for a good $X$. Denoting the individual demand of each consumer with $x_j^*$ as you have it, if $X$ is the aggregate demand, it is just the sum of every individual demand:


Then for your case it's: $x_1^*+x_2^*=frac{(I_1+I_2)}{2P_X}$, and the same with $Y$.

Answered by nrivera on August 21, 2020

Add your own answers!

Related Questions

Accounting for household work in the GDP

1  Asked on March 16, 2021 by ishan-kashyap-hazarika


variance of error term(econometrics)

0  Asked on March 15, 2021 by user30426


Interpreting the Reference Outcome in Thaler (1985)

1  Asked on March 15, 2021 by serkan


Understanding the “Treasury auction results” press release

0  Asked on March 11, 2021 by pascal-dufresne


Tendency of the rate of profit to fall

1  Asked on March 9, 2021 by wallows


Demand function for good x

1  Asked on March 6, 2021 by jumbo09


Ask a Question

Get help from others!

© 2022 All rights reserved. Sites we Love: PCI Database, MenuIva, UKBizDB, Menu Kuliner, Sharing RPP, SolveDir