# 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

Thanks.

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:

$$X=sum_{j=1}^{J}x_j^*$$

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

## Related Questions

### Accounting for household work in the GDP

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

### Is there any economic explanation why industrialization first occured in Britain?

1  Asked on March 16, 2021 by ezekiel

### If $x succsim_i x_i^*$ then $p cdot x_ige w_i.$ (MWG 16.C.2)

1  Asked on March 15, 2021 by shk910

### 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

### Many or few variables when testing for Granger causality?

1  Asked on March 13, 2021 by emmanuel-ameyaw

### What is an estimate of the value of the world’s assets?

1  Asked on March 12, 2021 by streawkceur

### Is It Possible for a Country to have a Gold Standard without a Fixed Price of Gold?

1  Asked on March 12, 2021

### Understanding the “Treasury auction results” press release

0  Asked on March 11, 2021 by pascal-dufresne

### Labour-saving vs. Labour-augmenting technical change

1  Asked on March 11, 2021 by london

### Log-linearization of CES production function

0  Asked on March 10, 2021 by econrider

### Tendency of the rate of profit to fall

1  Asked on March 9, 2021 by wallows

### How to average CDFs of one variable across years

2  Asked on March 9, 2021

### Optimisation and Theory of Comparative Advantage

1  Asked on March 9, 2021

### What is the problem of making an instrument valid on condition of a factor?

0  Asked on March 8, 2021 by isabella-green

### Real wages fluctuation as per classical economics

2  Asked on March 7, 2021 by harsh-sharma

### The Effect of Two income Households on Housing Prices

3  Asked on March 7, 2021 by nigel

### Demand function for good x

1  Asked on March 6, 2021 by jumbo09

### Can PPP adjusted values be compared over time?

2  Asked on March 6, 2021 by riskymaor

### Price of Anarchy when the cost is to society and not to the selfish agents

1  Asked on March 6, 2021