<p>Step 1, as it were, would be to write down the expenditure function (4x+y).  Next, think about what happens if income is $0; the optimal choices of x and y are easy, as only (0,0) can be consumed. Then ask "what happens as income increases?" and you're off to the races!</p>

CC BY-SA 3.0
2017-07-12T03:07:07.393Z
2017-07-12T03:07:07.393Z
David Croson
<p>The way I would attack this is to solve the utility function <span class="math-container">$u(x,y)=xy$</span> subject to the budget constraint: <span class="math-container">$4x+y=m$</span>. This is using Lagrange method
It turns out that <span class="math-container">$x=m/8$</span> and <span class="math-container">$y=m/2$</span>.</p>

<p>The Engel curve show the relationship between income and the quantity of the good demanded, so substitute values for <span class="math-container">$m$</span> and find the corresponding <span class="math-container">$x$</span> or <span class="math-container">$y$</span> demanded and plot the Engel curve for good x or good y. </p>

CC BY-SA 4.0
2018-11-05T21:35:14.923Z
2018-11-06T02:52:46.220Z
2018-11-06T02:52:46.220Z
Humble Maddison
<p>I have $U(x,y)=xy$, $p_1=4$ and $p_2=1$. Income is unknown. Where do I start?</p>

CC BY-SA 3.0
2017-07-05T02:53:21.927Z
Use the fact that slope of IC equals slope of the budget line in equilibrium and then use the budget equation to get the demand as a function of income and that's your Engel curve.
Amit
CC BY-SA 3.0
2017-07-05T06:14:14.840Z
Possible duplicate of [Deriving Equation for Engel Curve](https://economics.stackexchange.com/questions/4618/deriving-equation-for-engel-curve)
luchonacho
CC BY-SA 3.0
2017-07-05T06:35:34.953Z
Start by reading your book chapter on Engel curves.
Giskard
<microeconomics><cobb-douglas>
Find Engel Curve with a Cobb-Douglas
Antonio
# Find Engel Curve with a Cobb-Douglas

(Asked by: username_0 on 2017-07-04)

I have $U(x,y)=xy$, $p\_1=4$ and $p\_2=1$. Income is unknown. Where do I start?

**Tags:** microeconomics, cobb-douglas

> **Comments:**
> **username_1**: Use the fact that slope of IC equals slope of the budget line in equilibrium and then use the budget equation to get the demand as a function of income and that's your Engel curve.  
> **username_2**: Possible duplicate of [Deriving Equation for Engel Curve](https://economics.stackexchange.com/questions/4618/deriving-equation-for-engel-curve)  
> **username_3**: Start by reading your book chapter on Engel curves.  

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## 2 answers

### Answer by username_4 on 2017-07-12. Score: 1

Step 1, as it were, would be to write down the expenditure function (4x+y). Next, think about what happens if income is $0; the optimal choices of x and y are easy, as only (0,0) can be consumed. Then ask "what happens as income increases?" and you're off to the races!


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### Answer by username_5 on 2018-11-05. Score: 0

The way I would attack this is to solve the utility function $u(x,y)=xy$ subject to the budget constraint: $4x+y=m$. This is using Lagrange method
It turns out that $x=m/8$ and $y=m/2$.

The Engel curve show the relationship between income and the quantity of the good demanded, so substitute values for $m$ and find the corresponding $x$ or $y$ demanded and plot the Engel curve for good x or good y.


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