<p>I would need help with the following problem about consumer theory. Let us say that <span class="math-container">$X$</span> is the amount of days at the sea and <span class="math-container">$Y$</span> is the amount of days on the cottage. We have some utility function <span class="math-container">$u(X,Y)$</span> and constraint <span class="math-container">$ 4X+9Y=I$</span>. I have found the optimal solution <span class="math-container">$(X^{\star}=\frac{I}{5},Y^{\star}=\frac{I}{3})$</span> and I am supposed to graphically illustrate and comment dependence <span class="math-container">$X^{\star}$</span> and <span class="math-container">$Y^{\star}$</span> on income <span class="math-container">$I$</span>. I am not sure if i understand exactly the task. Could you help me with the solution? Thank you.</p>

CC BY-SA 4.0
2021-01-04T13:40:05.700Z
I feel like X should be the amount of days at the sea and Y should be the amount of days on the cottage and then you should have some some utility function $U(X,Y)$ which you can express with indifference curves.
Bayesian
CC BY-SA 4.0
2021-01-04T14:01:46.680Z
I have changed the task, would you know now?
Laura
<microeconomics><mathematical-economics><utility><supply-and-demand><consumer-theory>
graph of dependent income
Laura
# graph of dependent income

(Asked by: username_0 on 2021-01-04)

I would need help with the following problem about consumer theory. Let us say that $X$ is the amount of days at the sea and $Y$ is the amount of days on the cottage. We have some utility function $u(X,Y)$ and constraint $ 4X+9Y=I$. I have found the optimal solution $(X^{\star}=\frac{I}{5},Y^{\star}=\frac{I}{3})$ and I am supposed to graphically illustrate and comment dependence $X^{\star}$ and $Y^{\star}$ on income $I$. I am not sure if i understand exactly the task. Could you help me with the solution? Thank you.

**Tags:** microeconomics, mathematical-economics, utility, supply-and-demand, consumer-theory
> **Comments:**
> **username_1**: I feel like X should be the amount of days at the sea and Y should be the amount of days on the cottage and then you should have some some utility function $U(X,Y)$ which you can express with indifference curves.  
> **username_0**: I have changed the task, would you know now?  

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## 0 answers

