demand function from utility

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thanks in advance.
I’m looking to find a way (apart from Lagrange and MUx/MUy=Px/Py) to derive demand function for x, not y. You see, whenever I try solving the problem, I get y’s Demand instead of x.
I have a function, $u(x,y)= 2sqrtx + y$
whenever I differentiate and then put in the budget constraint equation, I end up getting the result of differentiation of x and the demand for y.
For example, $$ MUx = frac1 sqrtx $$

$MUy=1$,
$$fracMUxMUy = fracPxPy$$

$$frac1sqrtx = fracPxPy$$

$$ x = fracPy^2Px^2$$



then, substituting x in Budget constraint equation yields $$ y = fracMPy - fracPyPx$$ with the impossibility to find x’s demand (or maybe I just don’t understand it)



MUx, MUy are marginal utilities of goods x and y respectively

Px, Py are prices of these goods

M is income, that comes from budget constraint equation (Px * x +Py * y=M)










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  • Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
    – José Carlos Santos
    Sep 10 at 9:15










  • It's tricky to understand the question. What do MU, M and P mean?
    – Matti P.
    Sep 10 at 10:05











  • I think you already have the demand for $x$, when you derive $x=fracP^2_xP^2_y$. Verify by taking your demand for $y$ and plugging it back into the budget constraint to get $x$.
    – Trurl
    Sep 17 at 19:38














up vote
0
down vote

favorite












thanks in advance.
I’m looking to find a way (apart from Lagrange and MUx/MUy=Px/Py) to derive demand function for x, not y. You see, whenever I try solving the problem, I get y’s Demand instead of x.
I have a function, $u(x,y)= 2sqrtx + y$
whenever I differentiate and then put in the budget constraint equation, I end up getting the result of differentiation of x and the demand for y.
For example, $$ MUx = frac1 sqrtx $$

$MUy=1$,
$$fracMUxMUy = fracPxPy$$

$$frac1sqrtx = fracPxPy$$

$$ x = fracPy^2Px^2$$



then, substituting x in Budget constraint equation yields $$ y = fracMPy - fracPyPx$$ with the impossibility to find x’s demand (or maybe I just don’t understand it)



MUx, MUy are marginal utilities of goods x and y respectively

Px, Py are prices of these goods

M is income, that comes from budget constraint equation (Px * x +Py * y=M)










share|cite|improve this question























  • Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
    – José Carlos Santos
    Sep 10 at 9:15










  • It's tricky to understand the question. What do MU, M and P mean?
    – Matti P.
    Sep 10 at 10:05











  • I think you already have the demand for $x$, when you derive $x=fracP^2_xP^2_y$. Verify by taking your demand for $y$ and plugging it back into the budget constraint to get $x$.
    – Trurl
    Sep 17 at 19:38












up vote
0
down vote

favorite









up vote
0
down vote

favorite











thanks in advance.
I’m looking to find a way (apart from Lagrange and MUx/MUy=Px/Py) to derive demand function for x, not y. You see, whenever I try solving the problem, I get y’s Demand instead of x.
I have a function, $u(x,y)= 2sqrtx + y$
whenever I differentiate and then put in the budget constraint equation, I end up getting the result of differentiation of x and the demand for y.
For example, $$ MUx = frac1 sqrtx $$

$MUy=1$,
$$fracMUxMUy = fracPxPy$$

$$frac1sqrtx = fracPxPy$$

$$ x = fracPy^2Px^2$$



then, substituting x in Budget constraint equation yields $$ y = fracMPy - fracPyPx$$ with the impossibility to find x’s demand (or maybe I just don’t understand it)



MUx, MUy are marginal utilities of goods x and y respectively

Px, Py are prices of these goods

M is income, that comes from budget constraint equation (Px * x +Py * y=M)










share|cite|improve this question















thanks in advance.
I’m looking to find a way (apart from Lagrange and MUx/MUy=Px/Py) to derive demand function for x, not y. You see, whenever I try solving the problem, I get y’s Demand instead of x.
I have a function, $u(x,y)= 2sqrtx + y$
whenever I differentiate and then put in the budget constraint equation, I end up getting the result of differentiation of x and the demand for y.
For example, $$ MUx = frac1 sqrtx $$

$MUy=1$,
$$fracMUxMUy = fracPxPy$$

$$frac1sqrtx = fracPxPy$$

$$ x = fracPy^2Px^2$$



then, substituting x in Budget constraint equation yields $$ y = fracMPy - fracPyPx$$ with the impossibility to find x’s demand (or maybe I just don’t understand it)



MUx, MUy are marginal utilities of goods x and y respectively

Px, Py are prices of these goods

M is income, that comes from budget constraint equation (Px * x +Py * y=M)







derivatives economics utility






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edited Sep 10 at 10:56

























asked Sep 10 at 9:13









Kate

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  • Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
    – José Carlos Santos
    Sep 10 at 9:15










  • It's tricky to understand the question. What do MU, M and P mean?
    – Matti P.
    Sep 10 at 10:05











  • I think you already have the demand for $x$, when you derive $x=fracP^2_xP^2_y$. Verify by taking your demand for $y$ and plugging it back into the budget constraint to get $x$.
    – Trurl
    Sep 17 at 19:38
















  • Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
    – José Carlos Santos
    Sep 10 at 9:15










  • It's tricky to understand the question. What do MU, M and P mean?
    – Matti P.
    Sep 10 at 10:05











  • I think you already have the demand for $x$, when you derive $x=fracP^2_xP^2_y$. Verify by taking your demand for $y$ and plugging it back into the budget constraint to get $x$.
    – Trurl
    Sep 17 at 19:38















Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Sep 10 at 9:15




Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to.
– José Carlos Santos
Sep 10 at 9:15












It's tricky to understand the question. What do MU, M and P mean?
– Matti P.
Sep 10 at 10:05





It's tricky to understand the question. What do MU, M and P mean?
– Matti P.
Sep 10 at 10:05













I think you already have the demand for $x$, when you derive $x=fracP^2_xP^2_y$. Verify by taking your demand for $y$ and plugging it back into the budget constraint to get $x$.
– Trurl
Sep 17 at 19:38




I think you already have the demand for $x$, when you derive $x=fracP^2_xP^2_y$. Verify by taking your demand for $y$ and plugging it back into the budget constraint to get $x$.
– Trurl
Sep 17 at 19:38















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