If i have a utility function e.g. - X(to the power of 0.5) x by Y(to the power of 0.5).how do i find demand
hi how do i go about finding the demand function for this utility function? thanks
Answers:
For a formal solution you should set up the Lagrangian function:
L = (x^.5)(y^.5) + z[m - xp(x) - yp(y)]
Assuming x>0 y>0 the First Order Conditions are
(0.5)(x^-0.5)(y^.5) = zp(x)
(0.5)(x^0.5)(y^-0.5) = zp(y)
Equating the z and normalizing the prices so P = P(x)/P(y) gives
y = xP
Then substitute this into the budget constraint
m = xP(x) + yP(y) to give
x = m/2P(x) and y = m/2P(y)
However this will only be correct if the price ratio P is equal to one, otherwise you would just demand all of the cheaper good and none of the more expensive good.
root xy i.e the square root of (x times y)
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Answers:
For a formal solution you should set up the Lagrangian function:
L = (x^.5)(y^.5) + z[m - xp(x) - yp(y)]
Assuming x>0 y>0 the First Order Conditions are
(0.5)(x^-0.5)(y^.5) = zp(x)
(0.5)(x^0.5)(y^-0.5) = zp(y)
Equating the z and normalizing the prices so P = P(x)/P(y) gives
y = xP
Then substitute this into the budget constraint
m = xP(x) + yP(y) to give
x = m/2P(x) and y = m/2P(y)
However this will only be correct if the price ratio P is equal to one, otherwise you would just demand all of the cheaper good and none of the more expensive good.
root xy i.e the square root of (x times y)
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