Given the utility function of good x and y as, `\U=\x^{3/4}\y^{1/4}`

Prices of good X and Y `\Px=6\and\Py=3`

Budget `\B=$120`

The point of tangency or the combination of good X and Y (maximum satisfaction) `\U=\frac{dUx}{dUy}=frac{Px}{Py}`.....(1)


differentiating with respect to x,




differentiating with respect to y



substituting the values in equation (i)


Diving the upper portion of the equation by 3, we get;


Cross multiplying;


or, `\x=\frac{3y}{2}`.......(iv)

The equation of budget line can be written as `Px.X+Py.Y=120`........(v)

Substitution the equation (iv) prices of x and y good in equation (v), we get;


or, `\9y+3y=120`

or, `12y=120`

or, `y=10`

Similarly again substituting the value of y in equation (iv) weget;


or, `\x=\frac{30}{2}`

or, `\x=15`

Hence the combination of 15 units of good x and 10 units of good y will be the point of tangency to the indifference curve.

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