For the following utility functions ucx y xy ucx yxy 10y ux...

For the following utility functions: U(X, Y) = XY U(X, Y) = XY + 10Y U(X, Y) = X + Y^2 Write the general equation of the MRS for each utility function. Write the equation for the indifference curve where utility is equal to 100 for each utility function. Determine whether these indifference curves for each of the utility functions are convex (that is, whether the MRS decreases as X increases) or are concave (and thus violate an assumption about preferences).

Transcript

00:01 All right so let here the utility function is given as let this is x y so this is x y square okay so i will i will calculate it for x y square so xy is simple one okay okay okay that's why i will calculate it for x y square okay now the mu x x is equal to y square and the m ux is equal to y square and the mu y is equal to 2xy okay now the m rc s will be mrrrrc s this will be equal to up xy this is that mu x or mu y this is y square over 2x y which is 1 over 2x okay so m r c up a x is marginal rate of satisfaction per x par y okay so mrs x up y will be equal to 1 over 2x so it implies in as much as x computation rises okay so 1 over 2x pulse that is mrs a up xy pulse so x increases uh consisting pulse in the mrs x y pulse so x then it have increased in mrx of xy, okay? so, for the utility level up 100, we have that x, y, square will be equal to 100, okay? this is 100 and y square is equal to 100 over x or y is just equal to square root 100 over x.

02:12 Is equal to 100 divided by y square so it means that x be the fourth and y be the pepth okay now in part b here uh that utility function is uh xy plus 10 y okay and mu x here is y and mu x here is y is x plus 10 right and m r s up xy is equal to m u of y so this is y divided by x plus 10 okay so it means that if we substitute x in that function it increases right so for the utility level of 100 we must have that x y plus 10 y is equal to 100 and y up x plus 10 is equal to 100 or y is equal to 100 divided by x plus 10 right and y up x plus 10 is equal to 100 is equal to 100 and x plus 10 10 is equal to 100 divided by y or x is equal to 100 divided by y minus 10 okay so it means that if x is 10 then y will be pi and if y is 10 then x will be 0 okay so if y is poor then x will be 15 right so let let draw that curve so this will be the this is y, this is x and the curve will be looking like this.

04:13 This is 100...

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