Question

show work please

6. Given an indifference curve U. = 100 = F S (F>O and S>0) of the indifference a) Use the implicit function rule to derive the slope curve. b) At S = 144, Calculate the slope.

Answer 1

Answer 6

(a)

Using Implicit rule of derivatives :

If F = f(x,y) = c where c is constant, then :

$\frac{\mathrm{d} y}{\mathrm{d} x} = -\frac{\frac{\partial F}{\partial x}}{\frac{\partial F}{\partial y}}$

Here U = F^1/2S^1/2

Using above rule :

(1/2) (F/S)1/2 (1/2) (S/F)1/2 = -F/S

Hence, Slope of indifference curve = -F/S

(b)

When S = 144, then U = F^1/2(144)^1/2 = 100

=> F^1/2 = 100/12

=> F = (100/12)²

Hence Slope = -F/S = -((100/12)²)/144 = -0.48