partial solution obtained

[harish]

Ambrose has indifference curves with the equation y = constant-4*(x)^1/2 where larger constants correspond to higher indifference curves. If x is drawn on the horizontal axis and y on the vertical axis, what is the slope of Ambrose's indierence curve when his consumption bundle is (16;9)?

(a) 16/9
(b) 9/16
(c) 0:50
(d) 13
(e) 4

The correct answer is 0.50

I have proceeded in this question by first trying to calculate the constant by applying the given values of x and y in the bundle.

So I have substituted x = 16 and y =9 in the equation y = constant-4*(x)^1/2

After substitution, I got the value of constant as 25

Now in order to find the slope, I need at least two bundles so that I can divide y2-y1 by x2-x1

Over here my x1 = 16 and y1 = 9

I have presumed my x2 to be as 9

Substituting x2 as 9 in the equation y=constant-4*(x)^1/2, I got my value of y2 as 13

So now I have

x1 = 16, y1 =9, x2=9 and y2 = 13

Upon calculating (y2-y1)/(x2-x1) I get my answer as -4/7

However answer is -0.5

Please tell me where I am going wrong.

Thanks in advance.

[Abhitesh]

Slope of IC = lim(x2->x1) (y2-y1)/(x2-x1) or simply dy/dx

[harish]

Ok, thanks. Is it always necessary to use differential in order to solve slopes ? Will the method of assigning values to calculate slopes turn out to be incorrect ?