Question

How do I find L? I found S easily by plugging it in. Please show the simplest way to solve, no unecessary extra steps.

(No need to draw IC)

3) Suppose Joe's utility for lobster (L) and soda (s) can be represented as U 0.5 50.5 Draw the indifference curve that yields a utility level of 9. Calculate the MUL, MUS, and MRS of L for S on that indifference curve when S 3.

Answer 1

Solution : Given the utility function U = L^0.5S^0.5, plug in the value of utility and s in this utility function:

U = 9 And S= 3

U = L^0.5 * 3^0.5

9 / 3^0.5 = L^0.5

3^2-0.5 = L^0.5

L =27.

And $\partial$U /$\partial$S = 0.5L^0.5S^( -0.5) = 0.5 27^(0.5)/3^0.5 = 0.5 * 3^(1.5 - 0.5) =0.5* 3 = 1.5.

And $\partial$U/$\partial$L = 0.5S^0.5L^(-0.5) = 0.5 (3^0.5 / 27^0.5) = 0.5 * 1/ 3^(1.5-0.5) = 1/6

MRS = -MUS/MUL = - $\partial U/\partial S / \partial U/\partial L$ = - 1.5 / (1/6) =-9.