Question

show working please

2. Ikisha has the utility function V (x1,x2) = 5x1 xz and Alleyne has the utility function W (x1,x2) = 5x + 3xz. For each individual, calculate the slope of the indifference curve at EACH point. a. (4,5) b. (6,2) c. (8,4) d. (10,14)

Answer 1

Slope of indifference curve = MRS = - MU1 / MU2, where

MU1 = $\dpi{80} \partial$ U/$\dpi{80} \partial$x1

MU2 = $\dpi{80} \partial$ U/$\dpi{80} \partial$x2

For Ikisha,

MU1 = $\dpi{80} \partial$ V/$\dpi{80} \partial$x1 = 10x1x2³

MU2 = $\dpi{80} \partial$ V/$\dpi{80} \partial$x2 = 15x1²x2²

MRS = - (10x1x2³) / (15x1²x2²) = - (2x2 / 3x1)

For Alleyne,

MU1 = $\dpi{80} \partial$ W/$\dpi{80} \partial$x1 = 10x1

MU2 = $\dpi{80} \partial$ W/$\dpi{80} \partial$x2 = 9x2²

MRS = - (10x1) / (9x2²)

Therefore:

(a) x1 = 4, x2 = 5

Ikisha's MRS = - (2 x 5) / (3 x 4) = - 10 / 12 = - 0.83

Alleyne's MRS = - (10 x 4) / (9 x 5 x 5) = - 40 / 225 = - 0.18

(b) x1 = 6, x2 = 2

Ikisha's MRS = - (2 x 2) / (3 x 6) = - 4 / 18 = - 0.22

Alleyne's MRS = - (10 x 6) / (9 x 2 x 2) = - 60 / 36 = - 1.67

(c) x1 = 8, x2 = 4

Ikisha's MRS = - (2 x 4) / (3 x 8) = - 8 / 24 = - 0.33

Alleyne's MRS = - (10 x 8) / (9 x 4 x 4) = - 80 / 144 = - 0.56

(d) x1 = 10, x2 = 14

Ikisha's MRS = - (2 x 14) / (3 x 10) = - 28 / 30 = - 0.93

Alleyne's MRS = - (10 x 10) / (9 x 14 x 14) = - 100 / 1764 = - 0.06