Question

Dimi has the following utility for goods x and y:

u(x,y) = x^2 + 2x + 1 - y

The marginal rate of substitution between the two goods is...

a) 2

b) 2x-2

c) 2x+2

d) -2x+2

Answer 1

Solution:

Marginal rate of substitution (MRS) = $\frac{Change \;in\; Good \;Y}{Change \;in\; Good \;X} = \frac{MU_{X} }{MU_{Y}}$

MRS_x,y = $\frac{MU_{X} }{MU_{Y}}$  

First derive MU_x:

MU_x  = $\frac{\partial U} {\partial X} = 2x +2$

MU_y  = $\frac{\partial U} {\partial Y} = -1$

Substitute to derive MRS_x,y:

MRS_x,y =  $\frac{MU_{X} }{MU_{Y}} = \frac{2x +2 }{-1} = -2x - 2$

MRS_x,y =$-2x - 2$