Answer to Question #146901 in Microeconomics for bora

Question

Consider the utility function U(x, y) = 3x + y, with MUx = 3 and MUy = 1. a) Is the assumption that more is better satisfied for both goods? b) Does the marginal utility of x diminish, remain constant,or increase as the consumer buys more x? Explain. c) What is MRSx,y ? d) Is MRSx,y diminishing, constant, or increasing as the consumer substitutes x for y along an indifference curve? e) On a graph with x on the horizontal axis and y on the vertical axis,draw a typical indifference curve (it need not be exactly to scale, but it needs to reflect accurately whether there is a diminishing MRSx,y).Also indicate on your graph whether the indifference curve will intersect either or both axes.Label the curve U1. f) On the same graph draw a second indifference curve U2,with U2 > U1.

Answer 1

$Solution$

a.

$MU_x=\frac{\delta u}{\delta x}=3>0, Hence\ MU_x>0\\ MU_y=\frac{\delta u}{\delta y}=1>0, Hence\ MU_y>0\\$

Since $MU_x$ and $MU_y$ are both greater than zero, the assumption that more is better satisfied for both goods.

b.

$\frac{\delta MU_x}{\delta x}=0$ . Hence marginal utility of $x$ remains constant as the consumer buys more $x$ .

c.

MRS_xy is the amount of $y$ consumer is willing to give for marginal unit of $x$, so that their utility remains the same.

d.

$MRS_{xy}=-\frac{MU_x}{MU_y}=-\frac{3}{1}=-3$

Hence $\frac{\delta MRS_{xy}}{\delta x}=0 \implies MRS$ is constant along an indifference curve.

e.

From the above graph with x on the horizontal axis and y on the vertical axis, we can see that the indifference curve is touching both axis, and as indifference curve is a straight line. Hence MRS is a constant well known as a perfect substitution.

f.

$U_2>U_1$

Both $U_1$ and $U_2$ are parallel hence they intersect both axes.