Question

Calculate MUx, MUy, MRSx,y; determine whether or not the property of “more is better” is satisfied for both goods; determine whether or not the marginal utility of x diminishes, remains constant, or increases as the consumer buys more x; determine whether or not the marginal rate of substitution diminishes, remains constant, or increases as the consumer substitutes x for y along an indifference curve; and sketch the graph of a typical indifference curve.

U(x,y)=xy+x

Answer 1

U = xy + x

(a)

MUx = U/x = y + 1

MUy = U/x = x

(b)

MRS_x,y = MUx/MUy = (y + 1)/x

(c)

The condition "More is better" is satisfied when MU of the good is always positive.

MUx = (y + 1) > 0, since y is non-negative.

Therefore, "More is better" is satisfied for x.

MUy = x >= 0, since x is non-negative.

Therefore, "More is better" is weakly satisfied for y.

(d)

Since MUx is independent of x, it remains constant as x increases.

Since MUy is independent of y, it remains constant as y increases.

NOTE: As per Chegg Answering Policy, 1st 4 parts have been answered.