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
U = xy + x
(a)
MUx = U/x = y + 1
MUy = U/x = x
(b)
MRSx,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.
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