4. (24 points) Suppose the utility function of someone who consumes goods a and

Question

4. (24 points) Suppose the utility function of someone who consumes goods a and v is given by U,+2 y. The corresponding marginal utility of z is thus MUs - 1/(2Va) and the marginal utility of y is MUy -1/Vy. (a) (6 points) Is the assumption that more is better' satisfied for both z and y? Explain. (b) (6 points) Does the marginal utility of y diminish, remain constant, or increase as the consumer buys more units of y? (c) (6 points) Calculate MRS. (d) (6 points) Is MRSy diminishing, constant, or increasing as the consumer sub- stitutes a for y along an indifference curve? Show this mathematically and/or interpret this result.

Explanation / Answer

Utility is the increasing function of x and y hence more is better assumption is valid here

MUy=1/?y.... Hence as y increases MU decrease that is diminishing returns to scale

MRS=MUx/MUy=?(y/x)*0.5

If we multiply x and y with some scalar @ then @MRS=MRS

Hence @=1 and MRS is constant return to scale.

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