Question

. The consumer’s utility function for goods X and Y is U = 2X^5/2 + 15Y....

. The consumer’s utility function for goods X and Y is U = 2X^5/2 + 15Y. Good X is placed on the x-axis and good Y is placed on the y-axis. Which of the following statements is TRUE? I. The marginal utility of good Y is 15 II. The MRSXY = 5X 15 III. The consumer is always willing to trade away 15 units of good Y for 1 unit of good X. a) I and II b) I only c) I and III d) I, II, and III

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Answer #1

The utility function is U = 2x5/2 + 15y

l) The marginal utility of y = = 15

The marginal utility of x = =5x5/2-1 = 5x-3/2

ll) MRSXY = MUx/MUy = 5x-3/2/ 15 = 1/3x3/2

lll) the consumer is willing to trade away 15 units of goods Y for 1 unit of x which means marginal rate of substitution MRSxy which is also equal to -dy/dx which implies how much unit of y has to be sacrificed to get an additional unit of x is 15. which is not true.

so the correct option is (b)

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