0.54 is the correct answer can anyone tell me how to get that? thank you. A util

Question

0.54 is the correct answer can anyone tell me how to get that? thank you.

A utility function is given as 501 45- 40- where B represents the quantity of books consumed and M represents magazines. This utility is shown via indifference curves in the diagram to the right. The level of utility at point V is 20 (round your answer to one decimal place) The marginal utility when moving from bundle T to bundle V is 0.54 (round your answer to two decimal places). 30- 15- 10- 65 10 15 20 25 30 35 40 45 S0 Books (B)

Explanation / Answer

Utility at V = (MB)^0.5 = (20*20)^0.5 = 400^0.5 = 20

Now marginal utility of a good is the derivative of total utility with respect to that good. We see that the quantity of books is reduced so we find MU of books B = 0.5*M^0.5/B^0.5.

MU of moving from V to T is given by MUB = 0.5*20^0.5/15^0.5 = 0.57

However we can use another rule for marginal utility where MU of a good = Difference in total utility / difference in consumption of that good.

Here Total utility at V = (20*20)^0.5 = 20 and total utility at T = (20*15)^0.5 = 17.321. Hence MU from moving V to T will be (20 - 17.321)/(20 - 15) = 0.54

Note: Both methods are correct and the answer box should accept both 0.54 and 0.57.

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