Suppose that U(f,c) = f + 8c^(1/2) is a utility function that describes Amelia’s preferences over two goods: fish (f)and custard (c). For the following, think of fish as the good graphed on the horizontal axis. a. Derive an expression for her marginal utility (Uf)from a small increase in f holding c fixed. Also find the marginal utility for custard (Uc). b. What is Amelia’s marginal rate of substitution (MRS)? Give a brief (2 sentences maximum) intuitive description of what MRS represents. If Amelia has 4 units of custard, holding her utility constant, how many units of custard would she be willing to give up in order to get one more unit of fish? c. Graph Amelia’s indifference curve for a utility level of 40. Be sure to specify at least 3 bundles of goods on the indifference curve. d. Does the fact that Amelia’s indifference curve intersects with the custard axis violate any of the 5 properties of indifference curves? Briefly support your answer. e. Give another utility function that represents Amelia’s preferences just as well as U(f,c) = f + 8c^(1/2)
Suppose that U(f,c) = f + 8c^(1/2)
is a utility function that describes Amelia’s preferences over two goods: fish
(f)and custard (c). For the following, think of fish as the good graphed on the horizontal axis.
a. Derive an expression for her
marginal utility for custard (Uc).
b. What is Amelia’s marginal rate of substitution (MRS)? Give a brief (2 sentences maximum) intuitive
description of what MRS represents. If Amelia has 4 units of custard, holding her utility constant, how
many units of custard would she be willing to give up in order to get one more unit of fish?
c. Graph Amelia’s indifference curve for a utility level of 40. Be sure to specify at least 3 bundles of goods
on the indifference curve.
d. Does the fact that Amelia’s indifference curve intersects with the custard axis violate any of the 5
properties of indifference curves? Briefly support your answer.
e. Give another utility function that represents Amelia’s preferences just as well as U(f,c) = f + 8c^(1/2)
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