Sally consumes two goods, X and Y. Her utility function is given by the expression U=3XY2. The marginal utility of X and marginal utility of Y are given by the following equations: MUX=3Y2 and MUY=6XY The current market price for X is $10, while the market price for Y is $5. Sally's current income is $500. A) Draw out Sally’s budget line. (show the points where it meets the vertical and horizontal axes) B) Determine the X,Y combination which maximizes Sally's utility, given her budget constraint. (Partial units for the quantities are possible.) [Hint: One of the ways to do this is to use the equal marginal principle to find the optimal ratio of X to Y and then use that in the budget equation]. C) How much is Sally’s utility? Now the price of X increases to $15. What is the ratio in which she will consume X and Y ?
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Sally consumes two goods, X and Y. Her utility function is given by the expression U=3XY2. The
MUX=3Y2 and MUY=6XY
The current market price for X is $10, while the market price for Y is $5. Sally's current income is $500.
A) Draw out Sally’s budget line. (show the points where it meets the vertical and horizontal axes)
B) Determine the X,Y combination which maximizes Sally's utility, given her budget constraint. (Partial units for the quantities are possible.) [Hint: One of the ways to do this is to use the equal marginal principle to find the optimal ratio of X to Y and then use that in the budget equation].
C) How much is Sally’s utility? Now the price of X increases to $15. What is the ratio in which she will consume X and Y ?
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