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Mathew has the utility function U = (XY) (where Y represents

Mathew has the utility function U = ?(XY) (where Y represents apples and X represents hot dogs), income of $20, and is deciding how to allocate that income between apples and hot dogs. Hot dogs cost $1.00 and apples cost $1.25 each. (5 + 3 marks)


Mathew?s utility function implies that the marginal utility of apples is 0.5 ?(X/Y) and the marginal utility of hotdogs is 0.5(Y/X). How many apples will Mathew buy?  How many hot dogs will he buy?


This year, the price of hot dogs rise to $3 each while Mathew?s income is unchanged. Mathew?s father decides to help him by giving him a gift of $20. Consider an indifference curve-budget line diagram with hot dogs on the x-axis and apples on the y-axis. After Mathew gets the $20 gift, will his new budget line lie above, lie below, or pass through his initial optimum? Justify your choice. Will Mathew be better or worse off than he was last year?

*** I am particularly confused with how to find MRS for part (i) so if you could explain this in a bit of detail it would be much appreciated :)


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