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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?


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