Question: Mathew has the utility function U = square root XY (where Y represents apples and X represents hot dogs), income of $20, and is deciding

Mathew has the utility function U = square root 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

a. Mathew’s utility function implies that the marginal utility of apples is 0.5 and the marginal utility of hotdogs is 0.5. How many apples will Mathew buy? How many hot dogs will he buy?

b. 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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