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Tom's income is $480and he spends it on two goods, X and Y. His utility function is U = XY. Both X and Y sells for $8 per unit.  

a. Use lagrangian function to calculate Tom's utility-maximizing purchases of X and Y. 

b. If the price of Y increased to $11.52, with no change in the price of X, by how much would his income have to increase to enable him to maintain his initial level of utility as in part (a) above?

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