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in this video were gonna look at solving for the income and substitution effect of a price change well start here with a consumers utility function good accent good Y both raise to the 0.5 power consumers income and prices are given here we want to see what happens if the price of good-x increases to $10 in other words we want to find the total effect substitution effect and income effect of the price change let me first look at this graphically and that might help a guide us in understanding the mathematics a little bit better let me move up here ok here we go so the first thing were gonna do is were going to maximize utility subject to the initial price of good-x equalling $5 price of good-y equaling $2 and we find that tangency occurs at Point a were gonna see mathematically the consumer by 2 units of AX and 5 units of y okay and then what were gonna do is were going to maximize utility subject to the new higher price for a good X when the price of good-x equals $10 thatll s