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1 The U-I Space Say you find a magic lottery ticket, that has a 50% chance of $1 million and a 50% chance of nothing. Your classmate offers to buy the ticket off of you for $499,999. 1.1 According to an expected value calculation, will you take this offer? 1.2 Consider decreasing marginal utility of income, where u(0) = 0, u($499, 999) = 10 and u($1, 000, 000) = 16. Calculate the expected utility. Should you take this offer? 1.3 Now assume u(x) is concave. Graph your utility function over income, labelling y-axis U and your x-axis I. Graph the magic lottery gamble on this graph. (Do not use exact numbers)