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Problem 2 Tyrion likes ice cream (good 1) and chocolate (good 2). Denote by (x1, X2) E X his consumption bundle consisting of x1 units of ice cream and x2 units of chocolate. Tyrion's preferences are represented by the Cobb-Douglas utility funtion: u($1, X2) = x4. Suppose the price for ice cream p1 is 2 and the price for chocolate p2 is 1. Furthermore, suppose that Tyrion has 10 dollars to spend for his consumption. Write down the equation for his budget line and draw it in a diagram. Determine Tyrion's most desirable consumption bundle (mi, 55;) that he can a'ord at price 331 = 2 and p2 = 1, and income m = 10. Illustrate Tyrion's optimal choice in the same diagram. 5. Suppose now that price 131 and p2 and income m are unknown. Derive Tyrion's demand for ice cream $'f(p1,p2,m) and m(p1,p2,m) as a function of any (phpg, m). 6. Suppose that Tyrion's utility function has been transformed by f = Zlnu. Does the new function f represent Tyrion's initial preferences? What is his marginal rate of substitution after the transformation? What are his new demand flmctions 31(p1, 102, m.) and 1:; (p1, p2, m) under the transformation f