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Problem 2 Tyrion likes ice cream (good 1) and chocolate (good 2). Denote by ($1,222) 6 X his consumption bundle consisting of :31 units of ice cream and $2 units of chocolate. Tyrion's preferench are represented by the Cobb-Douglas utility flintion: 1. Derive the equation of the indi'erence curve that passes through the consumption bundle (1,1). Draw that indifference curve in a diagram with quantities of ice cream 31 on the horizontal axis and quantities of chocolate 2:2 on the vertical axis. In the same diagram, draw the indi'erence curve along which Tyrion's utility is 4. 2. Are Tyrion's preferences monotonic? Are they strictly monotonic? Does Tyrion exhibit convex preferences? Are Tyrion's preferences strictly convex? 3. Compute Tyrion's marginal utility of ice cream (M U1). Calculate Tyrion's marginal utility of chocolate (M U2). Determine the marginal rate of substitution (MRS) for Tyrion. Does Tyrion have a diminishing marginal rate of substituion? What is Tyrion's marginal rate of substitution at point (1,1) and (, %)? 4. 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 (sf, 3:5) that he can afford at price 101 = 2 and p2 = 1, and income 11:. = 10. Illustrate Tyrion's optimal choice in the same diagram. 5. Suppose now that price p1 and p2 and income m are unknown. Derive Tyrion's demand for ice cream $I(p1,p2,m) and x(p1,p2,m) as a function of any (131,102,111). 6. Suppose that Tyrion's utility function has been transformed by f = 21nu. 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 functions xi (p1, p2, m) and x2(p1, p2, m) under the transformation f