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Problem 4 Cersei likes to consume apples(good 1) and cookies (good 2). Denote by (x1, X2) E X her con- sumption bundle consisting of x1 units of apple and x2 units of cookies. Cersei's preferences are represented by quasi -linear preferences: u(x1, X2) = 2VX1+ 2 1. Derive the equation of the indifference curve that passes through the consumption bundle (4, 2). Draw that indifference curve in a diagram with quantities of ice cream x1 on the horizontal axis and quantities of chocolate T2 on the vertical axis. In the same diagram, draw the indifference curve along which Cersei's utility is 4. 2. Compute Cersei's marginal utility of apples (MU1). Calculate Cersei's marginal utility of chocolate (MU2). Determine the marginal rate of substitution (MRS) for Cersei. Does Cersei have a diminishing marginal rate of substituton? What is Cersei's marginal rate of substitution at point (1,1) and (16,2)?3. Suppose the price for ice apple p1 is 5 and the price for chocolate p2 is 1. Furthermore, suppose that Cersei has 30 dollars to spend for his consumption. Determine Cersei's most desirable consumption bundle (x], x2) that she can afford at price p1 = 5 and p2 = 1, and income m = 30. 4. Is the law of demand satisfied? (i.e. is x1* decreasing in p1). Explain