1.A. Draw a simple set of indifference curves featuring bundles A, B, and C and depicting a consumer’s preferences where the following preference relations hold: B≻C, A∼C.B. Consider the following indifference curve. Explain why such an indifference curve is irrational, referencing the standard assumptions about preferences.2. For each of the utility functions below, draw a set of three indifference curves showing the bundles of X and Y which yield utility levels U1=16, U2=18, and U3=20.[Example: you will draw two preference maps, one for (A) and one for (B) each with three indifference curves representing the different levels of utility. Labeling 3-4 bundles on each curve will be sufficient to approximate their shape—so for the first curve for (A), show how (2,4), (4,2), and (8,1) are all on the same curve].A. U=2(XY)B. U=X+YC. What is unique about the preferences depicted in B?3. Suppose a consumer has an income of $100 and purchases two goods, gasoline (G, at a price of $2/unit) and food (F, at a price of $5/unit).A. Write the equation for the budget constraint.B. Draw a graph of the budget constraint, placing gasoline (G) on the horizontal axis and food (F) on the vertical axis.C. Assume income increases to $120. On the same graph, draw a new budget constraint and indicate the change in the opportunity set.4. Suppose Cersei consumes two goods, wine (W) and jewelry (J). She spends $1,500 across these goods, with the price of wine (PW) $50 per unit and the price of jewelry (PJ) $250 per unit. If her utility function is U(W,J)=W2J, this implies that her marginal utilities are MUW=2WJ and MUJ=W2.A. Write out the equation for the budget line. Draw a graph of the budget line with W on the horizontal axis. What is its slope?B. What is Cersei’s marginal rate of substitution? (Hint: how does marginal utility relate to MRS?)C. What is the relationship between W and J when Cersei is maximizing her utility subject to the budget constraint? (Hint: what is the relationship between your answers to (A) and (B) when utility is maximized? Solve in terms of either J or W).D. Find the utility-maximizing bundle for Cersei, and show on your graph depicting the budget constraint by adding an indifference curve. (Hint: plug your answer to (C) into the budget constraint and solve for the bundle of W and J).
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