ANSWER THE QUESTIONS BELOW ONE BY ONE AND CORRECTLY
1. For each of the utility functions below, draw a set of three indifference curves showing possible bundles of X and Y which yield utility levels U1=8, U2=12, and U3=16.
[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 2-3 bundles on each curve will be sufficient to approximate their shape—for example, for the first curve for (A), show how (2,2), (4,1), and (1,4) are all on the same curve].
C. What is unique about the preferences depicted in B?
2. Suppose a consumer has an income of $60 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 the price of gasoline increases to $4. On the same graph, draw a new budget constraint and indicate the change in the opportunity set.
3. Suppose Tom consumes two goods, rings (R) and avocados (A). He spends $240 across these goods, with the price of rings (PR) $10 per unit and the price of avocados (PA) $8 per unit. If his utility function is , this implies that his marginal utilities are and .
A. Write out the equation for the budget line. Draw a graph of the budget line with R on the horizontal axis. What is its slope?
B. What is Tom’s marginal rate of substitution? (Hint: how does marginal utility relate to MRS?)
C. What is the relationship between R and A when Tom is maximizing his 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 R or A).
D. Find the utility-maximizing bundle for Tom, 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 R and A).
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