__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].

A. U=2(XY)

B. U=2(X+Y)

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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