# intermediate microeconomics 7 ###### Business portfolio | Management homework help
July 22, 2021 ###### Which twentieth-century perspective in psychology is correctly matched with its emphasis? a)…
July 22, 2021

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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