Intermediate Microeconomics problems

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$\succ$C, A$\sim$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+Y

C. 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 $U\left(W,J\right)=W^{2}J$, this implies that her marginal utilities are $M{U}_W=2WJ$ and $M{U}_J=W^2$.

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).