Four Economic 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: BLaTeX: succC, ALaTeX: simC.

B. Consider the following indifference curve. Explain why such an indifference curve is irrational, referencing the standard assumptions about preferences.

up indiff curve.jpg

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 LaTeX: Uleft(W,Jright)=W^2JU(W,J)=W2J, this implies that her marginal utilities are LaTeX: MU_W=2WJMUW=2WJ and LaTeX: MU_J=W^2MUJ=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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