Question

1. Paul plays guitar in a band. He wants to have as many guitars as possible, regardless of what kind they are. Let x1 denote the number of rhythm guitars and x2 denote the number of bass guitars. The prices of x1 and x2 are p1 and p2, respectively. Paul has an income of m.

a. How would you describe Paul’s preferences for rhythm guitars and bass guitars? What is a utility function that could represent these preferences? What is his budget constraint?

b. Suppose that p1 < p2. Sketch Paul’s budget constraint and the highest possible indifference curve. Clearly label the axes, origin, curves and optimal choice of x1 and x2. What are the equations for Paul’s optimal choice of x1 and x2? Now suppose that Paul gets a raise. Based on the equations for x1 and x2, what will happen to the optimal quantities of x1 and x2? On the same graph, sketch his new budget constraint and highest possible indifference curve. Clearly label the curves and new optimal choice of x1 and x2. Starting at the origin, draw a line that connects Paul’s optimal choices as his income increases. This is an income offer curve. Label the curve and provide a formal definition. Is x1 a normal or inferior good? Explain in one sentence.

c. In one sentence, what is an Engel curve? Continuing from part (b), sketch Paul’s Engel curve for x1 in a separate graph. Clearly label the axes, origin and curve. What is the equation of this curve? What is the slope of the curve? In a separate graph, sketch Paul’s Engel curve for x2. Clearly label the axes, origin and curve. What is the equation of this curve?

Answer 1