Question

Alisa consumes only cellos (X) and cello bows (Y). These goods are perfect complements for Alisa, in a one-to-one ratio.

a. Suppose the price of a cello is $50,000 and the price of a bow is $10,000. Draw three budget constraints for Alisa corresponding to her annual income being $60,000, $120,000, and $180,000. Sketch in her indifference curves (remember: perfect complements) and show the optimal bundle she would choose on each of the three budgets.

b. Draw Alisa’s Engel curve for cellos based on the information from part (a).

c. Now suppose Alisa’s income is fixed at $120,000, and bows still cost $10,000 each. Draw the three budget constraints corresponding to the price of a cello being $20,000, $30,000, and $50,000. Sketch in her indifference curves and show the optimal bundle she would choose on each of the three budgets.

d. Draw Alisa’s demand curve for cellos based on the information from part (c).

Answer 1

(a) The budget constraint would be or . For different incomes, graph is as below. The indifference curves would be , as Alisa likes them in one-to-one ratio.

The solutions would be where the indifference curve have the corner, which is at where X=Y. As can be seen, the optimal bundles are .

(b) Putting Y=X in the constraint , we have or . The Engel curve is as below (note that the graph would not be quite visible without scaling the X-axis).

(c) The budget constraint would be as . For different price of X, the BL's are as below.

As can be seen, the optimal bundles are .

(d) The optimal bundles would always be at where Y=X. Putting this in the constraint, we have or or . The above points would be as below.