Bernice’s preferences can be represented by u(x, y) = min{x, y}, where x is pairs of earrings and y is dollars to spend on other things. She faces prices (px, py) = (2, 1) and her income is 12.
(a) Draw in pencil on the graph below some of Bernice’s indifference curves and her budget constraint. Her optimal bundle is _________ pairs of earrings and _________ dollars to spend on other things.
(b) The price of a pair of earrings rises to $3 and Bernice’s income stays the same. Using blue ink, draw her new budget constraint on the graph above. Her new optimal bundle is _________ pairs of earrings and _________ dollars to spend on other things.
(c) What bundle would Bernice choose if she faced the original prices and had just enough income to reach the new indifference curve? _________. Draw with red ink the budget line that passes through this bundle at the original prices. How much income would Bernice need at the original prices to have this (red) budget line? _________.
(d) The maximum amount that Bernice would pay to avoid the price increase is _________. This is the (compensating, equivalent) variation in income. _________.
(e) What bundle would Bernice choose if she faced the new prices and had just enough income to reach her original indifference curve? _________. Draw with black ink the budget line that passes through this bundle at the new prices. How much income would Bernice have with this budget? _________.
(f) In order to be as well-off as she was with her original bundle, Bernice’s original income would have to rise by _________. This is the (compensating, equivalent) variation in income. _________.