Abishag Appleby owns 20 quinces and 5 kumquats. She has no income from any other source, but she can buy or sell either quinces or kumquats at their market prices. The price of kumquats is four times the price of quinces. There are no other commodities of interest.
(a) How many quinces could she have if she was willing to do without kumquats? ____ How many kumquats could she have if she was willing to do without quinces? ____.
(b) Draw Abishag’s budget set, using blue ink, and label the endowment bundle with the letter E. If the price of quinces is 1 and the price of kumquats is 4, write Abishag’s budget equation. __________. If the price of quinces is 2 and the price of kumquats is 8, write Abishag’s budget equation. _________. What effect does doubling both prices have on the set of commodity bundles that Abishag can afford? ______.
(c) Suppose that Abishag decides to sell 10 quinces. Label her final consumption bundle in your graph with the letter C.
(d) Now, after she has sold 10 quinces and owns the bundle labeled C, suppose that the price of kumquats falls so that kumquats cost the same as quinces. On the diagram above, draw Abishag’s new budget line, using red ink.
(e) If Abishag obeys the weak axiom of revealed preference, then there are some points on her red budget line that we can be sure Abishag will not choose. On the graph, make a squiggly line over the portion of Abishag’s red budget line that we can be sure she will not choose.