Smith and Jones are stranded on a desert island. Each has in her possession some slices of ham (H) and cheese (C). Smith prefers to consume ham and cheese in the fixed proportion of 2 slices of cheese to each slice of ham. Her utility function is given by Us = min(10H, 5C). Jones, on the other hand, regards ham and cheese as substitutes – she is always willing to trade 3 slices of ham for 4 slices of cheese, and her utility function is given by UJ = 4H + 3C. Total endowments are 100 slices of ham and 200 slices of cheese. a. Draw the Edgeworth Box diagram for all possible exchanges in this situation. What is the contract curve for this exchange economy? b. Suppose Smith’s initial endowment is 40 slices of ham and 80 slices of cheese (Jones has the remaining ham and cheese as her initial endowment). What mutually beneficial trades are possible in this economy and what utility levels will Smith and Jones enjoy from such trades? c. Now imagine a new endowment in which Smith has 60 slices of ham and 80 slices of cheese (Jones has the remaining ham and cheese as her initial endowment). What mutually beneficial trades might occur and what utility levels would be experienced by Smith and Jones?
Smith and Jones are stranded on a desert island. Each has in her possession some slices of ham
(H) and cheese (C). Smith prefers to consume ham and cheese in the fixed proportion of 2 slices
of cheese to each slice of ham. Her utility function is given by Us = min(10H, 5C). Jones, on the
other hand, regards ham and cheese as substitutes – she is always willing to trade 3 slices of ham
for 4 slices of cheese, and her utility function is given by UJ = 4H + 3C. Total endowments are
100 slices of ham and 200 slices of cheese.
a. Draw the Edgeworth Box diagram for all possible exchanges in this situation. What is
the contract curve for this exchange economy?
b. Suppose Smith’s initial endowment is 40 slices of ham and 80 slices of cheese (Jones has
the remaining ham and cheese as her initial endowment). What mutually beneficial
trades are possible in this economy and what utility levels will Smith and Jones enjoy
from such trades?
c. Now imagine a new endowment in which Smith has 60 slices of ham and 80 slices of
cheese (Jones has the remaining ham and cheese as her initial endowment). What
mutually beneficial trades might occur and what utility levels would be experienced by
Smith and Jones?
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