G30 Microeconomics Assignment 2
Answer all questions. Where notation is provided, use that particular notation.
Where notation is not provided, use standard notation and explain what each symbol denotes.
Question 1 (40 Marks): Suppose that in a pure exchange economy (i.e. an economy without produc-
tion), we have two hobbits, Frodo and Sam, and two goods, Fish and Ale. Frodo and Sam have
the utility functions:
uf = Minfxff ; xaf g and us = Minfxfs; (xas)
where xff and xaf are Frodo’s consumption of sh and ale; xfs and xas are Sam’s con-
sumption of sh and ale.
Frodo starts with an endowment of 30 units of sh and none of ale, while Sam starts with an
endowment of 20 units of ale and none of sh. Neither can consume negative amounts of a good.
a. If both Frodo and Sam are price takers, what is the equilibrium? [20 Marks]
b. Suppose instead Frodo starts of with only 5 units of sh, while Sam’s initial endowment
remains the same. What happens now? [20 Marks]
Question 2 (30 Marks): Consider a pure exchange economy with i=1,2, where consumers have Cobb-
Douglas utility functions and !`i 0 8 ` = 1; 2 ^ i = 1; 2, where notation is standard.
a. Solve for the Walrasian (competitive) equilibrium price ratio, fp1
b. Discuss the implications for the Walrasian price ratio of a small negative change in !22.
Question 3 (30 Marks): Joey and Ross are the two consumers of our `Friends’ economy. There are 100
units of sandwiches and 100 units of salt water taes. Joey and Ross are each endowed with
50 units of each good. Joey says, `I can take or leave salt water taes, but I love sandwiches’.
Ross says, `I love salt water taes, but I can take or leave sandwiches’. Note: for parts (a) and
(b) you are not required to provide a mathematical approach. Also neither Joey’s nor Ross’
preferences are lexicographic.
a. Draw an Edgeworth box for our `Friends’ economy and sketch Joey and Ross’ prefer-
ences. Explain. [15 Marks]
b. Find all Walrasian equilibria for this economy and discuss. [15 Marks]
Dr Ufuk Gunes Bebek
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