Economics 411: Public (Sector) Economics
Assignment #3
Due at 3:30pm on Wednesday, October 2, 2024
5 Points
ASSIGNMENT POLICY: Please read carefully and follow these instructions EXACTLY
(i) You may work with up to two other students, i.e. โco-workersโ
(ii) Each student submits their own unique assignment (NO copying). Co-workers may receive different
grades.
(iii) Write you name in the upper-right corner of the first page and CIRCLE it. Write โAssignment #Xโ in
the top-middle of the page, where X is the assignment number
(iv) STAPLE your pages together. Non-stapled assignments are not accepted. (Dog-eared assignments will
be burned!) DO NOT put this printed sheet on the front.
(v) If you have co-workers, write โCO-WORKERSโ ad their names (not circled) beneath your name
(vi) PAPERCLIP your assignment with your co-workers assignments in alphabetical list by LAST name.
Submit them together.
1. Don Draper and Roger Sterling consume whiskey (x) and cigars (y). Don is person 1, and Roger is
person 2. They have Cobb-Douglas utility functions
๐๐1(๐ฅ๐ฅ1,๐ฆ๐ฆ1)=(๐ฅ๐ฅ1)1/2(๐ฆ๐ฆ1)1/2
๐๐2(๐ฅ๐ฅ2,๐ฆ๐ฆ2)=(๐ฅ๐ฅ2)3/4(๐ฆ๐ฆ2)1/4
Where x1 is Donโs consumption of whiskey, etc. The exponents in these Cobb-Douglas utility
function describe each personโs expenditure share on whiskey. Roger always spends at least three
times as much on whiskey as on cigars, while Don divides his expenditures evenly.
Don has an endowment (๐ฅ๐ฅ๎ชง1,๐ฆ๐ฆ๏ฟฝ1)=(4,0) of whiskey and cigars, while Roger has an endowment
(๐ฅ๐ฅ๎ชง2,๐ฆ๐ฆ๏ฟฝ2) = (0,4). The relative price of whiskey to cigars is p.
(a). What are Donโs (gross) demand functions for whisky and cigars,
๐ฅ๐ฅ1
๐๐(๐๐) and ๐ฆ๐ฆ1
๐๐(๐๐) ?
What are Rogerโs (gross) demand functions,
๐ฅ๐ฅ2
๐๐(๐๐) and ๐ฆ๐ฆ2
๐๐(๐๐) ?
(b) What are Don and Rogerโs indirect utility functions
๐๐๐๐(๐๐)=๐๐๏ฟฝ๐ฅ๐ฅ๐๐
๐๐(๐๐),๐ฆ๐ฆ๐๐
๐๐(๐๐)๏ฟฝ,๐๐= 1,2 ?
(c) Take the derivative of ๐๐๐๐(๐๐) with respect to p, i.e. ๐๐๐๐๐๐/๐๐๐๐. Does Donโs utility increase or decrease
with the relative price of whiskey? What about Rogerโs?
(d) Say Don and Roger are both price-takers in the market for cigars, despite being the only two
people in the economy. What price ๐๐โ will clear the market?
