1. PPP-adjusted exchange rates and cross country comparisons In class, we briefly discussed how a country’s perceived in

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1. PPP-adjusted exchange rates and cross country
comparisons
In class, we briefly discussed how a country’s perceived income
relative to the United States would
depend on how closely consumption in the country matched the
‘representative bundle’ used to calculate
the PPP exchange rate. In this question, you are going to solve an
exercise that helps you understand
the concept of purchasing power party (PPP) comparisons
better.
Set-up:
•Consider 2 countries: US and IT and a basket of commodities only
comprising of food (F) and
clothing (C).
•Assume that the set of prices for the commodities in the countries
in consideration are: PFUS = 20,
PCUS = 30, PFIT = 100, PCIT = 400.
•Additionally, assume that the utility function of a representative
consumer in the US is given
by: UUS(FUS,CUS) = F.5C.5 while the utility function of a
representative consumer from IT is:
UIT(FIT,CIT) = F.6C.4.
•Per-capita income in US is 2,000 units of US’ currency, while in
IT, it’s 20,000 units of IT’s
currency.
Questions:
(a) Using utility maximization, determine which bundle a consumer
from the US vs a consumer from
IT will consume. Who is better off?
(b) Suppose the OECD decides that the representative bundle is 30
articles of clothing and 50 units
of food. Which country’s chosen bundle seems ‘closer’?
(c) What is the PPP exchange rate for IT relative to US? Using this
exchange rate, calculate per-
capita income for IT in PPP-adjusted units, i.e.. Who has the
larger per-capita income? By how
much?
(d) Now suppose the OECD had chosen a basket with 120 units of food
and 20 units of clothing.
Calculate the PPP exchange rate and use it to calculate per-capita
income in IT. How have the
results changed? Why?