ECN223 Select Topics in Macroeconomics 2016 Past Paper Questions and Model Answers

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Select Topics in Macroeconomics – 2016
Questions and Answers


Section A

Question (a)




Friedman’s Permanent Income model allows us to consider how an individual’s consumption varies
across their lifetimes. Individuals value consumption across their lifetimes, and this is captured
within their utility function, U(C) which is increasing in C and is strictly concave. Households wish to
maximise their lifetime utility, and assuming that the subjective discount factor is 1, then they wish
to maximise:


𝑈 = 𝑢(𝑐 )


However, households are bound by their intertemporal budget constraint, which required that at
the beginning of their lifetime (which we assume is infinite), the present discounted value of their
income and initial assets must be equal to the present discounted value of their consumption, as
expressed below:
𝐶 𝐶
𝐶 + + + ...
1 + 𝑟 (1 + 𝑟)(1 + 𝑟)
𝑤 𝑤
𝐵 𝑤 𝑃 𝐿 𝑃 𝐿
= (1 + 𝑟) ( + 𝐾 )+ 𝐿 + + + . ..
𝑃 𝑃 1 + 𝑟 (1 + 𝑟)(1 + 𝑟)
Since we assume that the interest rate is equal to 0, ad that W/P = 1, we can express this budget
constraint as:

𝐵
𝑐 = (1 + 𝑟) ( + 𝐾) + 𝐿
𝑃

This budget constraint, combined with the concavity of the utility function as discussed above, leads
to households smoothing consumption across their lifetimes. Consumption is governed by the Euler
equation:

𝑐 = 𝐸 [𝑐 ]