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Select Topics in Macroeconomics – 2017
Questions and Answers
Section A
Question 1
Friedman’s Permanent Income model posits that individuals value both consumption and leisure,
and would like to consume more. This is captured within their utility function, U(C,L) which is
increasing in both C and L. Households therefore wish to maximise their lifetime utility:
𝑈 = 𝛽 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 + 𝑖 (1 + 𝑖)(1 + 𝑖)
𝑤 𝑤
𝐵 𝑤 𝑃 𝐿 𝑃 𝐿
= (1 + 𝑖) ( + 𝐾 )+ 𝐿 + + + . ..
𝑃 𝑃 1 + 𝑖 (1 + 𝑖)(1 + 𝑖)
This budget constraint, combined with the concavity of the utility function as discussed above, leads
to households smoothing consumption across their lifetimes. According to this model, the
consumption function for the macroeconomy is C = c x permanent income. A household’s
permanent income is the long-term expected average of income throughout their entire lifetimes,
rather than just their current income. The marginal propensity to consume out of permanent income
is 1 if consumers want a constant consumption profile. This is because any change in the permanent
income will translate directly into an equal change in their consumption in event period.
For consumption in each period to be constant, we have to assume that (1) the utility function is
quadratic and (2) (1 + 𝑟)𝛽 = 1. Then, consumption is governed by the Euler equation:
𝑐 = 𝐸 [𝑐 ]
Then, assuming there is no uncertainty in the household’s future income, we can state that ct = ct+1 =
… = c (i.e. it is equal to a constant in each period).
ECONOMICS HELP, visit LondonEconomicsTutors.co.uk.
Discounted prices compared to all other websites
Select Topics in Macroeconomics – 2017
Questions and Answers
Section A
Question 1
Friedman’s Permanent Income model posits that individuals value both consumption and leisure,
and would like to consume more. This is captured within their utility function, U(C,L) which is
increasing in both C and L. Households therefore wish to maximise their lifetime utility:
𝑈 = 𝛽 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 + 𝑖 (1 + 𝑖)(1 + 𝑖)
𝑤 𝑤
𝐵 𝑤 𝑃 𝐿 𝑃 𝐿
= (1 + 𝑖) ( + 𝐾 )+ 𝐿 + + + . ..
𝑃 𝑃 1 + 𝑖 (1 + 𝑖)(1 + 𝑖)
This budget constraint, combined with the concavity of the utility function as discussed above, leads
to households smoothing consumption across their lifetimes. According to this model, the
consumption function for the macroeconomy is C = c x permanent income. A household’s
permanent income is the long-term expected average of income throughout their entire lifetimes,
rather than just their current income. The marginal propensity to consume out of permanent income
is 1 if consumers want a constant consumption profile. This is because any change in the permanent
income will translate directly into an equal change in their consumption in event period.
For consumption in each period to be constant, we have to assume that (1) the utility function is
quadratic and (2) (1 + 𝑟)𝛽 = 1. Then, consumption is governed by the Euler equation:
𝑐 = 𝐸 [𝑐 ]
Then, assuming there is no uncertainty in the household’s future income, we can state that ct = ct+1 =
… = c (i.e. it is equal to a constant in each period).
