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4.6 You are planning a study of consumer demand. You have a data set which gives the expenditure of individual consumers on each of n goods. It is sug- gested to you

that an appropriate model for consumer expenditure is the Linear Expenditure System:(Stone 1954)

l

ei �ipi + ai Iy – , pj �j I

j=l

where pi is the price of good i, ei is the consumer's expenditure on good i, y

is the consumer's income, and al, …, a , �l, …, � are non-negative parameters

j=l

such that

aj 1.

1. Find the effect on xi, the demand for good i, of a change in the consumer's income and of an (uncompensated) change in any price pj .

2. Find the substitution effect of a change in price pj on the demand for good

i.

3. Explain how you could check that this demand system is consistent with utility-maximisation and suggest the type of utility function which would yield the demand

functions implied by the above formula for consumer expenditure. {Hint: compare this with Exercise 4.3]

198.

4.6 You are planning a study of consumer demand. You have a data set which gives the expenditure of individual consumers on each of n goods. It is sug- gested to you

that an appropriate model for consumer expenditure is the Linear Expenditure System:(Stone 1954)

l

ei �ipi + ai Iy – , pj �j I

j=l

where pi is the price of good i, ei is the consumer's expenditure on good i, y

is the consumer's income, and al, …, a , �l, …, � are non-negative parameters

j=l

such that

aj 1.

1. Find the effect on xi, the demand for good i, of a change in the consumer's income and of an (uncompensated) change in any price pj .

2. Find the substitution effect of a change in price pj on the demand for good

i.

3. Explain how you could check that this demand system is consistent with utility-maximisation and suggest the type of utility function which would yield the demand

functions implied by the above formula for consumer expenditure. {Hint: compare this with Exercise 4.3]

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