1.A consumer has preferences represented by the utility functionU(x)E- ,In(x)'i = 1where x; denotes the quantity consumed of good i and n> 3.(a)Assuming that the consumer has fixed income y and can buy good i at price p; , find theordinary and compensated demand elasticities for good 1 with respect to p; , j = 1, .. , n.(b)Suppose that the consumer is legally obligated to purchase an amount A, of good n (e.g.heating oil) where p„An < y. If there are no constraints on the choices of the other n-1goods, then find the ordinary and compensated demand elasticities for good 1 withrespect to p;, j = 1, ... , n. Compare your answers to part (a) above.(c)Now suppose that the consumer is legally obligated to purchase an amount Ak of good kwhere k = n-r,n and 0

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ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

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Question

1.
A consumer has preferences represented by the utility function
U(x)
E- ,In(x)
'i = 1
where x; denotes the quantity consumed of good i and n> 3.
(a)
Assuming that the consumer has fixed income y and can buy good i at price p; , find the
ordinary and compensated demand elasticities for good 1 with respect to p; , j = 1, .. , n.
(b)
Suppose that the consumer is legally obligated to purchase an amount A, of good n (e.g.
heating oil) where p„An < y. If there are no constraints on the choices of the other n-1
goods, then find the ordinary and compensated demand elasticities for good 1 with
respect to p;, j = 1, ... , n. Compare your answers to part (a) above.
(c)
Now suppose that the consumer is legally obligated to purchase an amount Ak of good k
where k = n-r,
n and 0 <r< n-2 and EP,AK < y. Use the arguments in parts (a) and (b)
%3D
above to explain what will happen to the elasticity of good 1 with respect to p; as r
increases (i.e. as the number of constraints increases) and comment on the results.

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