ISI 2004

[s]

A consumer consumes electricity Xe and other goods Xo .
The price of other goods is unity. To consume electricity the consumer has
to pay a rental charge R and a per unit price p. However, p increases with
the quantity of electricity consumed according to the function p=1/2Xe .
The utility function of the consumer is U=XE+Xo and his income is
I > R .
(i) Draw the budget line of the consumer.
(ii) If R = 0 and I = 1, find the optimum consumption bundle.
(iii) Find the maximum R that the electricity company can
extract from the consumer.


will the budget line be concave with intercepts xe=square root(2(I-R)) and xo=I...? optimal bundle is xe=1 and xo=1/2 ??...need suggestions for last part

:)

[anon_econ]

Hi s,
i think if at all he consumes a positive amount of xe, then he wud consume xe=1 and xo=I-R-0.5. this wud make his utility = I-R+0.5. now if R is any higher than 0.5, he wud choose to consume 0 of xe and get a utility = I w/o paying any rent. thus R can't be higher than 0.5.

[anon_econ]

Actually i dont know how to incorporate the possibility that he could consume 0 of x0..if v continue to work with the values from the 2nd part then that problem won't arise..

[Harpreet Singh]

what about the budget line ?
is it a straight line or not?

[Abhitesh]

R + Xe^2/2 + Xo = I