ISI 2004 Micro doubt

[MohitG]

QNo. 5
 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=1/2(Xe) .
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
Please help :( :(

[MohitG]

I'm getting 1/2 for the third query......just want to know if I am right......

[Granpa Simpson]

Compute optimum Xe...from that compute p(e),.....Now [p(e)+R]/X(e)<=1, from this inequality u can get the maximum R that can be charged...!!!!

[Granpa Simpson]

Also you can compute the slope of the budget line and compare it with the inequality p(xe)/p(x0)<=1, p(xe) will be a term in R from that compute the maximum value that R can take...This is because according to the utility function given, goods are perfect substitute so in order to get xe s.t xe>0, its per unit price has to be less than one..you can use either of the inequalities from the problem formulated...!!!!