Procedure: Consider the case of a single person where the person will consume x1 only if slope of the IC will be greater than the slope of the budget line, which means 1/β>(1+r), on rearranging it will come down to β<(1/1+r). For a single cnsumer the demand will depend on Pr(β<(1/1+r)) which for a continuous distribution can be written as Pr(β<=(1/1+r)) which is nothing but F(X=1/1+r)=C.D.F. For a uniform distribution defined on [a,b] the C.D.F is given by F(X)=(X-a)/(b-a), here in this case X=1/1+r and the pdf is defined on [1/2,1], using the formula we get Pr(β<=(1/1+r))=F(x=1/1+r)=[(1/1+r)-(1/2)/1/2]=(1-r)/(1+r)............................(1)
(1) gives the demand for a single consumer, so for N consumers the demand will be N*[(1-r)/(1+r)].
Spent almost an hour on this solution and got this as the only way to proceed, however plz do check and comment on the validity...Akshay plz check the solution for the second part.
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