Solution
Sandeep Kumar answered on
Oct 18 2021
2)
Consider the given problem here U(X), be the utility function, and “f” be the strictly increasing function, => f’ > 0.
Now if we max “U”, subject to the budget constraint PX <= M, where ,where ”P” and “X” be the price and commodity vector, then at the optimum we will get MRS = MU1 / MU2 = P1 / P2.
Now, let’s say that V(X)=f(U(X)), the positive monotonic transformation of U, now if we maximize “V” subject to the same budget constraint, PX <=M. we will get the same condition, => the V, and U have the same preference relation.
If V(X) = f[U(X)], so MV1 = f’ MU1 and MV2 = f’ MU2, => MRS = MV1 / MV2
=> MU1 /MU2, same as the above => the 2 preference relation is same.
ii)
now, consider that the “f” be the strictly increasing function, => f’ > 0 and U have “= >” type preference.
Now if we max “U”, subject to the budget constraint PX <= M, where ,”P” and “X” be the price and commodity vector, then at the optimum we will get MRS = MU1 / MU2 = P1 / P2.
Now, let’s say that V(X)=U(f(X)), the positive monotonic transformation , now if we maximize “V” subject to the same budget constraint, PX <=M. we will get the same...