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Consider an economy with one good X and two people, indexed 1 and 2, who both...

Consider an economy with one good X and two people, indexed 1 and 2, who both have the same log utility function U^i(X_i) = ln(X_i). Suppose that the social planner has the ability to allocate any positive amount of the good to each person, subject to a total resource constraint of 30 units of X. Suppose that the social welfare function is:

SWF = 1/3ln(X_1)+ 2/3ln(X_2)

- What are the optimal quantities of X given to persons 1 and 2?

Now suppose that the social welfare function changes. Specifically, the whole function is multiplied by 10, so that the new function is:
SWF= 10/3ln(X_1)+ 20/3ln(X_2)
- What are the optimal quantities of X given to persons 1 and 2?

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Answer #1

Or you can try finding the MUx1/MUx2 , you will see that the no. that has been multiplied gets cancelled and does play any role after wards. hence no change in optimum choice. it will just increase the scale of social welfare function by 10 times.

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