2. Suppose a household\'s preferences were represented by the utility function u

Question

2. Suppose a household's preferences were represented by the utility function u(x,y)- x1/3y2/3 and they faced the following budget constraint: pxx + p,y S M.We discussed constraints and when they are/aren't binding. You have three constraints for this problem: The budget constraint pzx + pyy s M and two non-negativity constraints (meaning the household is not allowed to purchase negative units of any good) for goods x and y (x 20,yz 0). For the constraints, your Lagrangian would have a Lagrangian multiplier on each constraint (we typically leave off the ones for x and y when we write the Lagrangian), so we will call the constraints gc,A, Xy, each named for the associated constraint. Given these three constraints, how many constraints would be binding (i.e. how many of the Lagrangian multipliers would have non-zero values?

Explanation / Answer

Given these three constraints namely the budget constraints and the the constraints for x and y only the budget constraint will be binding because utility increases with increase in consumption so consumer will consume on the budget constarint.

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