Question

A classic constrained utility maximization problem is to maximizing Utility function Ulx;y) by choosing the optimal quantities of x and y such that; given prices px 0 and Py > 0, total spending does not exceed budget M > 0. In this model,x and y are endogenous variables; Pr: Py and M are exogenous parameters_ Assume that we don t know anything about the shape of U except that it is a continuous function for all non-negative (x,y). max U(x,y) TJ S _ x>0 J20 Prr + pyy < M The set {(x,y) Ix20,y2 0,Pxr+Pyy < M_ is called the budget set: Is the budget set open? (ii) Closed? (iii) Bounded? Prove all three answers. (b) Based on the information given; can we guarantee that there is always a solution to this constrained maximization problem? Why? (c) How would your answer in (b) change if the first two constraints "x Z 0 andy 2 0" are replaced by 0 andy > 0"? Why?

          A classic constrained utility maximization problem is to maximizing Utility function Ulx;y) by choosing the optimal quantities of x and y such that; given prices px 0 and Py > 0, total spending does not exceed budget M > 0. In this model,x and y are endogenous variables; Pr: Py and M are exogenous parameters_ Assume that we don t know anything about the shape of U except that it is a continuous function for all non-negative (x,y). max U(x,y) TJ S _ x>0 J20 Prr + pyy < M
The set {(x,y) Ix20,y2 0,Pxr+Pyy < M_ is called the budget set: Is the budget set open? (ii) Closed? (iii) Bounded? Prove all three answers. (b) Based on the information given; can we guarantee that there is always a solution to this constrained maximization problem? Why? (c) How would your answer in (b) change if the first two constraints "x Z 0 andy 2 0" are replaced by 0 andy > 0"? Why?

a classic constrained utility maximization problem is to maximizing utility function ulxy by choosing the optimal quantities of x and y such that given prices px 0 and py 0 total spending do 45334

Added by Sarah B.

Question

Please give Ace some feedback