ECONnotes5 - 03:56...

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03:56 Note- MRS= MUf/MUc (F- x intercept)- MRS of food for clothing Constrained Optimal-  Utility maximization and spend all your money  assumption. A point on the budget constraint that is not on the indifference curve  is less utility (if you make a northeast direction on the indifference curve).  Constrained optimization (math part not really imp) Max U(X,Y)     I = PxX + PyY L= U(X,Y) + ∂[I- PxX-PyY]   If X(best choice) > 0 and Y*>) and I>0    [corner  solutions] dL/dx= dU/dx= -∂Px= 0 dL/dy= dU/dy= -∂Py=0 dL/d∂= I – PxX – PyY= 0  (spend all your money rule) Max function means all derivatives must equal zero. (If at best choice)  Hence ∂Px=dU/dx and ∂Py=dU/dy. So dU/dx/Px= ∂ and du/dy/Py= ∂. If you  equate the lambdas, you get dUx/Px= dUy/Py which along with I= PxX + PyY is  the solution to the max function problem.  Question- U=CF. I= 100, Pf= 10, Pc= 5.  MRS= MUf/MUc= C/F= 10/5; C/F= 2. C= 
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ECONnotes5 - 03:56...

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