●o。 Graphical Optimization H Leisure. I 15
Graphical Optimization 15
●● Outcome o Slope of indifference curve equals slope of budget constraint o Slope of budget constraint: wage W o Result wage= MRS o This is a very general result: the Mrs between any two goods is given by the relative price 16
Outcome 16 Slope of indifference curve equals slope of budget constraint Slope of budget constraint: wage w Result: wage = MRS This is a very general result: the MRS between any two goods is given by the relative price!
●●° Mathematical Optimization o Substitute constraints into U(C, D) maxU(C=(h-1)+p-7,) o First-order condition with respect to I 0=-wU/+ o Result(once again wage= MRS 17
Mathematical Optimization Substitute constraints into U(C,l) First-order condition with respect to l: Result (once again): wage = MRS 17 max ( ( ) , ) U C w h l p T l = − + − 0 C l wU U C l U w U = − + =
●● Example o U(C, 1=logC +log/ o wage equals 10 coconuts per hour o Time:24 hours o Profit and tax: p=30 and T=30 oC=10×(24-) 18
Example wage equals 10 coconuts per hour Time: 24 hours Profit and tax: p=30 and T=30 18 U C l C l ( , ) log log = + C l = − 10 (24 )
●● Example o Maximization problem max(log(240-100)+log/ o Solution 10 0 240-10l =12,C=120 19
Example Maximization problem: Solution: , 19 max{log(240 10 ) log } − + l l 10 1 0 240 10l l = − + − l =12 C =120