140Economic Dynamics14.f1(x) andf2(x) are linearly dependent if and only if there exist constantsb1andb2, not all zero, such thatb1f1(x)+b2f2(x)=0for everyx. If the set of functions isnotlinearly dependent, thenf1(x) andf2(x) are linearly independent. Show thaty1=Y∗andy2=tY∗are linearly independent.15.Given the following version of the Solow model with labour augmentingtechnical progressYt=F(Kt,AtLt)Kt+1=Kt+δKtSt=sYtIt=StLt+1−LtLt=nAt=γtA0(i)show thatˆkt+1=(1−δ)ˆkt+sf(ˆkt)γ(1+n)whereˆkis the capital/labour ratiomeasured in efficiency units, i.e.,ˆk=(K/AL).(ii)Approximate this result aroundˆk∗>0.16.Given the modelqdt=a−bptb>0qst=c+dpetd>0pet=pet−1−λ(pt−1−pet−1)0< λ <1(i) Show that price conforms to a first-order nonhomogeneous differ-ence equation.
This is the end of the preview.
access the rest of the document.