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This problem set is meant to give you practice using Dynamic Programming. It may seem tedious but by the end you should be getting an idea about the intuition behind optimal intertemporal trade-os. Have fun and talk to your classmates about your solutions. 1 Problem #1 Consider the following consumption-savings problem. The household has a pe- riod utility function dened on consumption to be a[c,} where u' \":3 ll, 11\" c: [l and lim,_._,.n u'Ec} = one. The household has accem to a production technology that produces output, yt, from capital available at the beginning of period t, kt. This production flmction is given by le), is strictly concave so that flit} :3- , and f"[k,} c: i], and satises Hill = , limkH,\" f'[.i:,] 2 co and liming\