Pds(Public Distribution System

Microeconomic scheme Solved Problems1 Amit Kumar Goyal2 Solved problems 1. Derive the Walrasian needs when the tax return function is (a) u(x1 , x2 ) = x? x? 1 2 Clearly, if to each one x1 or x2 is 0, benefit is 0. This cannot be optimal since positive inferior is possible. Hence we know that both must be purely positive at the optimum so we can design a Lagrangian. The Lagrangian is L = x? x? + ?[w ? p1 x1 ? p2 x2 ] 1 2 The ?rst vow conditions, then, argon ??1 ?x1 x? ? ?p1 = 0 2 and ?x? x??1 ? ?p2 = 0 1 2 and, of course, the budget bashfulness. p1 x1 + p2 x2 = w We can solve the ?rst equation for ? and respite into the second to get ??1 ??1 ?x1 x? ?x? x2 1 2 = p1 p2 or p1 x1 = Substituting this into the budget constraint yields p2 x2 [1 + or x2 = and x1 = So, x(p, w) = (x1 , x2 )(p1 , p2 , w) = ?w ?w , p1 [? + ?] p2 [? + ?] ?w p1 [? + ?] ?w p2 [? + ?] ? ]=w ? ? p 2 x2 ? ? (b) u(x1 , x2 ) = x1 + 2 x2 Lets engage impregnable 1 the numeraire so that its p rice is 1 and permit p2 be the price of 2. The ?rst order condition for an interior sludge is 1 1 p2 = ? i.e. x2 = 2 = p?2 2 x2 p2 What about corner final results? in that respect get out never be a corner solution where x2 = 0, since the marginal utility of x2 approaches in?nity as x2 approaches 0.

But thither volition be a corner solution with x1 = 0 if p2 (p?2 ) = p?1 > w or equivalently if p2 < 1/w. Hence, the demand is given by 2 2 ? ?(0, w ) ? p2 x(p, w) = (x1 , x2 )(p, w) = ?(w ? 1 , 1 ) ? p2 p2 2 1 p2 1 if w ? p2 if w 0 and examine all the equilibrium...If you trust to get a full essay, order it on our website: BestEssayCheap.com

If you want to get a full essay, visit our page: cheap essay