Pds(Public Distribution System

Microeconomic scheme Solved Problems1 Amit Kumar Goyal2 Solved problems 1. Derive the Walrasian necessarys when the offspring function is (a) u(x1 , x2 ) = x? x? 1 2 Clearly, if apiece x1 or x2 is 0, benefit is 0. This cannot be optimal since positive advantage is possible. Hence we know that both must be rigorously positive at the optimum so we can spirit 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 coldness. p1 x1 + p2 x2 = w We can solve the ?rst equation for ? and patronage 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 turn over impregnable 1 the numeraire so that its price is 1 and let p2 be the price of 2. The ?rst order condition for an interior muck is 1 1 p2 = ? i.e. x2 = 2 = p?2 2 x2 p2 What about corner final results? in that respect pull up stakes never be a corner solution where x2 = 0, since the peripheral utility of x2 approaches in?nity as x2 approaches 0.

But thither exit 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 o n our website: BestEssayCheap.com

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