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Help with this homework 1 answer below » Please help me with all the questions Document Preview: Homework #6 ECO 4401, Fall 2015 Due: Friday, December 4th at the beginning of class. 1. Classify each of the following functions as strictly convex, strictly concave, or neither a. ??=??(??)=v(1+??2) b. ??=??(??,??)=3??4+5??2??-??3 c. ??=??(??,??)=-5??2-??2+2????+6??+2??+7 d. ??=??(??,??)=2??2-4????+3??2-10??+14??+3 2. Find the coordinates for all critical points of each of the following functions. Then classify each critical point View complete question » Please help me with all the questions Document Preview: Homework #6 ECO 4401, Fall 2015 Due: Friday, December 4th at the beginning of class. 1. Classify each of the following functions as strictly convex, strictly concave, or neither a. ??=??(??)=v(1+??2) b. ??=??(??,??)=3??4+5??2??-??3 c. ??=??(??,??)=-5??2-??2+2????+6??+2??+7 d. ??=??(??,??)=2??2-4????+3??2-10??+14??+3 2. Find the coordinates for all critical points of each of the following functions. Then classify each critical point as a local maximum, a local minimum, or neither. a. ??=??(??,??)=??4+??2-6????+3??2;(??,??)?R2 b. ??=??(??,??)= 3??2-??3+12????-36??; (??,??)?R2 c. ??=??(??,??,??)=??2+4????+??2-3????+3??2-10??-5??-15??; (??,??,??)?R3 3. Consider a perfectly competitive firm endowed with production function: ??=??1/3??1/3. The firm can purchase as much capital (K) and labor (L) as it likes at their exogenously determined market prices: r >0 (the rental price of capital) and w >0 (the wage rate). It can sell as much output as it likes at the exogenously determined market price for its product: p>0. a. Verify that the firm’s profit function, ??(??,??)=????1/3??1/3-(????+????), is strictly concave at all points where K, L = 0. b. If the firm chooses K and L to maximize profit, what will its capital and labor demand functions be (i.e. – ??* and ??* as functions of p, w, and r)? c. Derive ????*/???? and ????*/???? and determine their signs. 4. A two product monopoly faces the following demand and cost functions: ? ??1??=40-2??1-??2 ? ??2??=35-??1-??2 ? ??=??12+2??22+10
a. Find the pair of prices, p1 and p2, that satisfy the first-order necessary conditions for a local maximum of the profit function: ??(??1,??2)=??1??1??(??1,??2)+??2??2??(??1,??2)-(??1??(??1,??2)2+2??2??(??1,??2)2+10) b. Check the second-order sufficient condition for local maxima. Can you conclude that the local maximum you have identified is also a global maximum? Explain. c. How much of each product will be produced and sold? What will the firm’s profit be? 5. Consider the problem of… Attachments: eco-for-math-….pdf View less » Nov 26 2015 02:11 AM

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