1) Check whether the following functions are concave, convex, strictly concave, strictly convex, or neither: a)...

  

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1) Check whether the following functions are concave, convex, strictly concave, strictly convex, or neither: a) z = x² b) z = x² + 2x² c) z = (x₁+x₂)(x₁ + x₂) 2) Are the following functions quasi-concave and quasi-convex? Strictly so? a) z = x² x > 0 b) z = ax + b x > 0 c) Z = x₁x₂ x1, x₂ > 0 3) Use bordered determinants to check the following functions for quasi-concavity and quasi-convexity: a) z = = x0.5y0.5 x > 0 b) z = (x + 1)²-(y + 2)² x,y > 0 4) Given the utility function U = (x+2)(y+1), income B, and prices Px and Py, a) Write the Lagrangian function and find x*, y*, and A* in terms of the parameters Px, Py and B. b) Check the second order condition for maximum. c) Can your solution (x* and y*) yield any comparative-static information? d) Find all the comparative-static derivatives you can, evaluate their signs, and interpret their economic meanings. 1) Check whether the following functions are concave, convex, strictly concave, strictly convex, or neither: a) z = x² b) z = x² + 2x² c) z = (x₁+x₂)(x₁ + x₂) 2) Are the following functions quasi-concave and quasi-convex? Strictly so? a) z = x² x > 0 b) z = ax + b x > 0 c) Z = x₁x₂ x1, x₂ > 0 3) Use bordered determinants to check the following functions for quasi-concavity and quasi-convexity: a) z = = x0.5y0.5 x > 0 b) z = (x + 1)²-(y + 2)² x,y > 0 4) Given the utility function U = (x+2)(y+1), income B, and prices Px and Py, a) Write the Lagrangian function and find x*, y*, and A* in terms of the parameters Px, Py and B. b) Check the second order condition for maximum. c) Can your solution (x* and y*) yield any comparative-static information? d) Find all the comparative-static derivatives you can, evaluate their signs, and interpret their economic meanings.

Answer rating: 100% (QA)

Solution 1 a zx is convex but not strictly convex b z x2 2x is convex and strictly conv... View the full answer