Two Microeconomic Problems
In all the problems that follow you can assume the Second Order Conditions for maximization
are satisfied.
1. Find the maxima of the following functions.
(a) f (x) = −x2 −x4.
(b) f (x) = −x2 +x.
(c) f (x,y) = −x2 −y4 +3.
(d) f (x,y) = xy−x2 −y2 +9y.
2. Find the solution of the following constrained maximization problems.
(a) maxx,y {f (x,y) = xy : 2x+4y = 8} .
(b) maxx,y {f (x,y) = x+y : 2x+4y = 8} .
(c) maxx,y {f (x,y) = min{x,y} : 2x+4y = 12} .
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