ECON 300 Problem Set 1 Solution 1. The function f is defined on (4,10). What is the value of ( 5)f ? Is this a well-defined function? The domain of f is the interval (4,10). Since -5 is not in the domain, ( 5)f is not defined. Nevertheless, the function is not affected since it only needs to be defined on its domain. 2. Consider the following function 2()f x x, is it convex, concave or both? fis convex since 2 2 21 2 1 2( (1 ) ) (1 )x x x x for all 12,xx. 3. Draw indifference curves of the following function 32( , )u x y x y Graph 123()kyx with k=1 and k=5. 01020304050607080901000 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.45 1ECON 300 Problem Set 1 Solution 4. Consider the following function and provide an argument about its concavity or convexity and monotonicity: 001 0 1()2 1 23 2 343xxfxxxx The function is monotone increasing since 1 2( ) ( )f x f x for any 21xx. The function is NOT convex or concave in its full domain. 0 1 2 3 4 1 2 3 4 The red line is not above the function between a and b. Hence it is not Convex The red line is not below the function between a and b. Hence it is not Concave a
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