As we saw in Figure 3.5, one way to show the convexity of indifference curves is to show that, for any two points (x₁, y₁) and (x₂, y₂) on an indifference curve that promises U = k, the utility associated with the point 

 

is at least as great ask. Use this approach to discuss the convexity of the indifference curves for the following three functions. Be sure to graph your results.

  

a. U(x, y) = min(x, y).

  

b. U(x, y) = max(x, y).

  

c. U(x, y) = x + y.
 

(x1+x2 y+y2) 2 2