Question

4. Problems 3.4 One way to show convexity of indifference curves is to show that for any two points (xi, yi) and (x2, y2) on an indifference curve that promises U -k, the utility associated with(, 2) is at least as great as k. In other words, one way to show convexity is to show that the following conditions hold and The following graph shows an indifference curve for the utility function U(x,y)-min(x,y), where U x,y) = min(x)) points (xı ,y-(4,8) and (x2, y2) - (8,4) that are on the indifference curve ki. The black line connects two Use the grey point (star symbol) to plot the midpoint of the black line. Then answer the questions below 10 Midpoint 9 1

Answer 1

• u(x,y) = min{x,y}

Mid point for graph joining (4,8) and (8,4) is (6,6)

Utility at this point = min{6,6} = 6.

This is greater than the utility level of 4 associated with the bundles (4,8) and (8,4). Thus for this bundles, condition of convexity holds.

• u(x,y) = max{x,y}

Mid point for graph joining (4,8) and (8,4) is (6,6)

Utility at this point = max{6,6} = 6.

This is lower than the utility level of 8 associated with the bundles (4,8) and (8,4). Thus for this bundles, condition of convexity doesn't holds. (or in other words, concavity holds)

• u(x,y) = x+y

Mid point for graph joining (2,6) and (6,2) is (4,4)

Utility at this point = 4+4=8

This is equal to the utility level of 8 associated with the bundles (2,6) and (6,2). Thus for this bundles, condition of convexity holds.