Suppose your friend is indifferent to the bundles (5, 6) and (6, 6). Are the preferences of your friend monotonic?
No, the preferences of my friend are not monotonic.
According to the definition of monotonic preferences, between any two bundles, if one bundle has more of at least one of the goods and no less of the other good compared to another bundle, then the consumer must prefer that bundle.
Comparing the two bundles: Bundle (6, 6) has more of good 1 (6 > 5) and no less of good 2 (6 = 6) compared to bundle (5, 6). If preferences were monotonic, my friend should have preferred bundle (6, 6) over bundle (5, 6). However, since my friend is indifferent between these two bundles, the preferences are not monotonic.
Explanation
The textbook clearly defines monotonic preferences as those where a consumer prefers a bundle that has more of at least one good and no less of the other good. In this case, bundle (6,6) strictly dominates (5,6) in terms of good 1 while having equal amounts of good 2. Under monotonic preferences, the consumer must strictly prefer (6,6). Being indifferent violates this condition, so preferences cannot be monotonic.
Solution Steps
Step 1: Compare bundles (5,6) and (6,6) - (6,6) has more of good 1 and equal good 2
Step 2: Apply definition of monotonic preferences - consumer should prefer (6,6)
Step 3: Since friend is indifferent (not preferring), preferences are NOT monotonic