32 1. True or False with justification and a graph if needed: a) The slope of the budget set is the ratio of the prices of commodities x and y. b) Nancy's economics teacher will her course grade that is the maximum of her scores on three midterm examinations. Nancy has convex preference over the possible combinations of midterm scores. 2. Consider a group of people A, B, C and the relation "at least as tall as," as in "A is at least as tall as B." Is this relation transitive? Is it complete? Explain your answer. 3. Are the preferences in the graphs below convex, strictly convex, monotone? Chocolate, 22 21 Ice Cream, 21 4. Consider a consumer who wants to consume only two commodities and has an income of LE100. Assume the price of good I is LE10 per unit and the price of good 2 is LE20 per unit. Now, inflation causes the price of good I to increase to LE20 per unit, while the price of good 2 increases to LE25 per unit. On the other hand, the consumer also gets a raise of LE100 (so her new income is LE200). Write down the equation for the consumer's budget constraint and graph it with labels. Is the consumer better off or worse off