c. The relation "is preferred to" between commodity bundles is just one example of a binary relation. Another example is the relation "is a full brother of" defined over the set of all human beings. Let xRy mean person x is a full brother of person y. Apply the properties of completeness, reflexivity, and transitivty to xRy. Is this relation complete, transitive, and reflexive? For each either prove the property or provide a counter example. 3. Assume Jenkins only cares about the total pounds of fast food that he consumes. The more pounds of fast food he consumes, that happier he is. Remember each burger is 1/4th of a pound and each taco is 1/8"h of a pound. a. Graph the indifference curve that passes through the point (4,2). If the indifference curve intercepts the axes, label where they intercept. Graph several other representative indifference curves as well. Draw an arrow showing the direction in which the indifference curves are increasing. What is Jenkin's marginal rate of substitution between tacos and hamburgers? b. Alternatively, instead of caring about the total pounds of food he eats, Jenkin only cares about the total number of burgers and tacos that he consumes The greater the total number of tacos and burgers he consumes the happier he is. Graph the indifference curve that passes through the point (4,2). Label the slope of the indifference curve. If the indifference curve intercepts the axes, label where they intercept. Graph several other representative indifference curves as well. Draw an arrow showing the direction in which the indifference curves are increasing. c. For both of the preferences above, what type of preferences are these? What wording in the description of Jenkin tipped you off? Are these preferences monotone? Are these preferences strictly convex? d. Suppose Jenkin's preferences match b. above. Also suppose he was currently consuming all burgers and no tacos. The EPA is debating between two policies to reduce pollution. One is to provide a per-unit subsidy on enviro-tacos and the other is to give a lump sum transfer in the form of a voucher for enviro-tacos. Which will be generally more effective at reducing the consumption of polluto burgers? Explain, if necessary explain by graphing how the budget constraint is changing under the two different policies. 4. There is a new fast food lover in town. Call her Ms. X. Ms. X always consumes tacos and hamburgers together. Specifically she consumes one taco with one hamburger and has no use for any additional tacos/hamburgers she is given. a. Graph the indifference curve that passes through the point (3,3). If the indifference curve intercepts the axes, label where they intercept. Graph several other representative indifference curves as well. Draw an arrow showing the direction in which the indifference curves are increasing