Question

1) Consider a consumer who is choosing among combinations of two goods: cookies (c) and donuts (d). A bundle of c cookies and d donuts is given by (c, d). Assume that both c and d can take values 0,1,2, or 3. The consumer's preferences over bundles of cookies and donuts are as follows: For any two bundles (c,d) and (c,d'): (c,d) (e,d') whenever c2c and d 2 d To understand how to use this definition, consider two bundles (c, d) (3,2) and (d,d)-(0,1). Since 320 and 2 1, we can say that (3,2) (0,1). We can also check the "other direction", i.e., let (c, d) = (0.1) and (c,d') (3,2), and find that we cannot say that (0,1) (3,2). Thus, the consumer strictly prefers (3, 2) to (0,1 a) Are these preferences complete? Hint: If they are complete, you should be able to rank any two bundles. If not, there is at least one pair of bundles that cannot be ranked. b) Are these preferences transitive? Hint: One way to do this is to check every combination of three rankable bundles using the definition of the preference and transitivity. You can use this method, but it will take a long time. Another way is to use three arbitrary bundles, say (C1, d), (C2, d2 and (c,d), and show that if (c1.4) (c2:4) and (c2 , d2): (C3, ds), then (C1, di): (C3, ds) using the definition of the preferences given above. c) Suppose the consumer has $6 to spend and that the price of a cookie is Pe $2 and the price of a donut is Pa = $4. Can you make a good prediction about what bundle the consumer will purchase? If so, what is it? If not, why not? (Assume that the consumer has no use for unspent money. For example the S6 is on a gift card that is about the expire.)