Homework help for microeconomics, thanks in advance. Much appreciated

1. In a two-good world, let - bundle x = 3 loaves of bread and 0 apples; - bundle y = 0 loaves of bread and 10 apples; - bundle z = 2 loaves of bread and 4 apples. a. Suppose a consumer weakly prefers x to y, weakly prefers y to z, and strictly prefers z to x. (So, this consumer's preferences violate transitivity.) Explain how you can extract money from this person. b. Do this consumer's preferences over x, y and z violate monotonicity? Why or why not? 2. Clare gets utility from only two goods, potatoes (P) and turnips (T). She generally prefers to have more of each good rather than less, but only for sufficiently large changes to a bundle; she is indifferent over small changes to a bundle. In particular, if x = (P, T) and y = (P+AP, T+AT), where AP and AT are positive numbers, then y > x if AP + AT > 1 y ~ xif AP+ AT = 1. (This pattern of preferences is sometimes called a "threshold effect") a. Explain, in words, what the conditions on y > x and y ~ x mean. b. Show that Clare's preferences violate monotonicity. (Le., find particular bundles such that the definition of monotoncity is not satisfied.) c. Show that Clare's preferences violate transitivity. 3. Tim gets utility from only two goods, rice (R) and beans (B). His preferences are represented by the utility function U(R, B) = R. B. a. Suppose a unit of rice costs $4, a unit of beans costs $5, and Tim's income is $60000. Find Tim's optimal bundle. b. Suppose the price of beans falls to $4. How does Tim's quantity of each good change? 4. In a two-good world, suppose a consumer views the goods as perfect substitutes. Draw a graph of the consumer's choice problem, with a budget constraint and a few indifference curves. (Assume the slope of the indifference curves is different from the slope of the budget constraint.) What is notable about the consumer's preferred bundle