Preferences and Utility

1. Give an example of preferences (i.e., a ranking of baskets) that do not satisfy the assumption that preferences are transitive.

1. What does the assumption that more is better imply about the marginal utility of a good?

1. Adam consumes two goods: housing and food. Suppose we are given Adam's marginal utility of housing and his marginal utility of food at the basket he currently consumes. Can we determine his marginal rate of substitution of housing for food at that basket?

1. Jimmy has the following utility function for hot dogs: U(H)=10HH², with MU_H=102H
   1. Plot the utility and marginal utility functions on two separate graphs.
   2. Suppose that Jimmy is allowed to consume as many hot dogs as he likes and that hot dogs cost him nothing. Show, both algebraically and graphically, the value of Hat which he would stop consuming hot dogs.

1. Consider the utility function U(x, y) = yx with the marginal utilities MUx = y/(2x) and MUy = x.
   1. Does the consumer believe that more is better for each good?
   2. Do the consumer's preferences exhibit a diminishing marginal utility of x? Is the marginal utility of y diminishing?

1. For the following sets of goods draw two indifference curves, U1 and U2, with U2 > U1. Draw each graph placing the amount of the first good on the horizontal axis.
   1. Hot dogs and chili (the consumer likes both and has a diminishing marginal rate of substitution of hot dogs for chili)
   2. Sugar and Sweet'N Low (the consumer likes both and will accept an ounce of Sweet'N Low or an ounce of sugar with equal satisfaction)
   3. Peanut butter and jelly (the consumer likes exactly 2 ounces of peanut butter for every ounce of jelly)
   4. Nuts (which the consumer neither likes nor dislikes) and ice cream (which the consumer likes)
   5. Apples (which the consumer likes) and liver (which the consumer dislikes)