Question

True/False Questions.

For each question below, please answer “true” or “false” and explain why.

6. A consumer with convex preferences who is indifferent between the bundles (5,2) and (11,6) will like the bundle (8,4) at least as well as either of the first two bundles. Assume these two goods are imperfect substitutes.

7. The marginal rate of substitution is always the same constant number when the goods are imperfect substitutes and no matter how many of each good is being consumed.

8. The transformation of a utility function described as f(u) = ln⁡ (α(U(x,y))) where α=-1 will retain the ordinal preferences of bundle A preferred to bundle B.

Answer 1

6). False

Reason: Given a convex indifference containing the set of all bundles (of two or more goods) that are all viewed as equally desired, the set of all goods bundles that are viewed as being at least as desired as those on the indifference curve is a convex preference .for any two distinct bundles that are each viewed as being at least as good as a third bundle, a weighted average of the two bundles (including a positive amount of each bundle) is viewed as being strictly better than the third bundle.

7). True

Reason: The marginal rate of substitution is an economics term that refers to the point at which one good is substitutable for another. It forms a downward sloping curve, called the indifference curve where each point along it represents quantities of good X and good Y that you would be happy substituting for one another. It is always changes when consumer consume substitutes

But when the goods are imperfect substitutes then it is possible that of each good is being consumed.

8). True.

The concept of consumer with convex Preference roughly corresponds to the concept of diminishing marginal utility without requiring utility functions. The indifference curve theory is based on the ordinal measurement of utility. That is why the numbers the utility function assigns to the alternative commodity combinations do not have any cardinal significance, they only have ordinal preference, i.e., they only indicate whether the utility level derived from a particular combination of the goods is higher or lower than that obtained from another combination according as the number assigned to the former is higher or lower than the latter.