For every pair of technically feasible consumption bundles, denoted by the vectors X^{0} and X^{1} , one and one of the following must be true:
X^{0} is preferred to X^{1}
X^{1} is preferred to X^{0}
X^{0} and X^{1} are equally preferred.
Define the assumption of transitivity:
If X^{2} is at least as good as X^{1}, and X^{1} is at least as good as X^{0}, then X^{2} is at least as good as X^{0}.
What is meant by Cardinal ordering?
Cardinal is a term used when the amount of difference between 2 goods have meaning. The difference between utility level u^{2} and u^{1} are the same as the difference between u^{1} and u^{0}. Or it could be replaced by a linear (or proportional) transformation of itself.
What is meant by ordinal utility ordering?
The utility function only tells us about the ordering of bundles and not about the distance between them in terms of desirability.
What is the assumption of dominance?
This assumptions says goods are goods. If x=(x1,x2) and x1 and x2 are goods, X^{0} is preferred to X^{'} if
Either x^{0}_{1} > x^{'}_{1} and x^{0}_{2}>=x^{'}_{2}
or x^{0}_{2} > x^{'}_{2} and x^{0}_{1}>=x^{'}_{1}
In either case X0 dominates X'.
The substitution effect (in any) of an income-compensated increase in p_{1} is a ....?
Negative change in X_{1}. Or equivalently, the compensated demand curve, which traces out the demand for x1 as p1 varies, utility held constant, is downward-sloping (or vertical or horizontal).
5-1. Can indifference curves cross? If not, which assumptions rule this out?
No, the assumption of dominance rules this out.
A household can buy x1 and x2 only. P2=1. In situations A and B he behaves as follows. Is his behavior consistent?
Situation Income P_{1} x_{1} purchased
A 40 1 20
B 60 2 25
No his behavior is not consistent. P2X was higher and he consumed more X1 when his original consumption bundle was available.
5-2i. A household can buy x1 and x2 only. P2=1. In situations A and B he behaves as follows. Is his behavior consistent?
Situation Income P1 x1 purchased
A 40 1 20
B 61 2 15
Yes his behavior is consistent. He could have consumed his original consumption bundle + one more unit of x2, but because the price of x1 increases he substitutes more x2 and less x1. This is consistent with the negative substitution effect.
Q5-5. Which of the following types of remarks corresponds to non-convex indifference curves:
A: "I would rather spend all my time in the country or all in the town, rather than divide myself between the two."
B: "I prefer a mixture of town and country life to being restricted to one or the other."
Which type of preferences will produce a more stable economy?
A is the remark that corresponds to a non-convex indifference curve.
Explain the concept of homogenity of degree zero.
Suppose we double all prices and income. The budget constraint does not move, since 2m/2p1=m/p1. Therefore, money illusion is ruled out by the assumption of consistency. Demand functions are homogenious of degree zero in prices and income.
Explain the adding up property.
The adding up property says that income effects must add up. The weighted average of income elasticities of demand is unity, the weights being relative shares of each good in total expenditure. From this it follows that some goods (like food) have income elasticities less than unity, and some other goods (like opera) must have income elasticities greater than unity.
Explain inferior and normal goods and what their income elasticities look like.
Goods with income elasticities between 0-1 are often called normal necessities. Those goods with income elasticities >1 are called luxuries. Goods with income elasticities <0 are referred to as inferior goods.
What is an Engle curve?
An Engle curve is the relationship between any good and income, holding prices constant.
True, False, or Uncertain: "The marginal utility of an inferior good is negative, which is why demand falls with income."
False, the marginal utility of an inferior good is still positive, however consumers subsititute into other goods as income increases.