3.1: The Laws of Preference
- The Axiom of Comparison: Consumers can compare options and form preferences
- The Axiom of Transitivity: Consumers rank preferences above one another
- Definitions: a good is a commodity for which more is preferred to less; a bad is a commodity for which the reverse holds
3.2: Utility and Preference
- Bentham: "Nature has placed mankind under the governance of two sovereign masters, pain and pleasure... the principle of utility recognizes this subjection." Equating happiness with pleasure.
- Definition: Utility is the variable whose relative magnitude indicates the direction of preference
- Indifference curves can be called constant utility curves and amount to the combinations of goods X and Y that bring about equal utility
3.3: Characteristics of Indifference Curves
Properties of indifference curves:
- Negative slope: diminishing marginal returns and opportunity cost (give up X for Y)
- Indifference curves never intersect: more is always preferred to less, so curves that overlap contradict themselves
- Coverage of indifference curves: many are available-- but each represents budget constraint
- Indifference curves are convex to the origin: based upon empirical observation of "diversity in consumption"
3.4: More on Goods and Bads
- Portfolios are chosen with an eve to desired features (average percent yield r) and undesired features (riskiness s)
- Indifferent curves between goods and bads always have a positive slope
3.5: The Sources and Content of Preferences
- Some preferences are stable (i.e. benevolence towards children). Interesting study shows that women leave their inheritance to their children more often than to their surviving spouse (and vice versa for men)
- Many are transitory-- how does marketing drive this?
4.1: The Optimum of the Consumer
- Budget lines show the baskets attainable for consumers who spend their whole incomes on two goods (intersect indifference curves twice)
- Consumer choice equation: \(P_x x + P_y y = I\)
- Slope of budget line: \(-\frac{P_x}{P_y}\)
- Conclusion: the optimum of the consumer is the point on the budget line that touches the highest attainable indifference curve. When convex, the optimum can be an interior solution where positive amounts of both commodities are bought. Or, it can be a corner solution where one on the commodities is not bought at all
- Consumption Balance Equality: \(\frac{MU_x}{P_x} = \frac{MU_y}{P_y}\)
- Remember, can only use marginal utility when thinking of it as a cardinal variable (adding up vs. ranking) and diminishing marginal utility is assumed
- For ordinal utility, we can use Marginal Rate of Substitution in Consumption (MRSc): \(MRS_c \equiv - \frac{\Delta y}{\Delta x}|_U\)
- \(MRS_c = \frac{P_x}{P_y}\)
4.2- 4.3: Complements, Substitutes and Consumer's Response
- Perfect complements curves will be at right angles
- Perfect substitutes curves are straight lines
- If we assume preferences do not change, the optimum of the consumer can vary only in response to changes in opportunities: his or her income and commodity prices
- Conclusion: For goods X and Y, a positively sloped Income Expansion Path indicates that the consumption of both goods rises as income grows (normal or superior goods).
- The curve connecting all the optimum positions of the goods is called the Price Expansion Path
Properties of PEP:
- As Px falls, income I is held constant, the conumer attains higher utility.
- When the PEP slopes downward, the consumer responds to a fall in Px by choosing more X but less of the numeraire good Y
- The intercepts are the "choke prices" where the consumer buys none of the good at the high price
- It may even curl backward like a Giffen good, where the lower price temporarily causes the consumer to buy less (violates law of demand)
4.4: Income and Substitution Effects of a Price Change
- Income effect: A fall in Px increases the consumer's real income-- meaning, he or she could buy the same bundle of goods as before but have some left over
- Pure Substitution Effect: Even if real income or utility had remained the same, more X would have been purchased anyway at the lower Px
4.5: From Individual Demand to Market Demand
Conclusion: the market demand curve is the horizontal sum of the individual demand curves: \(X \equiv \sum^ N _{i = 1} x_i\)
Class Notes:
Wheat Corn
Anderson 30(1\3) 10(2/3)
Brooks 20(1/3) 20(2/3)
Total: 50 30
Who specializes in what?
- Anderson's total time in wheat: 90
- Worst terms of acceptable trade: 60W = 10C
- Brooks's total time in corn: 30
- Worst terms of acceptable trade: 10C = 20W
Terms of trade: 20W = 10C
After specialization and trade:
- Anderson: 50 wheat and 10 corn
- Brooks: 40 wheat and 20 wheat
Now..
Wheat Corn