Chapter 3 A Consumers Constrained Choice If this is coffee, please bring me som
Jacks, Richard, Meteorologist has reference to this Academic Journal, PHwiki organized this Journal Chapter 3 A Consumers Constrained Choice If this is coffee, please bring me some tea; but if this is tea, please bring me some coffee. Abraham Lincoln Chapter 3 Outline 3.1 Preferences 3.2 Utility 3.3 Budget Constraint 3.4 Constrained Consumer Choice 3.5 Behavioral Economics Chapter 3: Model of Consumer Behavior Premises of the model: Individual tastes or preferences determine the amount of pleasure people derive from the goods in addition to services they consume. Consumers face constraints, or limits, on their choices. Consumers maximize their well-being or pleasure from consumption subject to the budget in addition to other constraints they face.
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3.1 Preferences To explain consumer behavior, economists assume that consumers have a set of tastes or preferences that they use to guide them in choosing between goods. Goods are ranked according to how much pleasure a consumer gets from consuming each. Preference relations summarize a consumers ranking is used to convey strict preference (e.g. a b) is used to convey weak preference (e.g. a b) ~ is used to convey indifference (e.g. a ~ b) 3.1 Preferences Properties of preferences: Completeness When facing a choice between two bundles of goods (e.g. a in addition to b), a consumer can rank them so that either a b, b a, or a ~ b. Transitivity Consumers rankings are logically consistent in the sense that if a b in addition to b c, then a c. More is Better All else the same, more of a commodity is better than less. In this regard, a good is different than a bad. 3.1 Preference Maps Graphical interpretation of consumer preferences over two goods:
3.1 Indifference Curves The set of all bundles of goods that a consumer views as being equally desirable can be traced out as an indifference curve. Five important properties of indifference curves: Bundles of goods on indifference curves further from the origin are preferred to those on indifference curves closer to the origin. There is an indifference curve through every possible bundle. Indifference curves cannot cross. Indifference curves slope downward. Indifference curves cannot be thick. 3.1 Indifference Curves Impossible indifference curves: 3.2 Utility Utility refers to a set of numerical values that reflect the relative rankings of various bundles of goods. The utility function is the relationship between utility measures in addition to every possible bundle of goods. Given a specific utility function, you can graph a specific indifference curve in addition to determine exactly how much utility is gained from specific consumption choices. Example: q1 = pizza in addition to q2 = burritos Bundle x contains 16 pizzas in addition to 9 burritos: U(x) = 12 Bundle y contains 13 pizzas in addition to 13 burritos: U(y) = 13 Thus, y x
3.2 Utility Utility is an ordinal measure rather than a cardinal one. Utility tells us the relative ranking of two things but not how much more one rank is valued than another. We dont really care that U(x) = 12 in addition to U(y) = 13 in the previous example; we care that y x. Any utility function that generated y x would be consistent with these preferences. A utility function can be trans as long as med into another utility function in such a way that preferences are maintained. Positive monotonic trans as long as mation 3.2 Utility in addition to Indifference Curves The general utility function ( as long as q1 = pizza in addition to q2 = burritos) is 3.2 Willingness to Substitute Between Goods Marginal Rate of Substitution (MRS) is the maximum amount of one good that a consumer will sacrifice (trade) to obtain one more unit of another good. It is the slope at a particular point on the indifference curve MRS = dq2 / dq1
3.2 Marginal Utility in addition to MRS The MRS depends on how much extra utility a consumer gets from a little more of each good. Marginal utility is the extra utility that a consumer gets from consuming the last unit of a good, holding the consumption of other goods constant. Using calculus to calculate the MRS: 3.2 Curvature of Indifference Curves MRS (willingness to trade) diminishes along many typical indifference curves that are concave to the origin. Different utility functions generate different indifference curves: 3.2 Curvature of Indifference Curves Perfect Substitutes Goods that a consumer is completely indifferent between Example: Clorox (C) in addition to Generic Bleach (G) MRS = -2 (constant) Perfect Complements Goods that are consumed in fixed proportions Example: Apple pie (A) in addition to Ice cream (I) MRS is undefined
3.2 Curvature of Indifference Curves Imperfect Substitutes Between extreme examples of perfect substitutes in addition to perfect complements are st in addition to ard-shaped, convex indifference curves. Cobb-Douglas utility function (e.g. ) indifference curves never hit the axes. Quasilinear utility function (e.g. ) indifference curves hit one of the axes. 3.3 Budget Constraint Consumers maximize utility subject to constraints. If we assume consumers cant save in addition to borrow, current period income determines a consumers budget. Given prices of pizza (p1) in addition to burritos (p2), in addition to income Y, the budget line is Example: Assume p1 = $1, p2 = $2 in addition to Y = $50 Rewrite the budget line equation as long as easier graphing (y=mx+b as long as m): 3.3 Budget Constraint Marginal Rate of Trans as long as mation (MRT) is how the market allows consumers to trade one good as long as another. It is the slope of the budget line:
3.4 Constrained Consumer Choice Consumers maximize their well-being (utility) subject to their budget constraint. The highest indifference curve attainable given the budget is the consumers optimal bundle. When the optimal bundle occurs at a point of tangency between indifference curve in addition to budget line, this is called an interior solution. Mathematically, Rearranging, we can see that the marginal utility per dollar is equated across goods at the optimum: 3.4 Constrained Consumer Choice The interior solution that maximizes utility without going beyond the budget constraint is Bundle e. The interior optimum is where 3.4 Constrained Consumer Choice If the relative price of one good is too high in addition to preferences are quasilinear, the indifference curve will not be tangent to the budget line in addition to the consumers optimal bundle occurs at a corner solution.
3.4 Consumer Choice with Calculus Our graphical analysis of consumers constrained choices can be stated mathematically: The optimum is still expressed as in the graphical analysis: These conditions hold if the utility function is quasi-concave, which implies indifference curves are convex to the origin. Solution reveals utility-maximizing values of q1 in addition to q2 as functions of prices, p1 in addition to p2, in addition to income, Y. 3.4 Consumer Choice with Calculus Example (Solved Problem 3.5): 3.4 Consumer Choice with Calculus A second approach to solving constrained utility maximization problems is the Lagrangian method: The critical value of is found through first-order conditions: Equating the first two of these equations yields:
3.4 Minimizing Expenditure Utility maximization has a dual problem in which the consumer seeks the combination of goods that achieves a particular level of utility as long as the least expenditure. 3.4 Expenditure Minimization with Calculus Minimize expenditure, E, subject to the constraint of holding utility constant: The solution of this problem, the expenditure function, shows the minimum expenditure necessary to achieve a specified utility level as long as a given set of prices: 3.5 Behavioral Economics What if consumers are not rational, maximizing individuals Behavioral economics adds insights from psychology in addition to empirical research on cognition in addition to emotional biases to the rational economic model. Tests of transitivity: evidence supports transitivity assumption as long as adults, but not necessarily as long as children. Endowment effect: some evidence that endowments of goods influence indifference maps, which is not the assumption of economic models. Salience: evidence that consumers are more sensitive to increases in pre-tax prices than post-tax price increases from higher ad valorem taxes. Bounded rationality suggests that calculating post-tax prices is costly so some people dont bother to do it, but they would use the in as long as mation if it were provided.
Figure 3.10 Optimal Bundles on Convex Sections of Indifference Curves
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