Consumer Preferences Utility Functions and Budget Lines Overheads Utility is a measure of satisfaction or pleasure Utility is defined as the pleasure or satisfaction obtained from consuming goods and services Utility is defined on the entire consumption bundle of the consumer Mathematically we define the utility function as u u q1 q2 q3 qn u represents utility qj is the quantity consumed of the jth good q1 q2 q3 qn is the consumption bundle n is the number of goods and services available to the consumer Marginal utility Marginal utility is defined as the increment in utility an individual enjoys from consuming an additional unit of a good or service Mathematically we define marginal utility as u q1 q2 q3 qn MUqj MUj qj If you are familiar with calculus marginal utility is u q1 q2 q3 qn MUqj qj Data on utility and marginal utility q1 1 q2 4 utility 8 00 2 4 10 08 3 4 11 54 4 4 12 70 5 4 13 68 6 4 14 54 7 4 15 31 8 4 16 00 9 4 16 65 10 4 17 24 11 4 17 80 12 4 18 32 marginal utility 2 08 1 46 1 16 Change q1 from 8 to 9 units 0 98 0 86 MU1 0 77 0 69 0 65 0 59 0 56 0 52 u q1 16 65 16 9 8 0 65 Marginal utility Marginal utility 3 0 2 5 mu1 q1 q2 3 2 0 mu1 q1 q2 4 1 5 1 0 0 5 0 0 0 2 4 6 8 10 12 q1 14 Law of diminishing marginal utility The law of diminishing marginal utility says that as the consumption of a good of service increases marginal utility decreases The idea is that the marginal utility of a good diminishes with every increase in the amount of it that a consumer has The Consumer Problem max q1 q2 q3 q n u q1 q2 q3 qn subject to p1 q1 p2 q2 p3 q3 pn qn I As the consumer chooses more of a given good utility will rise but because goods cost money the consumer will have to consume less of another good because expenditures are limited by income The Consumer Problem 2 goods max u q1 q2 q1 q2 subject to p1 q1 p2 q2 I Notation u utility Income I Quantities of goods q1 q2 qn Prices of goods p1 p2 pn Number of goods n Optimal consumption is along the budget line Given that income is allocated among a fixed number of categories and all goods have a positive marginal utility the consumer will always choose a point on the budget line Why Budget Constraint 0 3q1 0 2q2 1 20 q1 5 4 3 Not Affordable 2 1 Affordable 1 2 3 4 5 6 7 q2 Marginal decision making To make the best of a situation decision makers should consider the incremental or marginal effects of taking any action In analyzing consumption decisions the consumer considers small changes in the quantities consumed as she searches for the optimal consumption bundle Implementing the small changes approach p1 p2 q1 q2 Utility 4 3 11 00 5 3 11 85 6 3 12 59 3 4 11 54 4 4 12 70 5 4 13 68 6 4 14 54 4 5 14 20 5 5 15 30 6 5 16 26 Marginal Utility 0 74 Consider the point 5 4 with utility 13 68 1 16 Now raise q1 to 6 and reduce q2 to 3 Utility is 12 59 0 85 0 98 0 86 Now lower q1 to 4 and raise q2 to 5 Utility is 14 20 q 4 5 is preferred to q 5 4 and q 6 3 1 10 0 96 Budget lines and movements toward higher utility Given that the consumer will consume along the budget line the question is which point will lead to a higher level of utility Example p1 5 p2 10 I 50 q1 2 q2 4 5 2 10 4 50 q1 4 q2 3 5 4 10 3 50 q1 6 q2 2 5 6 10 2 50 Budget Constraint p1 5 11 q 1 10 9 8 7 6 5 4 3 2 1 0 p2 10 I 50 6 2 4 3 2 4 0 1 2 3 4 q1 6 q2 2 utility 10 280 2 4 4 3 10 080 10 998 5 6 q2 Exp I 50 Exp I 50 Exp I 50 Indifference Curves An indifference curve represents all combinations of two categories of goods that make the consumer equally well off Example data and utility level q1 8 2 83 1 54 1 0 72 q2 1 2 3 4 5 utility 8 8 8 8 8 Graphical analysis Indifference Curve 14 q1 12 10 8 u 8 6 4 2 0 0 1 2 3 4 5 6 q2 7 Example data with utility level equal to 10 q1 15 625 8 q2 1 1 utility 10 00 8 00 Example data with utility level equal to 10 q1 15 625 5 524 3 007 1 953 1 398 1 063 0 844 q2 1 2 3 4 5 6 7 utility 10 00 10 00 10 00 10 00 10 00 10 00 10 00 Graphical analysis with u 10 Indifference Curves 18 q1 16 14 12 10 8 6 4 2 0 u 10 0 1 2 3 4 5 6 q2 7 Graphical analysis with several levels of u Indifference Curves 20 q1 18 16 14 12 10 8 6 4 2 0 u 8 u 10 u 12 u 15 0 1 2 3 4 5 6 q2 Slope of indifference curves Indifference curves normally have a negative slope If we give up some of one good we have to get more of the other good to remain as well off The slope of an indifference curve is called the marginal rate of substitution MRS between good 1 and good 2 Indifference Curves 20 q1 18 16 14 12 10 8 6 4 2 0 u 12 0 1 2 3 4 5 6 q2 Slope of indifference curves MRS The MRS tells us the decrease in the quantity of good 1 q1 that is needed to accompany a one unit increase in the quantity of good two q2 in order to keep the consumer indifferent to the change Indifference Curves 20 q1 18 16 14 12 10 8 6 4 2 0 u 12 0 1 2 3 4 5 6 q2 Shape of Indifference Curves Indifference curves are convex to the origin This means that as we consume more and more of a good its marginal value in terms of the other good becomes less The Marginal Rate of Substitution MRS 40 q1 35 30 25 20 15 10 5 0 u 12 0 1 2 3 4 5 q2 6 The MRS tells us the decrease in the quantity of good 1 q1 that is needed to accompany a one unit increase in the quantity of good two …
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