Consumer Theory and X1

Hal R. Varian. Intermediate Microeconomics, A Modern Approach. W. W. Norton & Comp whatever, Inc. 1 figure CONSTRAINT Consumer theory - how consumers buy their redeeming(prenominal)s? Economists assume consumers choose the best plenty up of untroubleds they can afford. 2 aspects -Consumers choose the most preferred computables. -They atomic number 18 restrain by economic condition. The cipher Constraint Consumption bundles ( , ) a c every last(predicate) of numbers of ripe(p)s and services. X = (x1, x2, , xn,) In the case of two peachys high-priced 1 and good 2. Bundle of goods X = (x1, x2) Prices of goods (p1, p2),The amount of money the consumer has to spend m. The consumers affordable consumption bundles, (x1, x2) satisfy p1x1 + p2x2 ? m. -The calculate set of the consumer ( ) . good 2 m/p2 O m/p1 good 1 Two Goods ar Often Enough Composite good -take x2 as everything else, the dollars spent on other(a)(a) goods. For example, x1 consumption of milk in quarts pe r month. The figure constraint depart take the form p1x1 + x2 ? m. The case of n goods Budget constraint p1x1 + p2x2++ pnxn ? m. Properties of the Budget Set Budget line( ) p1x1 + p2x2 = m. Vertical intercept m/p2Horizontal intercept m/p1. Slope p1/p2 Economic interpretation of slope For the bundle (x1, x2) p1x1 + p2x2 = m. After a change in bundle (? x1, ? x2) p1(x1+? x1) + p2(x2+? x2) = m. good 2 x2 ?x2 ?x1 O x1 good 1 Subtracting the first equation from the second gives p1? x1 + p2? x2 = 0. This gives The number of good 2 the consumer moldiness give up when he increases his consumption of good 1 by 1 unit, and keeps the money spent unchanged. Opportunity cost of devour good 1- in order to consume more of good 1 you have to give up some consumption of good 2.Budget Line win overs How the budget line changes when prices and incomes change? Change in income Change in m results in a parallel shift of the budget line. Intercepts m/p2 and m/p1 ordain change. Slope p1/p2 keeps un changed. good 2 m/p2 O m/p1 good 1 Changes in prices Increasing p1 will not change the vertical intercept, but p1/p2 will become larger. good 2 m/p2 O m/p1 good 1 What happens to the budget line when we change the prices of good 1 and good 2 at the same time? proportionally (tp1)x1 + (tp2)x2 = m.What happens to the budget line when we change the prices of good 1 and good 2 and the consumers income at the same time? good 2 m/p2 O m/p1 good 1 Proportionally (tp1)x1 + (tp2)x2 = tm. Some observations If one price declines and all others stay the same, the consumer must be at least as well-off. If the consumers income increases and all prices remain the same, the consumer must be at least as well-off as at the lower income A perfectly balanced inflation cannot change anybodys optimal choice. 2 PREFERENCES Consumer Preferences( Consumer ranks consumption bundles by his satisfaction from use of goods, contrasted to the prices. The case of two goods Given any two consumption bundles, X=( x1, x2) and Y=(y1, y2), the consumer can rank them in one of three doable ways (x1, x2) is strictly better than (y1, y2) (y1, y2) is strictly better than (x1, x2) (x1, x2) and (y1, y2) are orthogonal. Two basic relations pic strictly preferred( ), (x1, x2) pic (y1, y2) the consumer strictly prefers (x1, x2) to (y1, y2). thoughtless ( ) (x1, x2) (y1, y2). he consumer is indifferent between (x1, x2) and (y1, y2). A composite relation pic weakly preferred ( ) (x1, x2) pic(y1, y2) the consumer prefers (x1, x2) to (y1, y2) or is indifferent between (x1, x2) and (y1, y2). Assumptions about Preferences Axioms about consumer preference (weakly preference) Complete( ). Given any X-bundle and any Y-bundle, consumer can say that (x1, x2)pic(y1, y2), or (y1, y2)pic(x1, x2). Reflexive( ). Consumer should say that any bundle is at least as good as itself (x1, x2)pic(x1, x2). Transitive ( ).If a consumer feels that (x1, x2)pic(y1, y2) and (y1, y2)pic(z1, z2) accordingly he feels that (x1, x2)pic(z1, z2). Indifference Curves Weakly preferred set all of the consumption bundles that are weakly preferred to (x1, x2). Indifference curves( ) -The boundary of weakly preferred set Good 2 x2 O x1 Good 1 Further assumptions Well-behaved preferences( ) Monotonicity ( )- more is better. If that x1 ( y1, x2 ( y2 and that x1 ( y1 , x2 ( y2 at least one hold, then (x1, x2) pic (y1, y2) -indifference curves have negative slope.A indifference curve is the set of bundles for which the consumer is just indifferent to (x1, x2). Good 2 O Good 1 Convexity ( )- averages are preferred to extremes. If (x1, x2) and (y1, y2) are indifferent, then the bundle (picx1+picy1, picx2+picy2) is strictly preferred to (x1, x2) and (y1, y2). -indifference curves are convex. Good 2 O Good 1 Examples of preferences entire Substitutes( ) The consumer is free to substitute one good for the other at a unremitting localise. Good 2 O Good 1Perfect Complements( ) Goods that are always consumed unneurotic i n fixed proportions. Good 2 O Good 1 Discrete Goods( ) x1 a discrete good that is only available in integer amounts. Suppose that x2 is money to be spent on other goods. Good 2 O Good 1 The Marginal rove of Substitution Marginal pose of substitution (MRS, ) slope of an indifference curve. - measures the rate at which the consumer is just willing to substitute one good for the other. MRS = pic nock MRS is a negative number. Good 2 (x2O (x1 Good 1 The other form of MRS MRS =pic Good 2 x2 O x1 Good 1 fashion of the Marginal Rate of Substitution Describe the indifference curves by the MRS. Perfect substitutes the marginal rate of substitution is constant. Perfect complements the MRS is either 0 or infinity, and nothing in between. In general case Monotonicity indifference curves must have a negative slope, i. e. negative MRS. Convex the marginal rate of substitution decreases as we increase x1, -diminishing MRS. pic