Consumer Theory and X1

Hal R. Varian. Intermediate Microeconomics, A Modern Approach. W. W. Norton & Company, Inc. 1 BUDGET CONSTRAINT Consumer theory - how consumers buy their goods? Economists assume consumers pick out the best bundle of goods they send away afford. Two aspects -Consumers choose the most favorite(a) goods. -They are limited by economic condition. The Budget Constraint Consumption bundles ( , ) a list of numbers of goods and services. X = (x1, x2, , xn,) In the case of two goods good 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 purpose bundles, (x1, x2) satisfy p1x1 + p2x2 ? m. -The cypher range of the consumer ( ) . good 2 m/p2 O m/p1 good 1 Two Goods Are oft Enough Composite good -take x2 as everything else, the dollars spent on other goods. For example, x1 consumption of milk in quarts per month. The budget constraint will take the take a leak p1x1 + x2 ? m. The case of n goods B udget 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 commentary of slope For the bundle (x1, x2) p1x1 + p2x2 = m. After a wobble 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 instant gives p1? x1 + p2? x2 = 0. This gives The number of good 2 the consumer must give up when he increases his consumption of good 1 by 1 unit, and keeps the money spent unchanged. chance cost of consuming good 1- in order to consume more of good 1 you have to give up some consumption of good 2.Budget Line Changes How the budget line changes when prices and incomes change? Change in income Change in m results in a par solelyel shift of the budget line. Intercepts m/p2 and m/p1 will change. Slope p1/p2 keeps unchanged. good 2 m/p2 O m/p1 good 1 Changes in prices Increasing p1 will not change the vertical int ercept, 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 wanton. 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 part of goods, irrelevant 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 executable ways (x1, x2) is stric tly better than (y1, y2) (y1, y2) is strictly better than (x1, x2) (x1, x2) and (y1, y2) are indifferent. Two basic relations pic strictly preferred( ), (x1, x2) pic (y1, y2) the consumer strictly prefers (x1, x2) to (y1, y2). indifferent ( ) (x1, x2) (y1, y2). he consumer is indifferent surrounded by (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) then he feels that (x1, x2)pic(z1, z2). flatness 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 Perfect Substitutes( ) The consumer is willing to substitute one good for the other at a constant quantity rate. Good 2 O Good 1Perfect Complements( ) Goods that are always consumed together in fixed proportions. Good 2 O Good 1 distinct Goods( ) x1 a discrete good that is only available in int eger amounts. Suppose that x2 is money to be spent on other goods. Good 2 O Good 1 The Marginal Rate of Substitution Marginal rate 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 Note 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 Behavior 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 each 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