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11: bChapter Consumer preferences and consumer choice Mapping the Utility Function Indifference Curves An indifference curve is a line that shows all the consumption bundles yielding the same amount of total utility for an individual An individual is indifferent between any two points lying on an indifference curve Indifference curves graph the same amount of utils A collection of indifference curves on the same axis is known as an indfference curve map Properties of Indifference Curves No two individuals have the same indifference curve maps because no two people have the same preferences However, it is believed that every indifference curve has two general characteristics... Indifference curves never cross they can never cross because each indifference curve graphs a different number of utils thus they can never intersect the farther an indifference curve lies from the origin the higher the level of total utility it indicates- this is justified because we consider more to be better Indifference curves are downward sloping because more is considered to be better Indiffernce curves are convex shaped because of diminishing marginal utility If a good satisfies these four properties of indifference curves it is an ordirnary good Indifference Curves and Consumer Choice The marginal rate of substitution Moving down the indifference curve will produce two opposing effects on total utility When moving down the indifference curve the loss in utlity of the good on the y axis is equal to the gain in utility of the good on the x axis...if this were not true, utility would change In general the change in total utility caused by a small change in consumption of a good is equal to the change in consumption multiplied by the marginal utility of that good. This change in utlity is equal between goods on the x and y axis of the indifference curves Change in quantity of good "y" divided by change in quantity of good "X" yields the slope of the indifference curve Change in marginal utlity of good "X" divided by marginal utility of good "Y" yields yields the ratio of marginal utility of good "X" to good "Y" The marginal rate of substitution or MRS is the ratio of marginal of good "X" to good "Y" the MRS is equal to the negative slope of the indifference curve The principle of diminishing marginal rate of substitution states that an individual who consumes a little bit of one good "X" and a lot of another good "Y" would be willing to trade off a lot of "Y" for one more good of "X" Ordinary goods in a conusmer's utility function are a pair of goods that requires the consumer to replace the utility lost of one good with the utility of another and the consumer experiences a diminishing marginal rate of substitution when substituting one good for another The Tangency condition optimal The consumption bundle is the one that lies on the highest indfiffernce curve one can reach give their budget constraints The tangency condition states that at the optimal consumption bundle, the budget line just barely touches the indifference curve (is tangent to the indifference curve) Prices and the marginal rate of substitution When the slope of the indifference curve is equal to the slope of the budget line that is the optimal consumption bundle Slope of indifference curve = - Marginal utility of good on x axis / marginal utitlity of good on y axis Slope of budget line price is price of good on x/ price of good on y The slope of the budget line is Px/Py is known as the relative price of x in terms of y Therefore the optimal consumption bundle occurs when the MUx/MUy=Px/Py this equation illustrates the relative price rule In other words at the optimal consumption bundle the marginal rate of substitution of one good in place of another is equivalent to the ratio of their prices However, either the relative price rule or the optimal consumption rule (MUx/Px=MUy/Py) can be used to find the optimal consumption bundle Preferences and choices Saying that consumers have different preferences really means that they have different utility functions Using indifference curves: Substitutes and Compliments Perfect Substitutes Perfect substitutes generate straight lined indifference curves, in economic terms, perfect substitutes state that the MRS of one good is equal to the MRS of another With perfect substitutes MRS does not depend on the composition of the consumption bundle, rather it depends only on whther or not the relative price of good x is greater than the MRS And if relative price is equal to MRS than any consumption bundle is optimal Perfect Compliments Goods are perfect compliments when a consumer wants to consume goods at the same ratio This means that for example if one wants to consume cookies and milk but only together, if one has 2 cookies and one glass of milk he will only be able to consume one cookie The graph of perfect compliments is L shaped The MRS with perfect compliments is undefined since the individuals preferences will not allow any substitution between goods Price, Income, and Demand The effects of a price increase An increase of the price of the goods on the x axis will cause the slope of the budget line to increase (because if the decrease in utility) Income and Consumption when inxome increases the budget line movies out further from the origin, this shift will cause the optimal consumption bundle lie on an indifference curve farther from the origin, the opposite is true if income decreases. The opposite if the above is true if the good is an inferior good such as bus tickets Income and Substitution effects

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