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Consumer Theory Consumer Theory The study about scarcity o Microeconomics is the study of choices & behaviour of individual decision- making units o How we can allocate the world limited resources o How can we allocate the world’s limited resources most efficiently? o How do we allocate our limited resources?.. Our limited time (hours in the week); . Our limited budgets; . Our limited supply of oil, gas, iron, etc. Consumer choice: budget constraint: o Budget constraint identifies what he can afford to buy . There are two goods X฀ and Y฀; . Good X฀ can be purchased at price PX and Y at price PY; . The consumer has an income of M. A consumption bundle (x,y) ฀ tells us that the consumer gets฀x units of good X฀ and y฀ units of good Y ฀. Bundle (x,y) is feasible if, and only if Px+Py≤M . ฀M or m฀ stands for income; . x฀ stands for the amount of good X฀; . y stands for the amount of good Y (and similarly for other goods); . PX or px stands for the price of good X฀and PY or py stands for the price of good Y (and similarly for other goods and prices). o We will call budget line or budget constraint the set of consumption bundles that cost exactly available income. o If we assume that the consumer will spend all of his income, and rearrange, we get the budget constraint: . y=(M/Py)-(Px/Py)x o “Relative” prices are illustrated by the slope of the budget line. Factors that affect the budget constraint position: The slope and position of the budget constraint are a function of two factors: income and relative prices: o Changes in income shift the budget constraint by changing the intercept; o Changes in the price of one good pivots the budget line by changing the slope. Comparative statistics overview: o If M, PX or PY change then we get a new budget constraint: . Changing M changes the intercept but not the slope. Changing PX or PY changes the slope. Why only two goods: o It makes our life easy without sacrificing too much. This is because we can think of one of the goods as a numeraire. o A numeraire or composite good is a good that stands for ‘everything else’. The obvious candidate is money. o If good Y is the numeraire then we set PY = 1 and the budget constraint shows how much of good X the consumer can afford as a function of M, y and Px. Taxes: o Value tax (also known as ad valorem tax): tax on the value (price) of purchased good or service . if the price of the good is ฀, then cost for the consumer will be: (1+t)p฀ or฀p+tp฀฀ where t is the value tax o Quantity tax: per purchased unit . IF the price of the good is p then the cost for the consumer will be P+t o Where t is the quantity tax Subsidies o Value subsidy: government gives back a share (%) of purchasd good or service: . (1- )P where is the value subsidy and p is the original price of the good 휎 휎 1 o Quantity subsidy: per purchased unit . p-s where s is the quantity subsidy Taxes subsidies and rationing: Lump-sum tax: government takes away a fixed amount, regardless of the consumer’s behaviour: o The budget line will shift inward, because the income was reduced. Rationing: maximum level of consumption is fixed. o Example: good x฀ is rationed so that no more than ฀ҧ can be consumed by one consumer. Combinations of taxes, subsidies and rationing: Good x can be consumed at price p below quantity x (with dash on top) and then a tax t can be introduced so that the cost for the consumer becomes (p+t) for any additional unit To sum up: o Microeconomics is about using simple models to get some understanding of ‘real world’ phenomena. Simplicity is gained through assumptions. o We were building a consumer choice model. Economic theory of the consumer is based on the idea that a consumer chooses: ‘the best bundle of goods that he/she can afford’. o A consumer’s budget constraint identifies what he can afford to buy: + = 푝 푥 푝 푦 푚 o Slope of the budget line:푥 rate푦 of substitution of one good for the other or the opportunity cost: ∆ / =-Px/Py . ∆ 푦 o If m, px or py change푥 then we get a new budget constraint: changing ฀m changes the intercept but not the slope; changing px or py changes the slope. o Taxes and subsidies affect prices; taxes, subsidies and rationing change budget line and budget set. Consumer choice: Preference: o Three typical assumptions are made on preference to give consistent preferences: . Completeness: Any two bundles can be compared, i.e. either A B, B A, or both. Interpretation: The consumer is able to express an opinion on each and every pair of consumption bundles ≽ ≽ . Reflexivity: Any bundle is at least as good as itself, i.e. A A. Transitivity: If bundle A is as good as B and bundle B as good as C then A should be . as good as C, i.e. if A B and B C then A C. ≽ o these assumptions or preferences properties are related to the key assumption: the representative consumer makes≽ rational ≽choices ≽ o Why require consistency? . If preferences are not consistent it is difficult for us to say anything useful about a consumer. It will be also much more difficult to build a model. o Additional assumption is often (but not always) made: nonsatiation (more is always better). Indifference curve o Plots a set of bundles between which the consumer is indifferent . Indifference curve are a way to describe preferences o Two goods are perfect substitutes if the consumer is willing to substitute one good for the other at a constant rate. The simplest example is one to one rate of substitution. In this case indifference curves have a constant slope. o Perfect complements are goods that are consumed together in a fixed proportion: 2 . In this case indifference curves are L-shaped. o A « bad » good is a good that the consumer doesn’t like, . In other words this type of goods gives our consumer some negative utility or disutility; . Observe carefully the direction of utility increase on the graph. o A « neutral » is a good that the consumer doesn’t care about, . The additional consumed unit gives zero utility; . Indifference curves are vertical lines. o There is an overall best bundle for the consumer, that we can illustrate by a satiation or a bliss point. The further away from this point the consumer is the worse off he is o Discrete goods . Sometimes it makes more sense to consider consumer’s demand in terms of discrete units. Indifference curves: behaviour o Monotonicity- indifference curves have a negative slope: . Nonsatition (more is better than less) o Convexity . Averages are preferred to extremes (diversity is preferred . Foe any t between 0 and 1 we have: ( 1 + (1− ) 1, 2 + (1− ) 2 ≥( 1, 2) o Continuity: .푡푥 A small푡 change푦 푡푥 in consumption푡 푦 푥 bundle푥 results in a small change in utility Are indifference curve well behaved in reality: o The assumption of well behaved indifference curves is much stronger than that of consistency. For example: if goods only come in whole units there cannot be continuity o Later we will examine examples where indifference curve are not well behaved Marginal rate of substitution (MRS): o The MRS of a good y for good x is the rate wat which the consumer is willing to trade or exchange good y for good x . IF you take away one unit of good x you need to give the consumer MRS units of good y to leave her indifferent . MRS is typically a negative number o The MRS measures the slope of the indifference curve . Change of y/ change of x o MRS is the marginal willingness to pay: . As we can suppose that good 2 represents all other goods o Example: . For perfect substitutes MRS is constant, for neutrals MRS is infinite, for perfect complements MRS is zero or infinity . For strictly convex indifferent curves, MRS is diminishing (in absolute value) The more you have of one good, the more willing you are to give up some of it in order to have the other one o Summary of MRS: . MRS is typically negative . Is about marginal amount of a good . Is about willingness to pay o Summary: . A consumers budget constraint identifies what he can afford to buy + = 푝 푥 푝 푦 푚 and the slope푥 of the푦 budget line is the rate of substitution of one good for the other ∆ / =-Px/Py . ∆ 푦 . If m, px, or py change푥 then we get a new budget constraint: changing m changes interception but not the slope; changing px or py changes the slope 3 . Preferences show which bundle is the best. Indifference curves were drawn and assumptions about their behaviour were made Utility function: o Is used to describe preferences: . Assigns a number to each possible consumption bundle so that a more-preferred bundle is assigned a higher number . Note: order matters, but not the number itself o We made several assumptions about consumer preferences: . Preferences are complete and can always be ranked . More is preferred to less . Ranking is consistent (transivity), etc . They will be used for utility function characteristics o Utility: ordinal vs cardinal: . Note that we consider ordinal utility functions and so all that matters is whether U(A) is bigger or smaller than U(B) This means the difference U(A)-U(B) is meaningless and we cannot make interpersonal comparisons .
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