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gives the optimal amounts of each of the goods as a function of the prices and income faced by the consumer. |
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x1=x1(p1,p2,m)
x2=x2(p1,p2,m)
left side: quantity demanded
right side: the function that relates the prices and income to that quantity. |
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How to write the demand function
whats left side stand for?
right side? |
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studying how a choice responds to changes in the economic enviornment |
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shifts it outward in a parallel fashion |
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how an increase in money income affects the budget line when prices are fixed |
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demand for these goods increases when income increases, and decreases when income decreases.
Quantity demanded always changes in the same way as income changes |
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normal goods equation
(showing that quantity demanded always changes in the same way as income changes) |
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this is a good where an increase of income results in a reduction in the consumption of one of the goods. |
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whether a good is inferior or not depends on the _ that we are examining |
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connects demanded bundles as we shift the budget line outward
-illustrates the bundles of goods that are demanded at the different levels of income |
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if both goods are normal goods, then the income expansion path (income offer curve) will _ |
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if we hold the prices of goods 1 and 2 fixed and look at how demand changes as we change income, this curve is generated.
(a graph of the demand for one of the goods as a function of income, with all prices being held constant) |
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increase consumption of good 1 |
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if p1 < p2, so that the consumer is specializing in consuming good 1, then if his income icnreases he will _ |
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if u(x1,x2) =( x^a/1)(x^1/2-a), the Cobb-Douglas demand for good 1 has the form _ |
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For a fixed value of p1, this is a linear funciton of m. Thus doubling m will _ |
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Straight lines through the origin |
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The fact that the demand functions for both goods are linear functions of income means that the income expansion paths will be_ |
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if the demand for a good goes up by a greater proportion than income, it is called a _ |
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if demand for the good goes up by a lesser proportion than income we say it is a _ |
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perfect substitutes, complements, and Cobb-Douglas are all this |
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when income is scaled up or down by any amount t > 0, the demanded bundle scales up or down by the same amount. |
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t times as much income and the same prices |
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If the indifference curve is tangent to the budget line at (x*1,x*2), then the indifference curve through (tx*1,tx*2) is tangent to the budget line that has _ |
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the case where all indifference curves are "shifted" versions of one indifference curve. |
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if preferences are quasilinear, we sometimes say that there is a _ for good 1. |
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the quantity demanded of good 1 should increase when its price decreases |
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suppose that we decrease the price of good 1 and hold the price of good 2 and money income fixed. Then what can happen to the quantity demanded of good 1? |
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budget line becomes flatter
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when the price of good 1 decreases, the budget line _ |
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well-behaved preferences for which a decrease in the price of a good 1 leads to a reduction in the demand for good 1. |
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Even though money income remains constant, a change in the price of a good will change _, and thereby change demand |
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this curve represents the bundles that would be demanded at different prices for good 1. |
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a plod of the demand function, x1 (p1,p2,m), holding p2 and m fixed at some predetermined values |
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ordinarily, when the price of a good increases, the demand for that good will decrease. Thus the price and quantity of a good will move in _ direction, which means the demand curve will typically have a _ slope. |
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if P1 is very high then the consumer will strictly prefer to consume _ units; if p1 is low enough the consumer will strictly prefer to consume _ unit. |
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the price at which the consumer is just indifferent to consuming or not consuming the good |
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measures the increment in utility necessary to induce the consumer to choose an additional unit of the good. |
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if the demand for good 1 goes up when the price of good 2 goes up, then we say that good 1 is a _ for good 2. |
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if the demand for good 1 goes down when the price of good 2 goes up, we say that good 2 is a _ to good 2. |
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gross substitutes/ complements |
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If good 1 can be used to substitute for good 3, but good 3 may be a complement for good 1. |
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the inverse demand function |
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is the demand function viewing price as a functin of quantity.
measures teh same relationship as the direct demand function, just from another point of view. |
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measuring the marginal willingness to pay. |
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a relation that holds between the bundle that is actually demanded at some budget and the bundles that could have been demanded at that budget. |
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The principle of revealed preference
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let (x1,x2) be the chosen bundle when prices are (p1,p2), and let (y1,y2) be some other bundle such that p1x1+p2x2 is greater than or equal to p1y1 + p2y2. Then if the consumer is choosing the most preferred bundle she can afford, we must have (x1,x2) > (y1,y2) |
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(x1,x2) > (y1,y2) and that (y1, y2) > (z1,z2)
(x1,x2)> (z1,z2) |
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Suppose that we happen to know that (y1,y2) is a demanded bundle at prices (q1,q2) and that (y1,y2) is itself revealed preferred to some other bundle (z1,z2) that is: q1ys+q2y2 is greater than or equal to q1z1+q2z2. Then we know:
From the transitivity assumption we can conclude that: |
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Indirectly revealed preferred |
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if bundle A is directly revealed preferred to B, and B to C, C to D... all the way to M, then bundle A is still _ to M. |
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if a bundle is either directly or indirectly revealed preferred to another bundle, we will say that teh first budnel is _ to the second. |
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Weak Axiom of Revealed Preferences
WARP |
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If (x1,x2) is directly revealed preferred to (y1,y2), and the two bundles are not the same, then it cannot happen that (y1,y2) is directly revealed preferred to (x1,x2).
(if the y-bundle is affordable when the x-bundle is purchased, then when the y-bundle is purchased, the x-bundle must not be affordable. |
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This consumer's behavior could not have been maximizing behavior |
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WARP requires that if X is _ revealed preferred to Y, then we should never observe Y being _ revealed preferred to X. |
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Strong Axiom Revealed Preference
SARP
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If (x1,x2) is revealed preferred to (y1,y2), either directly or indirectly, and (y1,y2) is different from (x1,x2), then (y1,y2) cannot be directly or indirectly revealed preferred to (x1,x2). |
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Since the underlying preferences of the consumer must be transitive, it follows that the revealed preferences of the consumer must be _ |
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if a consumer is always choosing the best things that he can afford, then his observed behavior must satisfy _ |
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the change in demand due to the change in the rate of exchange betweent the two goods |
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the change in demand due to having more purchasing power |
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this _ operation gives us a convenient way to decompose the change in demand into two pieces. |
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is a movement where teh slope of the budget line changes while its purchasing power stays constant |
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a movement where the slope stays constant and the purchasing power changes. |
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the idea is that teh consumer is being compensated for a prices rise by having enough income given back to him to purchase his old bundle |
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if the demand for a good increases when income increases, then the demand for that good must decrease when its price increases |
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slutsky substitution effect |
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Change in deamnd when prices change but a consumer's purchasing power is held constant, so that the original bundle remains affordable. |
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comparative statistics analysis of ordinary demand functions |
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the study of how ordinary demands x1*(p1,p2,m) and x2*(p1,p2,m) change as prices p1,p2 and income (m) change |
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the p1- price offer curve |
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the curve containing all the utility maximizing bundles traced out as p1 changes, with p2 and m constant is _ |
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ordinary demand curve for commodity 1 |
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the plot of the x1-coordiante of the p1-price offer curve against p1 is the _ |
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given p1', what quantity is demanded of commodity 1? |
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inverse demand function of a commodity |
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taking quantity demanded as given and then asking what must be the price describes the _ |
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a plot of quantity demanded against income |
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Engel curves are straight lines if the consumer's preferences are _ |
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A normal good's Engel curve is _ sloped |
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An income inferior good's Engel Curve is _ sloped |
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a good is always called _ if the quantity demanded of it always increases as its own price decreases |
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if, for some values of its own price, the quantity demanded of a good rises as its own price increaeses then it is called _ |
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If an increase in p2 increases demand for commodity 1 then commodity 1 is a _ for commodity 2. |
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if an increase in p2 reduces demand for commodity 1 then commodity 1 is a _ for commodity 2 |
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assumptions about preferences |
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-do not change while the choice data are gathered
-are strictly convex
-are monotonic |
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x* is revealed directly as preferred to y |
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Suppose that bundle x* is chosen when the bundle y is affordable. Then x* is _ otherwise y wouldve been chosen |
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x is revealed indirectly as preferred to z. |
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Suppose x is revealed directly preferred to y, and y is revealed directly preferred to z. Then, by transitivety, _ |
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To apply revealed preference analysis, choices must satisfy two criteria - |
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never the case that y is revealed directly as preferred to x |
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if the bundle x is revealed directly as preferred to the bundle y then it is _ |
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then it is never the case that y is revealed (directly or indirectly) as preferred to x |
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if the bundle x is revealed (directly or indirectly) as preferred to the bundle y and x doesn't equal y, then _ |
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a price-weighted average of quantities demanded |
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a quantity-weighted average of prices |
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changes in price indices are sometimes used to adjust wage rates or transfer payments. this is called _ |
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occurs when the wages or payments are increased at the same rate as the price index being used to measure the aggregate inflation rate. |
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happens when the commodity is relatively cheaper so the consumer goes for relatively more expensive other commodities |
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happens when the consumer's budget of $m can purcahse more than before |
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changes to quantities demanded due to this 'extra' income are the income effect of the _ |
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pure substitution effect and an income effect |
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slutsky discovered that changes to demand from a price change are always the sum of a _ |
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if, at the new prices, less income is needed to buy the original bundle then "real income" is _ |
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if, at the new prices, more income is needed to buy the original bundle then "real income " is _ |
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