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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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Definition
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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Definition
| 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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Definition
| 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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Definition
| 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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Definition
| 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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Definition
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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Definition
| 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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Definition
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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Definition
| 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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Definition
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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Definition
| 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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Definition
| 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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Definition
| 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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Definition
| 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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Definition
| 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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Definition
| 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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Definition
| 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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Definition
| 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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Definition
| the plot of the x1-coordiante of the p1-price offer curve against p1 is the _ |
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Definition
| given p1', what quantity is demanded of commodity 1? |
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| inverse demand function of a commodity |
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Definition
| 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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Definition
| 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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Definition
| 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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Definition
-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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Definition
| 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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Definition
| 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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Definition
| 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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Definition
| 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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Definition
| 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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Definition
| if, at the new prices, more income is needed to buy the original bundle then "real income " is _ |
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