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# 经济代写|微观经济学代考Microeconomics代写|ECON2516 Indifference Curves

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## 经济代写|微观经济学代考Microeconomics代写|Indifference Curves

If we only have two goods, we can illustrate different baskets that the individual if indifferent between with indifference curves. All points on an indifference curve are baskets that the individual perceives are equally good. She is, in other words, indifferent between them. An example of a typical indifference curve is shown in Figure 3.3.

After having made the four assumptions above, we can say a lot about what an indifference curve must look like. All points in the diagram (i.e. all possible combinations of good 1 and 2) correspond to a basket. Since the preferences are complete, there must be some preference curve that runs through any point in the diagram. Another way to say the same thing: Pick any point in the diagram; whichever point you picked, there is an indifference curve running through that point.
We now randomly select a point in the diagram, say point A. Since the individual is non-satiable, all points where she gets more of either good 1, or good 2, or of both are better for her. This corresponds to the grey area northeast of point A. Similarly, all points where she gets less, the grey area southwest to $\mathrm{A}$, must be worse for her. Consequently, she cannot be indifferent between basket $\mathrm{A}$ and any point in the grey areas. Therefore, a preference curve that runs through A cannot also run through any point in the two grey areas. This means that an indifference curve will slope downwards. (See, however, the case of complementary goods in Section 3.6)

The assumption of convexity implies that the slope will become smaller and smaller as we move to the right. Convexity means that, if we randomly choose any other point on the indifference curve that runs through $\mathrm{A}$, say point $\mathrm{B}$, and then choose a point in between them, say point $\mathrm{C}$, then point $\mathrm{C}$ must be better than (or at least as good as) A and B. C must therefore lie on a higher indifference curve than the one that runs through $\mathrm{A}$ and $\mathrm{B}$. If this is true for any choices of A, B, and C, then the curve must slope less and less the farther to the right we get.

## 经济代写|微观经济学代考Microeconomics代写|Indifference Maps

Since the preferences are complete, some indifference curve must run through each point, i.e. each basket. If we randomly choose four baskets, A, B, C, and $\mathrm{D}$, there will be some indifference curve that runs through each point (see Figure 3.4).

If we move to the northeast in the diagram, the level of utility increases. Labeling the indifference curves $\mathrm{I}_1, \mathrm{I}_2, \mathrm{I}_3$, and $\mathrm{I}_4$, they must therefore represent higher and higher levels of utility. A collection of several indifference curves in one figure is called an indifference map. It is common to compare indifference maps to elevation contours on a regular map: It is like walking up or down a hill when one moves from one indifference curve to another.

After we have drawn the indifference curves, we can also compare points that do not lie to the northeast or southwest of each other. In the figure, point $B$ is not to the northeast of point $\mathrm{A}$, but it does lie on an indifference curve that is “higher” than the one that runs through A. Consequently, point B represents a basket that is better than the one represented by point A. We can also see this in the following way: Note that there are points on $\mathrm{I}_2$ that lie to the northeast of point A (between the two dotted lines that originate at A). Those points must therefore be better than A. Moreover, all points on $\mathrm{I}_2$ are equally good for the individual (since she, by definition, is indifferent between all of them). Consequently, point B represents a level of utility that is exactly the same as the points on $\mathrm{I}_2$ that are to the northeast of $\mathrm{A}$. Therefore, $\mathrm{B}$ must be better than A is. Note that if we argue that way, we have used the assumption of transitivity.

# 微观经济学代写

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