How Do You Know if an Indifference Curve Is Kinked

Many quantities fail to respond smoothly to price changes. This column stresses that the 'endowment event' – a well-known behavioural economics concept – implies kinks in indifference curves at the current consumption bundle price. Such kinks may business relationship for the stickiness of prices, wages, and interest rates.

It is important to update the style we teach indifference curves. The standard version is still being taught to millions of students annually, despite the discovery more than three decades agone of a crucial inconsistency in its conceptualisation, namely that it fails to signal the reference point or the electric current level of consumption (Knetsch and Sinden 1984, Kahneman et al. 1990, Knetsch et al. 2012).

According to conventional indifference curve diagrams, when deciding between two goods – say, food and vesture – information technology is as though we've never consumed them earlier. Thus, we are assumed to come to the trouble in a pristine country, without indicating the amount of the goods in question we consumed in the prior menstruum or are adapted to. Yet, this is contradictory, because if we have not consumed these items before, how are we supposed to know how much utility nosotros should expect from them?

Hence, the customary indifference bend depends on the implicit assumption that choices along indifference curves are reversible. That is, if an individual owns 10 and is indifferent between keeping it and trading it for y, then when owning y the individual should be indifferent nigh trading it for x. If loss aversion is present, yet, this reversibility will no longer agree (Knetsch 1989, Kahneman et al. 1991). Knetsch and Sinden (1984) were the get-go to point out that the standard supposition pertaining to the equivalence of losses and gains is contradicted past the experimental evidence: "the bounty measure out of value seems to exceed significantly the willingness to pay measure, which would appear to call into some question … interpretations of indifference curves".

Indifference curves with reference-dependent utility

Thus, the mainstream representation of indifference curves is outdated, inconsistent, and misleading, considering it overlooks the ample empirical testify that current consumption (or the current endowment) matters for subsequent consumption decisions, equally it becomes a reference indicate to which other states of the world are compared (Rabin 2008). The endowment outcome implies that there is an extra discomfort associated with giving something upwardly, in addition to the loss of the pleasure associated with consuming it. Permit us suppose that the current level of consumption is (Q_x1, Q_y1) (Effigy ane). So point a becomes the origin of the coordinate organisation and the relevant reference betoken for the current menstruum 1. While recently there has been some word near how to define the reference signal in various circumstances (Heffetz and Listing 2013), in this example it is straightforward – it is simply the current level of consumption at point a.

Figure 1. Behavioural indifference curves in menses 1 showing initial endowment

We divide the plane into iv quadrants (numbered anticlockwise) with the axis going through the origin at point a. In quadrant 1 the reference point is irrelevant equally both ten and y are increasing. In this quadrant the standard convex-to-the-origin indifference bend is unchanged. Nonetheless, x decreases in quadrant 2 while y increases; in quadrant 3 both ten and y decrease; and in quadrant four 10 increases while y decreases. (All changes are relative to the axes that go through the initial reference point a in Effigy ane).

Thus, lowering consumption of x below the initial level, Q_x1, requires a larger amount of a compensating good y in order to maintain the same level of utility than the amount of y required to be given upward if there were an identical increase in x beyond Q_x1. In other words, at point a the loss in marginal utility of giving up a unit of 10 is larger (in absolute value) than the marginal utility of obtaining a unit of measurement of x – decreasing one's consumption from the current level is more painful than increasing consumption from the current level is beneficial. This is critical, because information technology implies that the indifference curves are kinked at the axis that go through signal a, with slopes steeper in quadrant 2 than in quadrant 4 – a factor overlooked in conventional treatments of indifference curves. David Just (2014: 81) works out the properties of such behavioural indifference maps with straight lines, i.e. with constant marginal rates of substitution, while Knetsch et al. (2012) demonstrate with indifference curves the discrepancy of evaluating welfare in the domains of gains and losses.

To demonstrate the impact of the endowment issue on the indifference map with declining marginal rates of exchange, let united states suppose that the standard marginal rate of substitution along an indifference map is:

and the endowment upshot of x at a point i is given by ε_xi and that of y is given by ε_yi, where ε>0 is the extra price (in terms of the other proficient) required to requite upwardly an object above the toll for which information technology would exist caused. Then the marginal charge per unit of substitution of the behavioural indifference curve in quadrant 2 relative to the reference point a is:

in quadrant iii is:

and in quadrant 4 is:

Hence, in quadrant 2 the slope of the indifference bend is steeper than the standard indifference curve, because in guild to give upwards ane unit of x one would need a greater amount of y every bit compensation on account of the pain of giving up x relative to the level to which 1 is accustomed. Similarly in quadrant four, except in this example the indifference curve is flatter than the standard indifference curve because in this case it is more than difficult to give upwardly y. In quadrant three the slope of the behavioural indifference bend relative to the standard one is cryptic, depending on the sizes of ε_xi and ε_yi; the curve is drawn in this quadrant in such a way and so that the endowment effects cancel each other and the standard indifference curve obtains.

The implication is that there is a kink in the behavioural indifference curves as they cross the axis from 1 quadrant to another. This implies that the utility part is not differentiable everywhere and that preferences are not homothetic. Moreover, upkeep lines cannot exist tangent to the indifference curve along the axis that divides the airplane into iv quadrants. For instance, budget lines 1 and 2 in Figure ii show that changes in price will not bring almost whatsoever change in the consumption bundle at bespeak a, contrary to conventional analysis. This may well explain the ofttimes-found stickiness in aligning to changes in wages, prices, and interest rates (Anderson 1998, Carlton 1986, Ausubel 1991).

Effigy 2. Behavioural indifference curves in period i with several budget constraints

Furthermore, let the states suppose that in period 1 the bodily budget line 3 is tangent to the indifference curve at b in quadrant four (b is not on an centrality in period 1). Thus, Figure 2 shows that with upkeep constraint 3 the new consumption bundle becomes (Q_x2, Q_y2) at indicate b. Once choosing to consume at point b in flow 1, all the same, the origin of the new axis of the behavioural indifference map shifts to b and, in turn, that becomes the new reference betoken in catamenia 2. This implies that the 2 sets of indifference maps cross over time, fifty-fifty if the consumer's tastes do not change over time.¹

Moreover, the new indifference map of period 2 is superimposed on the previous one of period i (Figure 3). However, the budget constraint that was tangent to the old indifference curve at b is no longer tangent to the new indifference bend at b (Figure 4). Therefore, the tangency with the new set of indifference curves will be elsewhere, implying that consumption volition change in catamenia 2 fifty-fifty if prices, income, and tastes remain unchanged. Thus, the consumption packet tin can change even if there is no primal alter in either the economic system or in the consumer's preferences. In other words, the adjustment to the new budget constraint occurs in two steps – the get-go stride uses the initial reference point in order to choose the optimal packet, and having fabricated that selection the reference point also shifts, implying that the whole indifference curve shifts. This, in plough, displaces the optimal consumption bundle once again to c, fifty-fifty if in that location are no other changes in the relevant parameters.

Figure 3. In period 2, behavioural indifference curves shift the origin from a to the new reference signal at b

Effigy 4. In menstruum ii, consumption changes to indicate c even if there is no change in tastes or the budget constraint

Terminal remarks

In sum, behavioural indifference curves are relative to a reference signal. The endowment effect implies that people are willing to requite up an object only at a college price than the price at which they are willing to buy it, i.e. information technology is psychologically more difficult to requite up an object than to larn it. This changes the shape and backdrop of the indifference map, which has far-reaching implications not just in classrooms, but as well in practical areas such as the evaluation of welfare states and the stickiness of economic variables such as wages, prices, and interest rates (Knetsch et al. 2012). This salient issue ought no longer to exist ignored, and needs a much wider research agenda than hitherto allotted to it at the margins of the subject area.

Even at this stage it is of import to comprise behavioural indifference curves into the curriculum and stop teaching outdated concepts. If you remember that behavioural indifference curves would be also complicated for beginners then I would urge you non to teach the conventional ones until the students are ready for the current version, because one should not mislead students by teaching inappropriate concepts. If the straight-talking Nobel-prize-winning physicist Richard Feynman (1918–1988) were still with usa, he would agree with this view. In his famous 1974 commencement address at the California Constitute of Technology, he beseeched the graduating class to practice scientific integrity, utter honesty, and to lean over backwards so equally not to fool themselves (and of course others) (Feynman 1985). I believe that the same is true for us – teachers of economics, it is time to start leaning over backwards and to stop teaching the standard indifference curves.

References

Andersen, T Chiliad (1998), "Persistence in sticky price models", European Economic Review, 42: 593–603.

Ausubel, L (1991), "The failure of competition in the credit card market", The American Economic Review, 81: l–81.

Carlton, D W (1986), "The rigidity of prices", The American Economic Review, 76: 637–658.

Feynman, R P (1985), "Cargo Cult Scientific discipline", in R P Feynman, R Leighton, and Due east Hutchings (eds.), Surely You're Joking, Mr. Feynman!, New York: Due west W Norton: 338–346.

Heffetz, O and J List (2014), "Is the Endowment Event an Expectations Effect?", Journal of the European Economic Clan, forthcoming.

Simply, D R (2014), Introduction to Behavioral Economics, New York: Wiley and Sons.

Kahneman, D, J Fifty Knetsch, and R H Thaler (1990), "Experimental Tests of the Endowment Upshot and the Coase Theorem", Journal of Political Economy, 98: 1325–1348.

Kahneman, D, J L Knetsch, and R H Thaler (1991), "Anomalies: The Endowment Effect, Loss Aversion, and Status Quo Bias", Journal of Economical Perspectives, 5 (ane): 193–206.

Knetsch, J 50 (1989), "The Endowment Issue and Evidence of Nonreversible Indifference Curves", The American Economic Review, 79: 1277–1284.

Knetsch, J Fifty and J A Sinden (1984), "Willingness to pay and compensation demanded: Experimental evidence of an unexpected disparity in measures of value", Quarterly Journal of Economics, 99: 507–521.

Knetsch, J L, Y E Riyanto, and J Zong (2012), "Proceeds and Loss Domains and the Choice of Welfare Measure of Positive and Negative Changes", Periodical of Benefit-Cost Analysis, 3, Article 1.

Rabin, Thousand (2008) "Kahneman, D. (born 1934)", The New Palgrave Dictionary of Economics, Second Edition, Steven N Durlauf and Lawrence E Blume (eds.), Palgrave Macmillan.

Footnote

one That indifference curves can intersect has been experimentally verified in a different setting (Kahneman et al. 1991: 197).

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Source: https://voxeu.org/article/sticky-prices-and-behavioural-indifference-curves