Finance:Complementary good
In economics, a complementary good is a good whose appeal increases with the popularity of its complement.[further explanation needed] Technically, it displays a negative cross elasticity of demand and that demand for it increases when the price of another good decreases.[1] If [math]\displaystyle{ A }[/math] is a complement to [math]\displaystyle{ B }[/math], an increase in the price of [math]\displaystyle{ A }[/math] will result in a negative movement along the demand curve of [math]\displaystyle{ A }[/math] and cause the demand curve for [math]\displaystyle{ B }[/math] to shift inward; less of each good will be demanded. Conversely, a decrease in the price of [math]\displaystyle{ A }[/math] will result in a positive movement along the demand curve of [math]\displaystyle{ A }[/math] and cause the demand curve of [math]\displaystyle{ B }[/math] to shift outward; more of each good will be demanded. This is in contrast to a substitute good, whose demand decreases when its substitute's price decreases.[2]
When two goods are complements, they experience joint demand - the demand of one good is linked to the demand for another good. Therefore, if a higher quantity is demanded of one good, a higher quantity will also be demanded of the other, and vice versa. For example, the demand for razor blades may depend on the number of razors in use; this is why razors have sometimes been sold as loss leaders, to increase demand for the associated blades.[3] Another example is that sometimes a toothbrush is packaged free with toothpaste. The toothbrush is a complement to the toothpaste; the cost of producing a toothbrush may be higher than toothpaste, but its sales depends on the demand of toothpaste.
All non-complementary goods can be considered substitutes.[4] If [math]\displaystyle{ x }[/math] and [math]\displaystyle{ y }[/math] are rough complements in an everyday sense, then consumers are willing to pay more for each marginal unit of good [math]\displaystyle{ x }[/math] as they accumulate more [math]\displaystyle{ y }[/math]. The opposite is true for substitutes: the consumer is willing to pay less for each marginal unit of good "[math]\displaystyle{ z }[/math]" as it accumulates more of good "[math]\displaystyle{ y }[/math]".
Complementarity may be driven by psychological processes in which the consumption of one good (e.g., cola) stimulates demand for its complements (e.g., a cheeseburger). Consumption of a food or beverage activates a goal to consume its complements: foods that consumers believe would taste better together. Drinking cola increases consumers' willingness to pay for a cheeseburger. This effect appears to be contingent on consumer perceptions of these relationships rather than their sensory properties.[5]
Examples
An example of this would be the demand for cars and petrol. The supply and demand for cars is represented by the figure, with the initial demand [math]\displaystyle{ D_1 }[/math]. Suppose that the initial price of cars is represented by [math]\displaystyle{ P_1 }[/math] with a quantity demanded of [math]\displaystyle{ Q_1 }[/math]. If the price of petrol were to decrease by some amount, this would result in a higher quantity of cars demanded. This higher quantity demanded would cause the demand curve to shift rightward to a new position [math]\displaystyle{ D_2 }[/math]. Assuming a constant supply curve [math]\displaystyle{ S }[/math] of cars, the new increased quantity demanded will be at [math]\displaystyle{ Q_2 }[/math] with a new increased price [math]\displaystyle{ P_2 }[/math]. Other examples include automobiles and fuel, mobile phones and cellular service, printer and cartridge, among others.
Perfect complement
A perfect complement is a good that must be consumed with another good. The indifference curve of a perfect complement exhibits a right angle, as illustrated by the figure.[6] Such preferences can be represented by a Leontief utility function.
Few goods behave as perfect complements.[6] One example is a left shoe and a right; shoes are naturally sold in pairs, and the ratio between sales of left and right shoes will never shift noticeably from 1:1.
The degree of complementarity, however, does not have to be mutual; it can be measured by the cross price elasticity of demand. In the case of video games, a specific video game (the complement good) has to be consumed with a video game console (the base good). It does not work the other way: a video game console does not have to be consumed with that game.
Example
In marketing, complementary goods give additional market power to the producer. It allows vendor lock-in by increasing switching costs. A few types of pricing strategy exist for a complementary good and its base good:
- Pricing the base good at a relatively low price - this approach allows easy entry by consumers (e.g. low-price consumer printer vs. high-price cartridge)
- Pricing the base good at a relatively high price to the complementary good - this approach creates a barrier to entry and exit (e.g., a costly car vs inexpensive gas)
Gross complements
Sometimes the complement-relationship between two goods is not intuitive and must be verified by inspecting the cross-elasticity of demand using market data.
Mosak's definition states "a good of [math]\displaystyle{ x }[/math] is a gross complement of [math]\displaystyle{ y }[/math] if [math]\displaystyle{ \frac{\partial f_x (p, \omega)}{\partial p_y} }[/math] is negative, where [math]\displaystyle{ f_i (p, \omega) }[/math] for [math]\displaystyle{ i = 1, 2 , \ldots , n }[/math] denotes the ordinary individual demand for a certain good." In fact, in Mosak's case, [math]\displaystyle{ x }[/math] is not a gross complement of [math]\displaystyle{ y }[/math] but [math]\displaystyle{ y }[/math] is a gross complement of [math]\displaystyle{ x }[/math]. The elasticity does not need to be symmetrical. Thus, [math]\displaystyle{ y }[/math] is a gross complement of [math]\displaystyle{ x }[/math] while [math]\displaystyle{ x }[/math] can simultaneously be a gross substitutes for [math]\displaystyle{ y }[/math].[7]
Proof
The standard Hicks decomposition of the effect on the ordinary demand for a good [math]\displaystyle{ x }[/math] of a simple price change in a good [math]\displaystyle{ y }[/math], utility level [math]\displaystyle{ \tau^* }[/math] and chosen bundle [math]\displaystyle{ z^* = (x^*, y^*, \dots) }[/math] is
[math]\displaystyle{ \frac{\partial f_x(p, \omega)}{\partial p_y} = \frac{\partial h_x (p, \tau^*)}{\partial p_y} - y^* \frac{\partial f_x(p, \omega)}{\partial \omega} }[/math]
If [math]\displaystyle{ x }[/math] is a gross substitute for [math]\displaystyle{ y }[/math], the left-hand side of the equation and the first term of right-hand side are positive. By the symmetry of Mosak's perspective, evaluating the equation with respect to [math]\displaystyle{ x^* }[/math], the first term of right-hand side stays the same while some extreme cases exist where [math]\displaystyle{ x^* }[/math] is large enough to make the whole right-hand-side negative. In this case, [math]\displaystyle{ y }[/math] is a gross complement of [math]\displaystyle{ x }[/math]. Overall, [math]\displaystyle{ x }[/math] and [math]\displaystyle{ y }[/math] are not symmetrical.
Effect of price change of complementary goods
References
- ↑ Carbaugh, Robert (2006). Contemporary Economics: An Applications Approach. Cengage Learning. p. 35. ISBN 978-0-324-31461-8. https://archive.org/details/contemporaryecon00robe/page/35.
- ↑ O'Sullivan, Arthur; Sheffrin, Steven M. (2003). Economics: Principles in Action. Upper Saddle River, New Jersey: Pearson Prentice Hall. p. 88. ISBN 0-13-063085-3. https://archive.org/details/economicsprincip00osul.
- ↑ "Customer in Marketing by David Mercer". Future Observatory. http://futureobservatory.dyndns.org/9432.htm.
- ↑ Newman, Peter (2016-11-30). "Substitutes and Complements". The New Palgrave: A Dictionary of Economics: 1–7. doi:10.1057/978-1-349-95121-5_1821-1. ISBN 978-1-349-95121-5. https://link.springer.com/referenceworkentry/10.1057/978-1-349-95121-5_1821-1?page=1. Retrieved 2022-05-26.
- ↑ Huh, Young Eun; Vosgerau, Joachim; Morewedge, Carey K. (2016-03-14). "Selective Sensitization: Consuming a Food Activates a Goal to Consume its Complements". Journal of Marketing Research 53 (6): 1034–1049. doi:10.1509/jmr.12.0240. ISSN 0022-2437.
- ↑ 6.0 6.1 Mankiw, Gregory (2008). Principle of Economics. Cengage Learning. pp. 463–464. ISBN 978-0-324-58997-9.
- ↑ Mosak, Jacob L. (1944). "General equilibrium theory in international trade". Cowles Commission for Research in Economics, Monograph No. 7 (Principia Press): 33. https://dspace.gipe.ac.in/xmlui/bitstream/handle/10973/38888/GIPE-014030.pdf?sequence=3.
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