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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 D 1 {\displaystyle D_{1}} . Suppose that the initial price of cars is represented by P 1 {\displaystyle P_{1}} with a quantity demanded of Q 1 {\displaystyle Q_{1}} . 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 D 2 {\displaystyle D_{2}} . Assuming a constant supply curve S {\displaystyle S} of cars, the new increased quantity demanded will be at Q 2 {\displaystyle Q_{2}} with a new increased price P 2 {\displaystyle P_{2}} . 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.⁷ 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 x {\displaystyle x} is a gross complement of y {\displaystyle y} if ∂ f x ( p , ω ) ∂ p y {\displaystyle {\frac {\partial f_{x}(p,\omega )}{\partial p_{y}}}} is negative, where f i ( p , ω ) {\displaystyle f_{i}(p,\omega )} for i = 1 , 2 , … , n {\displaystyle i=1,2,\ldots ,n} denotes the ordinary individual demand for a certain good." In fact, in Mosak's case, x {\displaystyle x} is not a gross complement of y {\displaystyle y} but y {\displaystyle y} is a gross complement of x {\displaystyle x} . The elasticity does not need to be symmetrical. Thus, y {\displaystyle y} is a gross complement of x {\displaystyle x} while x {\displaystyle x} can simultaneously be a gross substitutes for y {\displaystyle y} .⁸

Proof

The standard Hicks decomposition of the effect on the ordinary demand for a good x {\displaystyle x} of a simple price change in a good y {\displaystyle y} , utility level τ ∗ {\displaystyle \tau ^{*}} and chosen bundle z ∗ = ( x ∗ , y ∗ , … ) {\displaystyle z^{*}=(x^{*},y^{*},\dots )} is

∂ f x ( p , ω ) ∂ p y = ∂ h x ( p , τ ∗ ) ∂ p y − y ∗ ∂ f x ( p , ω ) ∂ ω {\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 }}}

If x {\displaystyle x} is a gross substitute for y {\displaystyle y} , 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 x ∗ {\displaystyle x^{*}} , the first term of right-hand side stays the same while some extreme cases exist where x ∗ {\displaystyle x^{*}} is large enough to make the whole right-hand-side negative. In this case, y {\displaystyle y} is a gross complement of x {\displaystyle x} . Overall, x {\displaystyle x} and y {\displaystyle y} are not symmetrical.

Effect of price change of complementary goods

• Substitute good

References

1. Carbaugh, Robert (2006). Contemporary Economics: An Applications Approach. Cengage Learning. p. 35. ISBN 978-0-324-31461-8. 978-0-324-31461-8 ↩

2. 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. 0-13-063085-3 ↩

3. "Customer in Marketing by David Mercer". Future Observatory. Archived from the original on 2013-04-04. https://web.archive.org/web/20130404042855/http://futureobservatory.dyndns.org/9432.htm ↩

4. Newman, Peter (2016-11-30) [1987]. "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. Retrieved 2022-05-26. 978-1-349-95121-5 ↩

5. 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. S2CID 4800997. /wiki/Doi_(identifier) ↩

6. Mankiw, Gregory (2008). Principle of Economics. Cengage Learning. pp. 463–464. ISBN 978-0-324-58997-9. 978-0-324-58997-9 ↩

7. Mankiw, Gregory (2008). Principle of Economics. Cengage Learning. pp. 463–464. ISBN 978-0-324-58997-9. 978-0-324-58997-9 ↩

8. Mosak, Jacob L. (1944). "General equilibrium theory in international trade" (PDF). 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 ↩