Once you have learned about elasticities on the demand side of the market, it is easy to translate the same concepts over to the supply side. In this course the convention will be to use the symbol \(\phi\) (the Greek letter phi) to refer to supply elasticities. Again, subscripts will be used in exactly the same fashion as above for demand elasticities. Moreover, the interpretation of supply elasticities is no different than demand elasticities. For example, the own-price elasticity of supply is defined as
\[\phi_{ii} = \dfrac{\% \Delta Q_{i}}{\% \Delta P_{i}}.\]
The difference is that \(Q_{i}\) is the quantity supplied, making this a supply elasticity as opposed to a demand elasticity.
Ranges for Supply Elasticities
Table \(\PageIndex{1}\) presents some magnitude-based classifications for supply elasticities. Fortunately, there is less to remember about ranges for supply elasticities. The own-price elasticity of supply is always non-negative. This reflects the law of supply. Again, the magnitude of the elasticity shows the responsiveness of quantity supplied to changes in the own-price, and it sometimes makes sense to talk about supply being elastic, unitary elastic, or inelastic. However, the non-negative own-price effect means that revenue to the producing industry always increases as price increases along the supply schedule, regardless of whether supply is responsive (elastic) or unresponsive (inelastic). The sign of the cross-price elasticities will depend on whether the related product in question is a competing product or whether it is a joint product. Finally, economic theory dictates that input price elasticities will be non-positive. If the price of an input used in production increases, the marginal cost of production increases. As explained in Chapter 2, this causes the market supply curve to shift inwards.
Table \(\PageIndex{1}\): Classifications based on magnitude of elasticity of supply
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Type
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Range
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Implication
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Own-price
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\(\phi_{ii} >1\)
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Supply for good \(i\) is elastic
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Own-price
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\(\phi_{ii} = 1\)
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Supply for good \(i\) is unitary elastic
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Own-price
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\(0 \leq \phi_{ii} <1\)
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Supply for good \(i\) is inelastic
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Cross-price
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\(\phi_{ij} > 0, i \neq j\)
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Good \(j\) is a joint product for good \(i\)
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Cross-price
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\(\phi_{ij} < 0, i \neq j\)
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Good \(j\) is a competing product for good \(i\)
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Input price
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\(\phi_{iW} \leq 0\)
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Input price elasticities are non-positive
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Calculating Supply Elasticities
The point and arc formulas presented in Table \(\PageIndex{2}\) are nearly identical to those learned for above for the case of demand. The only difference is that quantities supplied are being used in the computations instead of quantities demanded. Again, it is important to emphasize the “all else held constant” provision when using an arc formula. For example, if you are computing an own-price elasticity of supply using the arc formula, you must be confident that the values of any other variables that could shift supply have not changed.
Table \(\PageIndex{2}\). Point and arc formulas for supply elasticities
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Type
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Point Formula
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Arc Formula
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Own-price elasticity
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\(\phi_{ii} = \dfrac{\Delta Q_{i}}{\Delta P_{i}} \times \dfrac{P_{i}}{Q_{i}}\)
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\(\phi_{ii} = \dfrac{Q_{i}^{1} - Q_{i}^{0}}{P_{i}^{1} - P_{i}^{0}} \times \dfrac{P_{i}^{1} + P_{i}^{0}}{Q_{i}^{1} + Q_{i}^{0}}\)
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Cross-price elasticity
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\(\phi_{ij} = \dfrac{\Delta Q_{i}}{\Delta P_{j}} \times \dfrac {P_{j}}{Q_{i}}, i \neq j\)
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\(\phi_{ij} = \dfrac{Q_{i}^{1} - Q_{i}^{0}}{P_{j}^{1} - P_{j}^{0}} \times \dfrac{P_{j}^{1} + P_{j}^{0}}{Q_{i}^{1} + Q_{i}^{0}}, i \neq j\)
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Input-price elasticity
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\(\phi_{iW} = \dfrac{\Delta Q_{i}}{\Delta W} \times \dfrac{W}{Q_{i}}\)
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\(\phi_{iW} = \dfrac{Q_{i}^{1} - Q_{i}^{0}}{W^{1} - W^{0}} \times \dfrac{W^{1} + W^{0}}{Q_{i}^{1} + Q_{i}^{0}}\)
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Elasticity for other supply shift variable \(Z\)
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\(\phi_{iZ} = \dfrac{\Delta Q_{i}}{\Delta Z} \times \dfrac{Z}{Q_{i}}\)
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\(\epsilon_{iZ} = \dfrac{Q_{i}^{1}-Q_{i}^{0}}{Z^{1} - Z^{0}} \times \dfrac{Z^{1} + Z^{0}}{Q_{i}^{1} + Q_{i}^{0}}\)
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Special Cases for Supply Elasticities
It will sometimes be useful to assume that supply is perfectly elastic or that supply is perfectly inelastic. An inverse supply curve with a slope of zero (a horizontal line) corresponds to perfectly elastic supply. What this means is that any quantity can be purchased at the prevailing market price. At first look, this makes absolutely no sense. However, this assumption is appropriate in certain contexts, usually in the case of a buyer who faces a perfectly elastic supply for a product or service. For example, trucking is an important service provided to blackberry marketers. The popularity of blackberries has grown in recent years, so more blackberries are being grown and shipped. The assumption that the blackberry industry faces a perfectly elastic supply for trucking is probably reasonable. Although blackberries shipments have grown, blackberries account for a tiny portion of trucking volume. The fact that more blackberries now need to be shipped has probably not materially affected freight rates. In other words, blackberry marketers can ship all they want at the going rates. As a matter of fact, this assumptions was reflected earlier in Figure 1. By drawing the farm and retail demand schedules parallel to each other, the implicit assumption was that firms in this industry faced a perfectly elastic supply of marketing inputs, the inputs needed to get products from the farm to the consumer.
An inverse supply curve with an infinite slope (a vertical line) corresponds to perfectly inelastic supply. This means that regardless of the price, the quantity supplied is fixed. This assumption may be reasonable in some short to intermediate run contexts in agriculture, especially when we are dealing with fresh and non-storable commodities coupled with production lags. However, it is very important to be careful with this assumption. Just because there is a fixed stock of a certain product does not mean that the supply for that product is perfectly inelastic. Consider, for example, the supply of van Gogh paintings. Van Gogh died in 1890. Consequently, there will never be another van Gogh painting, unless some heretofore unknown paintings turn up in a vault somewhere. Nevertheless, that does not mean the supply of van Gogh paintings is perfectly inelastic. As the prices of van Gogh paintings rise, art collectors and museums are more likely to offer the van Gogh paintings in their collections up for sale and we would expect more Van Gogh paintings to be placed on the market at higher prices and less at lower.