Final answer:
Price elasticities of supply are always positive numbers, reflecting the direct relationship between price changes and quantity supplied. They can be categorized as elastic, inelastic, or unitary, depending on their responsiveness to price changes. Taxes affect tax incidence but do not inherently increase the elasticity of supply.
Step-by-step explanation:
Price elasticities of supply are always positive numbers. This is because, as price increases, the quantity supplied tends to increase, and as price decreases, the quantity supplied tends to decrease. Unlike the price elasticity of demand, which is typically negative since price and quantity demanded move in opposite directions, the price elasticity of supply moves in the same direction as price. Hence, price elasticities of supply indicate the responsiveness of quantity supplied to a change in price. If the elasticity is greater than one, it is considered elastic; if it is less than one, it is inelastic; and if it is exactly one, it is unitary elasticity. The imposition of a tax affects the tax incidence but doesn't inherently increase the price elasticity of supply.