91Ó°ÊÓ

The concept of constant unitary elasticity in supply is fundamental in economics. It refers to a situation where the percentage change in the quantity supplied is exactly equal to the percentage change in price.
This means that if the price of a good increases by 10%, the quantity supplied will also increase by 10%. To express this mathematically, we use the formula for elasticity of supply, which is given by: \[ \text{Elasticity of Supply (} E_s \text{)} = \frac{\Delta Q_s}{Q_s} \times \frac{P}{\Delta P} \] where:

• \( \Delta Q_s \) = Change in quantity supplied
• \( Q_s \) = Original quantity supplied
• \( P \) = Original price
• \( \Delta P \) = Change in price

With constant unitary elasticity, this ratio is always equal to 1. This balance maintains a proportional relationship between changes in price and quantity, characterizing it as special and simplifying the form of the supply curve.

Elasticity of supply is a measure of how responsive the quantity supplied of a good is to changes in its price. When supply elasticity is greater than 1, the supply is elastic; less than 1, it is inelastic; and exactly 1, it is unitary. The formula to calculate the elasticity of supply \( E_s \) is:\[ E_s = \frac{\% \text{Change in Quantity Supplied}}{\% \text{Change in Price}} \]In practical terms:- If \( E_s \) > 1, suppliers react strongly to price changes, increasing or decreasing quantity supplied significantly.- If \( E_s \) < 1, suppliers are unresponsive, with little change in quantity supplied. - If \( E_s \) = 1, as in our original exercise, every percentage change in price leads to an equivalent percentage change in quantity supplied.Understanding elasticity helps businesses and economists predict how supply will adjust to price variations and make strategic economic decisions.

In economics, a straight-line supply curve arises when the percentage change between price and quantity is constant across all points. For constant unitary elasticity, the supply curve is a perfect example of this. The supply curve we're discussing has the form of a straight line because the constant unitary elasticity maintains a balanced rate of change. This concept results in the linear equation:\[ P = kQ_s + C \]where \( k \) is a constant derived from the proportional changes, and \( C \) is an integration constant representing starting conditions. A straight-line supply curve is easy to analyze, and its constant slope is indicative of predictable supply reactions to price changes. This form simplifies understanding how shifts in supply may influence market dynamics.

Percentage change is a crucial component in understanding supply elasticity and constant unitary elasticity. It captures how a small variation in one variable influences the relative change in another, highlighting the economy's dynamic nature. To compute percentage change, use the formula: \[ \% \text{Change} = \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100 \]For instance, if the price of a commodity rises from \(50 to \)55, the percentage change is:\[ \% \text{Change in Price} = \frac{55 - 50}{50} \times 100 = 10\% \]Applying this, the concept plays a significant role in analyzing constant unitary elasticity where both price and quantity supplied change by the same percentage. This synchronous change ensures a straight-line relationship is maintained.